
                             Students' QuickField

                        Finite Element Analysis System

                                 Version 3.2

                                 User's Guide


 Copyright (C) Tera Analysis, 1993-1995
 All rights reserved.

 Tera Analysis Co.
 P.O. Box 571086,
 Tarzana, CA 91357

 E-mail:   teracom@netcom.com
 Tel:      818 831 9662
 Fax:      805 493 2172


 QuickField is a trademark of Tera Analysis.
 i286, i386, i486 and Pentium are trademarks of Intel Corporation.
 DXF is a trademark of Autodesk, Inc.
 IBM PC/AT and PC-DOS are trademarks of International Business Machines
 Corporation.
 Microsoft and MS-DOS are registered trademarks, and Windows is a trademark
 of Microsoft Corporation.
 PostScript, Adobe, Adobe Illustrator are registered trademark of Adobe
 Systems, Inc.

 All other brand and product names are trademarks or registered trademarks
 of their respective owners.

 Table of Contens

 1. Introduction
    1.1 What Is QuickField System?
    1.2 Required Hardware Configuration
    1.3 Keyboard Notation
    1.4 How to Use this Manual

 2. Getting Started
    2.1 QuickField Installation
    2.2 Starting QuickField
    2.3 Quitting QuickField

 3. Introductory Guide
    3.1 Basic Organization of QuickField
    3.2 Overview of Analysis Capabilities
      3.2.1 Magnetostatic Analysis
      3.2.2 Electrostatic Analysis
      3.2.3 Current Flow Analysis
      3.2.4 Thermal Analysis
      3.2.5 Stress Analysis

 4. Basic Skills
    4.1 Terminology
    4.2 Working with Menus
    4.3 Working with Dialog Boxes
      4.3.1 Command Buttons
      4.3.2 Text Boxes
      4.3.3 List Boxes
      4.3.4 Drop-Down List Boxes
      4.3.5 Option Buttons
      4.3.6 Check Boxes
    4.4 Selecting the Geometric Objects
    4.5 Using the Rubber Band Rectangle

 5. Problem Description
    5.1 Structure of Problem Database
    5.2 Creating a New Problem
    5.3 Establishing Coupling Links
    5.4 Choosing the Length Units

 6. Model Geometry Definition
    6.1 Terminology
    6.2 How to Create the Model
      6.2.1 Starting and Quitting the Model Editor
      6.2.2 Objects Selection
      6.2.3 Region Geometry Description
      6.2.4 Labeling Vertices, Edges and Blocks
      6.2.5 Building the Mesh
      6.2.6 Graphics Window Management
      6.2.7 Obtaining Model Information
    6.3 Additional Options
      6.3.1 Saving Model
      6.3.2 Opening Model File
      6.3.3 DXF File Import
      6.3.4 Discretization Visibility Options
      6.3.5 Attraction Distance Parameter

 7. Problem Parameters Description
    7.1 Creating a New Label
    7.2 Editing Label Data
      7.2.1 Editing Data in Electrostatics
      7.2.2 Editing Data in Magnetostatics
      7.2.3 Editing Data with Current Flow Problems
      7.2.4 Editing Data with Heat Transfer Problems
      7.2.5 Editing Data with Stress Analysis Problems
      7.2.6 Editing the Curves
    7.3 Copying, Renaming and Deleting the Label
    7.4 Merging and Copying Data Files

 8. Solving the Problem

 9. Analyzing Solution
    9.1 Starting and Quitting the Postprocessor
    9.2 Building the Field Picture on the Screen
      9.2.1 Interpreted Quantities
      9.2.2 Field Presentation Methods
      9.2.3 Field Picture Constructing
      9.2.4 Window Scaling Management
    9.3 Access to Local Field Data
    9.4 X-Y Plots
      9.4.1 Editing Contours
      9.4.2 X-Y Plot Management
      9.4.3 Zooming the X-Y Plot
    9.5 Calculating Integrals
    9.6 Saving Prepared Results to Files
      9.6.1 Saving the Screen Picture
      9.6.2 Exporting Local Values to the Table File
      9.6.3 Exporting Field Values along the Contour to the Table File
      9.6.4 Fast Printing the Results
    9.7 Additional Options
      9.7.1 Saving the Postprocessor State
      9.7.2 Dispaying the Legend for the Field Picture and X-Y Plot
      9.7.3 Changing the Color Scheme

 10. EXAMPLES
    10.1 MAGN1: Nonlinear Permanent Magnet
    10.2 MAGN2: Solenoid Actuator
    10.3 MAGN3: Ferromagnetic C-Magnet
    10.4 ELEC1: Microstrip Transmission Line
    10.5 ELEC2: Two Conductor Transmission Line
    10.6 HEAT1: Slot of an Electric Machine
    10.7 HEAT2: Cylinder with Temperature Dependent Conductivity
    10.8 STRES1: Perforated Plate
    10.9 COUPL1: Stress Distribution in a Long Solenoid
    10.10 COUPL2: Hollow Thick-Walled Cylinder Subject to Temperature and
       Pressure
    10.11 COUPL3: Temperature Distribution in an Electric Wire



                               1. INTRODUCTION

 Welcome to QuickField System.

 In this chapter, you will find:
 *    A description of QuickField system.
 *    QuickField hardware requirements.
 *    An explanation of how to use this manual.


           1.1 What Is QuickField System?

 QuickField is  PC-oriented  interactive  environment  for  electromagnetic,
 thermal and stress analysis. Standard analysis types include:
 *    Electrostatics.
 *    Linear and nonlinear magnetostatics.
 *    Linear and nonlinear heat transfer and diffusion.
 *    Linear stress analysis.
 *    Coupled problems.

 During a  15-minute  session,  you  can  describe  the  problem  (geometry,
 material properties, sources  and other conditions),  obtain solution  with
 high accuracy and analyze field details looking through full color picture.
 With QuickField,  complicated  field problems  can  be solved  at  your  PC
 instead of  large mainframes  or workstations.  At usual  PC with  standard
 configuration, QuickField  is able  to  solve problems  of  electrostatics,
 magnetostatics  and  heat  transfer  with   up  to  500  nodes   (Students'
 QuickField) or  100,000 nodes  (Professional  QuickField), and  for  stress
 analysis  up  to   250  nodes  (Students'   QuickField)  or  50,000   nodes
 (Professional QuickField)


           1.2 Required Hardware Configuration

 Computer:           A  286,  386,   486  or  Pentium   based  IBM  PC/AT
                     compatible.

 Coprocessor:        Intel 80x87 math coprocessor.

 Memory:             640K.

 Display:            EGA, VGA color or LCD monochrome.

 Mouse:              Microsoft mouse or  100% compatible  with Microsoft
                     mouse driver, version 8.00 or above.

 Operating System:   MS-DOS or PC-DOS (Rev. 3.3 or above).


           1.3 Keyboard Notation

 In this  manual we  use capitals  to  specify the  names  of keys  on
 your keyboard. For example,  ENTER, ESC, or  alt. Four arrows  on the
 keyboard, collectively named the direction keys, are named for the
 direction the  key points: up arrow, down arrow, right arrow, and left
 arrow.

 A plus sign (+) between key  names means to hold  down the first key  while
 you press the second key. A comma (,) between key names means to press  the
 keys one after the other.


           1.4 How to Use this Manual

 This manual is divided into eleven chapters:

 Chapter 1, "Introduction", briefly discusses QuickField capabilities.

 Chapter 2, "Getting Started", describes first steps of using QuickField. In
 this chapter, you will learn how to install and start the package.

 Chapter 3, " Introductory Guide", briefly  describes  the organization  of
 QuickField and gives an overview of analysis capabilities.

 Chapter 4,  "Basic  Skills ",  tells  you   about  working  patterns   with
 QuickField.

 Chapter 5, "Problem Description", explains how to specify the analysis type
 and general problem features.

 Chapter 6, "Model Geometry Definition ", explains how to  describe geometry
 of the model, build the mesh,  and define material properties and  boundary
 conditions.

 Chapter 7, "Problem Parameters Description ", introduces non-geometric data
 file organization, and the way to attach this file to the model.

 Chapter 8, "Solving the Problem", describes how to start the solver.

 Chapter 9, "Analyzing Solution ", introduces QuickField  Postprocessor, its
 features and capabilities.

 Chapter 10, " EXAMPLES", contains  description  of some  example  problems,
 which can be analysed using QuickField.


                             2.  GETTING STARTED


           2.1 QuickField Installation

 Distribtuion kit of QuickField 3.2  (Students' QuickField) consist of  four
 archive files:QFLD32-1.ZIP, QFLD32-2.ZIP, QFLD32-3.ZIP, QFLD32-4.ZIP

 After unzipping (don't  forget -d  switch to  restore directory  structure)
 QuickField directory should contain:

 six ASCII files:
 *    FILE_ID.DIZ    - descriptor;
 *    README.TXT     - primary information;
 *    MANUAL.TXT     - system documentation;
 *    REG_FORM.TXT   - registration form;
 *    VENDOR.TXT     - information for shareware distributors;
 *    FAQ.TXT        - frequently asked questions about QuickField.

 and two subdirectories:
 *    BIN       - contains all the files needed to run QuickField;
 *    EXAMPLES  - contains example problems.

 The BIN directory  contains all  the necessary  to run  the package.  These
 files are to  be copied  to the  special directory  on the  hard disk,  for
 example, C:\QF\BIN. For your convenience, we recommend to include the  name
 of this directory to DOS PATH environment variable.

 The  EXAMPLES  directory  contains  a   number  of  problems  solved   with
 QuickField. We suggest you to look through the examples in the area of your
 interest, before you start with your own problems.

 To operate with large amount of data, QuickField creates temporary file  in
 the current working  directory. You can  specify alternate  place for  this
 file by assigning  path of the  preferred directory  to QFTEMP  environment
 variable, e.g.,  to store  temporary files  in the  C:\TEMP directory,  you
 could include SET QFTEMP=C:\TEMP line in your AUTOEXEC.BAT.

 QuickField can use  the extended memory  of PC. This  feature is  available
 through the XMS driver, e.g., HIMEM.SYS distributed with MS-DOS 5.0 and 6.x
 and Microsoft Windows 3.x.

      Note. QuickField uses  part of the  extended memory  that is  not
      occupied by RAM  disks, disk  caching systems  or other  resident
      programs.

 The BIN directory of QuickField distribution  kit contains four files  with
 .CFG extension. These files contain optional color tables:

 SCREENC.CFG  - color table for VGA and EGA color monitors;

 SCREENL.CFG  - color table for LCD monitor of Laptop;

 SCREENG.CFG  - gray scale color  table, can be  used when obtaining  screen
                hard copy on a monochrome printer;

 SCREEN.CFG   - default color table, the same as SCREENC.CFG.

 You can change the default by replacing SCREEN.CFG on your hard disk with a
 copy of the color table you prefer.

 Installation under Windows

 If you are not planning to run  QuickField under Windows, you can skip  the
 rest of this section.

 The installation  under Windows  3.x is  done after  completion the  normal
 istallation procedure. While in Program  Manager, select the program  group
 you want  to  add QuickField  to,  or create  a  new program  group  called
 QuickField. From the File menu of  Program Manager, choose New. In the  New
 Program Item dialog box,  select the Program Item  option, and then  choose
 the OK button.. In  Program Item Properties  dialog box., type  "QuickField
 3.2" in Description line.  Choose the Browse button,  and in Browse  dialog
 box, select the QFIELD.PIF file from  the QuickField BIN directory.  Choose
 the OK button to return to  Program Item Properties dialog box. Choose  the
 Change Icon button.  Choose OK  button to get  to Change  Icon dialog  box.
 Choose the  Browse button  and  select the  QFIELD.ICO  file from  the  BIN
 directory. Choose the OK  button three times  to complete the  installation
 process.

 Now you can start QuickField under Windows by double clicking its icon.


           2.2 Starting QuickField

 To start QuickField,  go to  the directory you  devoted for  this work  and
 enter QFIELD  at your  system  prompt. The  command  line may  include  the
 problem file name. If it does not,  the name is taken from QFIELD.INI  file
 of the previous session.

 If QFIELD.INI is absent in the current  directory, or does not contain the
 problem file name, QuickField will ask you for  the name of the problem to
 work with.


           2.3 Quitting QuickField

 To exit from QuickField to operating  system environment, choose Exit  from
 the File menu (ALT+F, X), or press ALT+F4.


                            3.  INTRODUCTORY GUIDE

 This chapter briefly  describes the  basic organization  of the  QuickField
 program. It presents an overview of the available capabilities.

 The aim of this chapter is to get you started with modeling in  QuickField.
 If you are new to the QuickField,  we strongly recommend you to study  this
 chapter. If  you  haven't  yet installed  QuickField,  please  do  so.  For
 information on installing QuickField see Chapter 2.


           3.1 Basic Organization of QuickField

 QuickField is a menu driven system,  when you just get into QuickField  you
 see the main  menus which are  located in a  horizontal bar on  top of  the
 screen. The four main menus are  "File", "Edit", "Results", and  "Options".
 Here, we briefly describe  the functions of these  menus and some of  their
 corresponding submenus.

 File menu contains all the tools for choosing and manipulating the database
 files. For example,  you can choose  a new problem  name or  select an  old
 problem in any existing directory. The detailed description of this utility
 is given in Chapter 5.

 Edit menu contains  all the  submenus and  tools for  creating the  problem
 model and defining all the necessary parameters. It consists of four parts,
 "Problem", "Geometry", "Data", and "Library Data".

 Problem provides you with a dialog box to describe the problem  parameters,
 such as  the  type  of analysis  ('Electrostatic',  'Magnetostatic',  'Heat
 transfer' and  etc.)  or  the model  type  (planar  or  axisymmetric).  The
 detailed description of how to do this is given in Chapter 5.

 Geometry, takes you to  another graphic interface  to define the  geometry,
 the part labels and  the mesh for your  model. The detailed description  of
 the geometric modeler is given in Chapter 6.

 Data provides  you with  dialog  boxes to  assign  the values  of  material
 properties, loadings and boundary conditions for different part labels, and
 Library Data allows  you to edit  the existing data  library. The  detailed
 description of how to specify properties  and boundary conditions is  given
 in Chapter 7.

 The Results  menu contains  all  the tools  for  solving your  problem  and
 analyzing the results. It consists of two parts, Solve Problem and Analyze.
 After completing the model and assigning all the necessary parameters,  you
 can choose Solve Problem to obtain  the solution for your problem.  Analyze
 takes you to a special graphic interface for graphic display of the results
 and other postprocessing functions. The detailed description of how to  get
 and explore results of the analysis is given in Chapters 8 and 9

 Using the  above features,  QuickField helps  you  build and  analyze  your
 design problems very quickly. In analyzing a problem, the typical  sequence
 of phases that you go through with QuickField is depicted in the  flowchart
 below:

    +--------------------------+
    ! Choose a problem name    !
    !                          !
    !         File: New        !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Specify the problem type !
    !                          !
    !      Edit: Problem       !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Define the geometry,     !
    ! part labels and          !
    ! mesh for your model      !
    !                          !
    !      Edit: Geometry      !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Provide the data for the !
    ! materials, loads,        !
    ! boundary conditions      !
    !                          !
    !         File: New        !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Obtain the solution      !
    !                          !
    ! Results: Solve Problem   !
    +--------------------------+
                !
                !
    +--------------------------+
    ! Review the results and   !
    ! obtain the postprocessing!
    ! parameters               !
    !                          !
    !    Results: Analyze      !
    +--------------------------+



           3.2 Overview of Analysis Capabilities

 This section provides you with the basic information on different  analysis
 capabilities.

       3.2.1 Magnetostatic Analysis

 Magnetic analysis is used to design  or analyze variety of devices such  as
 solenoids, electric motors, magnetic  shields, permanent magnets,  magnetic
 disk drives,  and  so  forth.  Generally  the  quantities  of  interest  in
 magnetostatic analysis are magnetic flux density, field intensity,  forces,
 torques, inductance, and flux linkage.

 QuickField can perform linear and nonlinear magnetostatic analysis for  2-D
 and axisymmetric  models.  The  program is  based  on  a  vector  potential
 formulation. Following options are available for magnetic analysis:

 Material properties: air, orthotropic materials with constant permeability,
 ferromagnets, current  carrying  conductors,  and  permanent  magnets.  B-H
 curves for ferromagnets can easily be defined through an interactive  curve
 editing utility, see the "Editing the Curves" section in Chapter 7.

 Loading sources:  current density,  uniform  external field  and  permanent
 magnets.

 Boundary conditions:  Prescribed  potential values  (Dirichlet  condition),
 prescribed values for tangential flux density (Neumann condition), constant
 potential constraint  for zero  normal flux  conditions on  the surface  of
 superconductor.

 Postprocessing results: magnetic potential, flux density, field  intensity,
 forces,  torques,   magnetic  energy,   flux  linkage,   self  and   mutual
 inductances.

 Special features: A postprocessing  calculator is available for  evaluating
 user defined integrals on  given curves and  surfaces. The magnetic  forces
 can be used  for stress analysis  on any  exiting part  (magneto-structural
 coupling).

       3.2.2 Electrostatic Analysis

 Electrostatic analysis is used to design  or analyze variety of  capacitive
 systems such  as fuses,  transmission lines  and  so forth.  Generally  the
 quantities of  interest in  electrostatic analysis  are voltages,  electric
 fields, capacitances, and electric forces.

 QuickField  can  perform   linear  electrostatic  analysis   for  2 -D  and
 axisymmetric models. The program is based on Poisson's equation.  Following
 options are available for electrostatic analysis:

 Material properties: air, orthotropic materials with constant permittivity.

 Loading sources: Voltages, and electric charge density.

 Boundary conditions:  Prescribed  potential values  (Voltages),  prescribed
 values for normal derivatives (surface charges), and prescribed constraints
 for constant potential boundaries with given charges.

 Postprocessing results: voltages, electric fields, flux densities (electric
 displacements), surface  charges,  self and  mutual  capacitances,  forces,
 torques, and electric energy.

 Special features: A postprocessing  calculator is available for  evaluating
 user defined integrals  on given curves  and surfaces. Floating  conductors
 with unknown voltages and given charges  can be modeled. The  electrostatic
 forces can be  used for stresses  on any  exiting part  (electro-structural
 coupling).

       3.2.3 Current Flow Analysis

 Current flow analysis  is used to  analyze variety  of conductive  systems.
 Generally the quantities of interest in current flow analysis are voltages,
 current densities, electric power losses (Joule heating).

 QuickField  can  perform   linear  current  flow   analysis  for  2 -D  and
 axisymmetric models. The program is based on Poisson's equation.  Following
 options are available for current flow analysis:

 Material properties: orthotropic materials with constant conductivity.

 Loading sources: Voltages, electric current density.

 Boundary conditions:  Prescribed  potential values  (Voltages),  prescribed
 values for normal derivatives  (surface current densities), and  prescribed
 constraints for constant potential boundaries.

 Postprocessing  results:  voltages,  current  densities,  electric  fields,
 electric current through a surface, and power losses.

 Special features: A postprocessing  calculator is available for  evaluating
 user defined integrals  on given curves  and surfaces.  The electric  power
 losses can be used  as heat sources  for thermal analysis  (electro-thermal
 coupling).

       3.2.4 Thermal Analysis

 Thermal analysis  plays  an important  role  in design  of  many  different
 mechanical and electrical systems. Generally the quantities of interest  in
 thermal analysis are temperature distribution, thermal gradients, and  heat
 losses.

 QuickField can perform linear  and nonlinear thermal  analysis for 2 -D and
 axisymmetric models. The program is based on heat conduction equation  with
 convection  and  radiation  boundary  conditions.  Following  options   are
 available for thermal analysis:

 Material  properties:   orthotropic   materials   with   constant   thermal
 conductivity, isotropic temperature dependent conductivities.

 Loading sources: constant and temperature dependent volume heat  densities,
 convective and radiative sources, Joule heat sources imported from  current
 flow analysis.

 Boundary  conditions:   Prescribed  temperatures,   boundary  heat   flows,
 convection, radiation, and prescribed constraints for constant  temperature
 boundaries.

 Postprocessing  results:   temperatures,  thermal   gradients,  heat   flux
 densities, and total heat losses or gains on a given part.

 Special features: A postprocessing  calculator is available for  evaluating
 user defined  integrals on  given curves  and surfaces.  Plate models  with
 varying thicknesses can be used for thermal analysis. The temperatures  can
 be used for thermal stress analysis (thermo-structural coupling).

       3.2.5 Stress Analysis

 Stress analysis  plays  an  important role  in  design  of  many  different
 mechanical and electrical components. Generally the quantities of  interest
 in stress analysis are displacements,  strains and different components  of
 stresses.

 QuickField can perform linear stress analysis  for 2-D plane stress, plane
 strain, and axisymmetric models. The program  is based on Navier  equations
 of elasticity. Following options are available for stress analysis:

 Material properties: isotropic and orthotropic materials.

 Loading  sources:  concentrated  loads,  body  forces,  pressure,   thermal
 strains, and imported  electric or  magnetic forces  from electrostatic  or
 magnetostatic analysis.

 Boundary conditions: prescribed displacements, elastic spring supports.

 Postprocessing  results:   displacements,  stress   components,   principal
 stresses, von Mises stress, Tresca, Mohr-Coulomb, Drucker-Prager, and  Hill
 criteria.


                                4. BASIC SKILLS

 This chapter  describes the  working environment  that  you will  use  with
 QuickField.

 QuickField is a menu driven system.  The meaning of the selected menu  item
 is explained by the prompt message occupying the bottom line of the screen.
 The same line is used for other messages.

 In most context  the ESC  key may be  used to  cancel or  to interrupt  the
 current action. The right mouse button is completely equivalent to the  ESC
 key. The left mouse button is used to click objects.


           4.1 Terminology

 The following terms  are used to  describe your actions  when working  with
 QuickField.

 Choose       - To use  a mouse  or key  combination to  pick an  item  that
                begins an action. For example, choosing a menu item  usually
                causes the execution of QuickField command.

 Click        - To press the mouse button while the tip of the mouse pointer
                rests on the item of choice.

 Double-click - To click the mouse button twice in rapid succession.

 Select       - To mark an item by highlighting it with key combinations or
                by clicking it with a mouse. Selecting does not initiate  an
                action.


           4.2 Working with Menus

 To choose a menu item click  it with a mouse. You can  also use the up  and
 down arrow keys to select the item you want; then press ENTER. If the  item
 name has an underlined letter, you can type it to choose the menu item with
 one step. To select an item on the horizontal menu bar press its underlined
 letter while holding down the ALT key.

 Pressing the ESC  key or  clicking the right  mouse button  returns to  the
 previous menu level. If you press ESC while in main menu, you will be asked
 about exiting to DOS.


           4.3 Working with Dialog Boxes

 QuickField uses  dialog  boxes to  get  information from  you  and  provide
 information  to  you.  For   example,  when  QuickField  needs   additional
 information to carry out a command  you have chosen, a dialog box  requests
 the information.  You complete  the dialog  box  by providing  the  missing
 information. Whenever  you see  an ellipsis  (...)  after a  menu  command,
 another menu or a dialog box follows.

 For example, when you choose Open from the File menu, QuickField displays a
 dialog box asking for the name of the file you want to open.

 Most dialog boxes  contain options,  each asking  for a  different kind  of
 information. After you supply all the  requested information, you choose  a
 command button to carry out the command.

 Often you  need  to  move  around  within a  dialog  box  to  make  several
 selections. The current option is marked by a highlight or dotted rectangle
 (or both) around the name of the option or button. To move within a  dialog
 box:
 *    Click the option you want to move to.
 *    Press tab to  move forward (generally  from left to  right and top  to
      bottom) or shift+tab to move in opposite direction.
 *    Use the direction keys to move in desired direction.
 *    Or, while you  hold ALT,  you can type  the underlined  letter in  the
      option name or group name.

 The options that are unavailable for some reason are dimmed.

 The next few sections  describe different dialog  boxes and the  procedures
 for selecting options.

       4.3.1 Command Buttons

 Command buttons initiate an  immediate action. One  command button in  each
 dialog box  carries  out the  command  you choose,  using  the  information
 supplied in the dialog box. This button is usually named OK. Other  command
 buttons let you cancel the command or choose from additional options.

 Command buttons marked with  an ellipsis (...) open  another dialog box  so
 you can  provide  more information.  The  currently selected,  or  default,
 button has a  highlighted green  name or, in  a monochrome  mode, a  darker
 border than  the other  buttons.  You can  choose  the selected  button  by
 pressing ENTER.

 You can  close the  dialog box  without completing  a command  by  choosing
 Cancel button.

 To choose a command button:
 *    Click it.
 *    Move to the  command button you  want. A dotted  rectangle around  the
      button text marks the selected button.  Press the spacebar (or  ENTER)
      to choose the button.
 *    Or, while you  hold ALT,  you can type  the underlined  letter in  the
      button name.

 Some dialog boxes are so small that do not contain any command button. Such
 dialog boxes are usually located at  the right-hand side of the screen  and
 have gray background.  In spite  of missing the  OK command  button, it  is
 still possible to use a  mouse to carry out  the command you choose.  Click
 the dialog box background anywhere outside options. The effect will be  the
 same as if using the OK command button.

       4.3.2 Text Boxes

 A text box is a rectangle into which you type information.

 When you move to an empty text box, a text cursor appears at the left  side
 of the box. The text you type starts at the cursor position.

 If the box already contains text when you move  to it, all the text in  the
 box is automatically selected  and any text you  type replaces it. Or,  you
 can erase  the existing  text by  pressing del.  To discard  the  selection
 simply move the cursor to the point where you want to enter or erase  text.
 Use left and right arrow, home or end keys to move the cursor.

 The text exceeding the length of the text box is scrolled automatically.

        4.3.3 List Boxes

 The list box shows a column of available choices. If there are more choices
 than can fit in the list box, a scroll bar is provided so that you can  use
 your mouse to move up and down quickly through the list.

 To scroll one line click one of the scroll arrows. To scroll one window  up
 or down click  the gray background  of the scroll  bar above  or below  the
 white rectangle.

 When the required item is already visible  in the list box, you can  select
 it by clicking  it with  a mouse.  You also  can double-click  the item  to
 choose it and complete the command at once.

 To select an item  using a keyboard press  up or down  arrow key until  you
 reach your  choice. You  also can  use page  up and  page down to  move one
 window a time, and home or end to move to the first or to the last item  of
 the list. Or, type  the first letter  of the item  you want, the  highlight
 will be moved to the first item that starts from that letter.

       4.3.4 Drop-Down List Boxes

 A drop-down  list box  appears  initially as  a  rectangular box  with  the
 current choice (default) displayed in the box. The arrow in a square box at
 the right opens into  a list of  available choices when  you select it.  If
 there are more choices than can fit in the drop-down list box, a scroll bar
 is provided.

 A selected drop-down  list box can  be opened without  a mouse by  pressing
 ALT+DOWN ARROW. An opened drop-down list box  is closed when you select  an
 item in it, select other option in the dialog box, or press ALT+DOWN ARROW.

       4.3.5 Option Buttons

 Option buttons  appear in  dialog boxes  as a  list of  mutually  exclusive
 items. From the list you can select only one option a time. You can  change
 a selection by selecting a different button.

 The selected option button contains a black dot.

 To select an option button:
 *    Click it.
 *    Press tab  to  move into  the  option group  you  want; then  use  the
      direction keys to select the option button you want.
 *    Or, if the  option name contains  an underlined letter,  you can  hold
      down ALT and press the underlined  letter from anywhere in the  dialog
      box to select an option button.

  In dialog boxes where all  options are represented by option buttons,  you
 can double-click an option button to choose it and complete the command  at
 once.

       4.3.6 Check Boxes

 Check boxes offer  a list of  options you can  switch on and  off. You  can
 select as many  or as few  check box options  as are  appropriate. When  an
 option in a check  box is selected,  it contains X.  Otherwise, the box  is
 empty.

 To select or clear check box options:
 *    Click the empty  check box you  want to select.  Click a selected  box
      again to clear the selection.
 *    Press tab to move to the empty check box you want to select. Press the
      spacebar to enter an X. Press the spacebar again if you want to  clear
      the selection.
 *    Or, if the check-box name has an underlined letter, hold down ALT  and
      press the underlined letter for each  check box you want to select  or
      clear.


           4.4 Selecting the Geometric Objects

 When editing the model  geometry or analyzing the  results you may need  to
 enter the  coordinates of  a point.  The  plus sign  cursor ( +) arises  to
 indicate the point  locating mode.  This cursor can  be moved  by mouse  or
 using the direction keys.  The home, end, page  down and page up keys move
 the cursor in four diagonal directions. You can control the keyboard cursor
 step by the  minus and plus  keys. The minus  key approximately halves  the
 cursor step, the plus  key increases it  back. You also  can get very  fine
 cursor movement by holding down ctrl while pressing the direction keys.

 To select a point of the  model move the cursor  to the position of  choice
 and click left mouse button or press the ENTER key. ESC or the right  mouse
 button  cancels  the  operation.  If  you  prefer  numerical  form  of  the
 coordinates input press tab  and you will  get a dialog  box with two  text
 boxes  for  coordinates  typing.  Press  ENTER  or  click  the  dialog  box
 background to complete the dialog and carry out the command.

 When working  with  the  model  you  often  need  to  select  some  of  its
 constituent geometric  objects. The  picking mode  is indicated  by the  X-
 shaped cursor. You can move  this cursor the same  way as while locating  a
 point. To pick a massive object like a block place the center of the cursor
 on that object and click the left mouse  button or press the ENTER key.  To
 pick a vertex or an edge it is not necessary to point cursor exactly on the
 object. The selected object is always the closest to the cursor.


           4.5 Using the Rubber Band Rectangle

 The rubber band rectangle is used to  zoom-in to a rectangular part of  the
 model or of the X-Y plot. The chosen part is  enlarged to occupy the whole
 available screen  area. The  rubber band  rectangle is  controlled using  a
 mouse or the direction keys. First,  choose the position of the lower  left
 hand corner, then of the upper right hand one.


                            5. PROBLEM DESCRIPTION


           5.1 Structure of Problem Database

 A special database is  built for each problem  solved with QuickField.  The
 core of the database  is the problem description,  which is stored in  file
 with the extension .PBM. The problem description contains the basics of the
 problem: its subject, plane, precision class, etc., and also references  to
 all other files, which constitute the problem database. These files are the
 model file, with  standard extension .MOD,  and physical  data files,  with
 extension .DES, .DCF, .DMS, .DHT, or .DSA, depending on the subject of  the
 problem.

 The problem description may refer to  one or two physical data files.  Both
 files have the same format, and differ only in purpose. Usually, the  first
 data file contains specific data concerning the problem, as the second file
 is a library of standard material properties and boundary conditions, which
 are common for a whole class of problems.

 Depending on the  problem type,  you may  share a  single model  file or  a
 single data file between several similar problems.

 While solving the  problem, QuickField creates  one more  file-the file of
 results with the extension .RES. This file always has the same name as  the
 problem description file, and is stored in the same directory.


           5.2 Creating a New Problem

 To create a new problem, choose New in the Files menu (ALT+F, N), and  then
 enter the name  of the  new problem.  While created,  new problem  inherits
 settings of the preceding problem. To change these settings, choose Problem
 in the Edit  menu (ALT+E, P).  The dialog box  appears, containing  problem
 description options. Here you can pick the problem type, model type (XY for
 2D planar, RZ for axisymmetric), precision level, and etc.

 To exit from problem description editing, choose OK. You can cancel editing
 by choosing Cancel button, or pressing ESC, or clicking right mouse button.

 Choosing the Browse button  allows you to  select a file  from the list  of
 files and directories when defining the model or data filename. The  button
 acts on that type of file, which is currently selected.

 Once the file is chosen, you can instantly open it for editing by  choosing
 the Open button. It acts upon the currently selected file. For example,  if
 you have selected geometry file, by  choosing Open, you would get into  the
 Model Editor


           5.3 Establishing Coupling Links

 The stress analysis and heat transfer problems can incorporate data,  which
 come from other analysis  types. The data  types are: electrostatic  and/or
 magnetic forces and temperature  field for the  stress analysis, and  power
 losses generated by the current flow for the heat transfer.

 To establish a link between the  problem that imports data and the  problem
 that originates them  choose Imported  Data button  in problem  description
 dialog box. The following dialog box will appear.

 To add a data link:
 *    Select the type of the data in the Data Type pull-down list box;
 *    Type a name of the source problem  in the Problem text box, or  choose
      Browse button  to  make  the  selection  from  the  list  of  existing
      problems;
 *    And, choose Add button to add the link to the list of data sources.

 To change a data link:
 *    Select the link of choice in the Data Sources list box;
 *    Change the source problem name as necessary;
 *    And, choose  Update button  to update  the link  in the  list of  data
      sources.

 To delete a link:
 *    Select the link of choice in the Data Sources list box;
 *    And, choose Delete  button to delete  the link from  the list of  data
      sources, or use Delete All button to delete all data links at once.

 The links to the imported data are considered  to be a part of the  problem
 description. The changes made in them  are preserved only if you choose  OK
 when completing the problem  description editing. And,  vice versa, if  you
 would choose Cancel  button or press  ESC, the changes  made in data  links
 will be discarded along with other changes in problem description.


           5.4 Choosing the Length Units

 QuickField allows  to  use  different metric  units  for  coordinates  when
 editing model's geometry.  You can use  microns, millimeters,  centimeters,
 meters, kilometers and even inches, feet,  miles. To set the units,  choose
 Length Units in the Options menu (ALT+O, U).

 Chosen unit is stored with the  problem description, you can choose it  for
 each problem  independently. The  choice of  length units  does not  affect
 units for other physical  parameters, which always  use standard SI  units.
 E.g., the current density  is always measured in  A/m2 and never in  A/mm2.
 The only physical quantity that is  measured in chosen units of length,  is
 the displacement vector in stress analysis problems.


                         6. MODEL GEOMETRY DEFINITION

 This chapter describes how to define the region geometry and build the mesh
 using QuickField preprocessing utility-the Model Editor.


           6.1 Terminology

 Vertex, edge, and block are three  basic types of geometric objects,  which
 the Model Editor operates with.

 Vertex is a  point on the  plane with coordinates  defined by  the user  or
 calculated automatically as intersection of the edges. For each vertex  you
 can define the  mesh spacing value  and the label.  The mesh spacing  value
 defines approximate distance between mesh nodes in the neighborhood of  the
 vertex. The label is used, for example, to describe a line source or load.

 Edge is a line segment or a circular arc connecting two vertices. It  can't
 intersect any other edge of the  region. If an edge being created  contains
 an existing  vertex,  two adjacent  edges  are created.  New  vertices  are
 automatically created in all points where new edge intersects the  existing
 ones and all intersected  edges are split by  these vertices. Edges can  be
 labeled, for example, to specify the boundary conditions.

 Block is a continuous subregion with  its boundary consisting of edges  and
 possibly isolated vertices. A block may  contain holes which can be  formed
 by chains of edges or by isolated vertices. Each block has to be labeled to
 describe material properties. Labels of the blocks are also used to  define
 distributed field sources. Non labeled block is not included in calculation
 of field even it is covered by the mesh. The mesh is created block by block
 automatically or according to the mesh spacing value defined for particular
 vertices.

 The Label is a string of up to 16 characters length, which establishes  the
 correspondence between geometrical parts of  the model and physical  values
 assigned to  them.  Any  printable characters  including  letters,  digits,
 punctuation marks, space character are  permitted, except for asterisk  (*)
 and question  mark  (?)  characters. The  label  cannot  begin  with  space
 character; trailing spaces are ignored. Labels are case-sensitive.

 The Mesh Spacing value is the  parameter of the units of length  associated
 with the vertex.  The spacing defines  the density of  the mesh around  the
 vertex. Changing  these  values,  you  can  control  the  accuracy  of  the
 solution.


           6.2 How to Create the Model

 Model development consists of three stages:
 *    geometry description;
 *    definition of properties, field sources and boundary conditions;
 *    mesh generation.

 To describe  model  geometry  you define  vertices  and  edges  which  form
 boundaries of all subregions having different physical properties. You  can
 create vertices  and edges;  move, copy  and delete  any geometric  objects
 using the selection mechanism or one by one.

 You  define  properties,  sources  and  boundary  conditions  by  means  of
 assigning labels to geometrical objects.

 There are two options  available for creating the  finite element mesh  for
 your model:
 *    Fully automated method which  generates a smooth  mesh with a  density
      based on region's  dimensions and sizes  of geometrical details.  This
      option does not require any information from the user.
 *    The second method allows you to choose the mesh density. In this  case
      you need to define the spacing values at few vertices of your  choice.
      Spacing values for other vertices are calculated automatically to make
      the mesh distribution smooth.

       6.2.1 Starting and Quitting the Model Editor

 To start the  Model Editor, choose  Geometry from Edit  menu (ALT+E, G)  or
 while editing the problem description select the model filename and  choose
 Edit button.

 The Model  Editor  uses  interactive  graphics.  Two  graphic  windows  are
 displayed on screen permanently. The small window presents general view  of
 the problem region, while the large one provides more detailed view.  Below
 the graphic windows is a prompt  line. Upper right screen area is  normally
 occupied by the  menu or  a temporary window  used for  editing values  and
 labels.

 The Model Editor has hierarchical structure of menus. Pressing ESC or right
 mouse button causes returning to preceding menu level or quitting the Model
 Editor in the main menu.

 To quit the Model Editor select Exit from the main menu or press ESC  while
 in main menu. You will be prompted to save the model.

       6.2.2 Objects Selection

 The Model Editor  provides possibility to  make some  group operation  upon
 several objects at once  if those have been  previously selected. To  enter
 select mode, choose Select and then one of  Select  Blocks, Select Edges or
 Select Vertices in a dialog box that will appear.

 While in select mode pick an object to select or unselect it. All  selected
 objects are highlighted on the screen.  To leave the select mode press  ESC
 or right  mouse  button. Objects  of  different types  cannot  be  selected
 simultaneously.

 Unselect All cancels all previous selection.

       6.2.3 Region Geometry Description

 It happens that improper elements rest out of window. Zoom Natural arranges
 window limits to contain all the elements of the model.

 Whenever a  new model is created,  the default window is set to  correspond
 to a unit square. For planar models the horizontal and vertical  directions
 correspond to X and Y axes, and. for axisymmetric models they correspond to
 Z and R  axes, respectively.  It is convenient  to assign  the window  with
 region's dimensions and create the outward  boundary of the model at  once,
 and then describe the details. To  change default window dimensions  choose
 Keyboard from Zoom submenu.  The default window  dimensions are saved  with
 the model to be restored in later editing sessions.

 To build the geometry of your problem go to Model submenu. First, you  need
 to create the vertices  using the Add  Vertex command. Locate  the required
 positions with  the cursor  or  press tab  to  enter coordinates  from  the
 keyboard. New vertex appears in the window. Then you can continue  creating
 vertices or return to Model menu by pressing ESC or right mouse button.

 If at least two  vertices are defined  in the region  you can connect  them
 with an edge. To do this, choose Add Edge and type in angle size in degrees
 for new edge. Zero  value corresponds to the  line segment. Positive  value
 defines an  arc directed  from  the first  vertex  to the  second  counter-
 clockwise, or clockwise if negative. Then pick the vertices to be connected
 by the edge in corresponding order. New edge appears in the window. Picking
 vertex by vertex you can create several edges of equal angle size. To break
 the chain and start new one, press ESC. To return to menu press ESC twice.

 Repeated geometry elements can  be easily created by  means of copying  any
 set of  objects to  new location,  using geometric  transformations  listed
 below. To make a copy:
 *    Select any number of objects (vertices,  edges or blocks) you want  to
      copy, choosing Select from the menu.
 *    Choose Copy  Selected.  The dialog  box  appears, asking  for  copying
      parameters.
 *    Select transformation, enter  its parameters  and choose  OK. The  new
      objects will appear on screen and the program will be waiting for your
      confirmation, so  you  could  be  sure  that  you  entered  parameters
      correctly.
 *    Choose Copy to confirm copying. New  objects will be 'implanted'  into
      the model, and selection will move to the last copy.

 The copy operation affects all explicitly set features of selected objects,
 including labels and spacing values. Only the mesh is not copied.

      Caution. Use  copy operation  with care,  because improperly  set
      transformation parameters may cause  creating new objects in  the
      wrong place interfering existing objects and generating a lot  of
      useless intersection points, which are hard to remove later.

 You can also move selected objects to other location with the  restriction,
 that region topology will not change, and no new intersection or coinciding
 will arise. To move selected objects,  choose Move Selected from the  menu.
 The dialog box which appears is very similar to Copy Selected dialog box.

 Geometric transformations available with move and copy operations are:

 Displacement - parallel displacement  is applied  to selected  objects  for
                specified displacement vector. With copy operation,  several
                copies can be  asked for,  it means  that copying  operation
                will be performed several times, each time being applied  to
                previous result. Parameters  needed are displacement  vector
                components.

 Rotation     - selected objects are rotated around the specified point  for
                the specified angle. With copy operation, several copies can
                be asked  for,  it  means that  copying  operation  will  be
                performed several times, each time being applied to previous
                result. Parameters needed are center of rotation coordinates
                and angle measured in degrees.

 Symmetry     - selected objects are mirrored; symmetry line is specified by
                coordinates of any  point on it  and the  angle between  the
                horizontal axis and the symmetry line. Positive value of  an
                angle means counter-clockwise direction. This transformation
                is available for copy operation only.

 Scaling      - selected objects  are  dilated  (constricted)  by  means  of
                homothetic transformation. Parameters  needed are center  of                homothety  and  scaling   factor.  This  transformation   is
                available for move operation only.

 You can remove auxiliary or incorrectly defined vertices, edges and  blocks
 by choosing Delete  Selected, Delete Vertex or Delete  Edge. If the  vertex
 being removed contacts exactly  two edges, which can  be treated as  single
 edge when eliminating  that vertex,  those are  joined together.  Otherwise
 confirmation will be asked to delete all the connected edges.

       6.2.4 Labeling Vertices, Edges and Blocks

 The  correspondence  between   geometrical  objects   and  their   physical
 properties, such as boundary conditions or field sources is established  by
 use of  labels. All  operation with  assigning,  editing and  checking  the
 labels is done in the Label menu.

 To assign a label, choose one  of Label Block, Label  Edge or Label Vertex,
 and then pick  the entity  which you  need to  label. The  dialog box  will
 appear, which allows you to  type in the label  from keyboard or to  select
 one from  the previously  defined labels  in  the model  or in  data  files
 assigned to  the problem.  After you  define the  label, you  can  continue
 picking the objects or return to the menu by pressing ESC key.

 You may assign the same labels to several entities of similar type at once.
 To do so,  first select  those objects by  using Select  command (for  more
 details see the  section on Object  Selections) and then  label them  using
 Label Selected.

 To check labels assignment or to select objects possessing the same  label,
 use Find Label. The dialog box will appear, which allows you to select the
 type of object, and contains the full list of labels as appear in the model
 for the given object type. Picking some label in the list would select  all
 the objects associated with that label.

       6.2.5 Building the Mesh

 After creating the geometry of the model or its parts, you can proceed with
 building the finite  element mesh.  With the  Model Editor  you can  easily
 build a nonuniform mesh for highly complex geometry. You may choose a  fine
 mesh in  some  regions and  very  coarse  in others,  since  the  geometric
 decomposition technique would  produce a  smooth transition  from large  to
 small element sizes.  Generally, the mesh  has to be  fine where the  field
 changes most  rapidly  (high  gradient),  and  also  where  you  need  high
 precision.

 If the geometry  is rather  simple, or  a draft  precision for  preliminary
 design analysis is satisfactory, it is suggested to use the fully automatic
 mode to create the mesh. With this option, once you built your geometry you
 would simply choose Build Mesh and a suitable mesh is automatically created
 without any information on the mesh size.

 You also have the option to pick the mesh  density if you choose to do  so.
 The mesh density is controlled by  spacing values in vertices. The  spacing
 value defines approximate distance between  mesh nodes around that  vertex.
 You never need  to define the  spacing in all  model's vertices. To  obtain
 uniform mesh you  can set  the spacing  in any  one vertex.  This value  is
 spread among all other vertices automatically. If you need the  non-uniform
 mesh, define spacing values  only in those vertices  where you need  finest
 and roughest mesh.  The spacing  values are  automatically interpolated  to
 other vertices to smooth the mesh density distribution. The group selection
 mechanism allows to assign the value to several vertices at once.

 After defining spacing values, you can proceed with the mesh building.  The
 mesh is built block by block. You may choose to build the mesh in one block
 or in selected blocks or in entire region at once.

 Changing the density  of a pre-built  mesh (e.g. if  solution results  show
 that you need more precision somewhere in the region) obey some rules:
 *    when you change the spacing value in some vertex, the mesh is  removed
      automatically in those blocks which are connected to that vertex;
 *    the mesh  that  is  not removed,  freezes  spacing  values  along  its
      boundary from recalculation as if those values were defined  manually;
      so if you  need major changes  in the mesh  density, first remove  the
      mesh in the whole region.

 All operation with  spacing values and  the mesh is  performed in the  Mesh
 submenu. To define the  spacing, choose Set  Spacing, then pick  the vertex
 and type in  the spacing value.  Then you can  alter spacing  at any  other
 vertex or return  to menu  by pressing ESC.  If there  are some  previously
 selected vertices, the spacing values are set  for all of them at once.  If
 some edges  are selected,  the  spacing values  are  set for  all  vertices
 situated at them.  The same  way, if there  are some  selected blocks,  the
 spacing values are  set for all  vertices situated at  their boundaries  or
 inside them.

 To build  the mesh,  choose Build  Mesh and  select an  option. Delete Mesh
 removes mesh in some blocks or in the entire region.

 If the spacing visibility switch is on (Show  Spacing in the Options menu),
 the explicitly set  spacing values are  shown as small  circles around  the
 vertices. You can check  out mesh building process  if Show Mesh toggle in
 the Options menu is on.

       6.2.6 Graphics Window Management

 There are two graphic  windows on the screen  while editing the model.  The
 small window  always displays  the general  view of  the model.  The  large
 window is used to present a more detailed picture of the whole model or its
 selected parts. Zoom menu provides several options to control the  displays
 in each graphic window.

 Keyboard allows you to type in dimensions of the visible region.  Specified
 region is displayed  in both  windows and becomes  the default.  This is  a
 normal way to  extend the  default visible  region. Limits  of the  visible
 region can be automatically adjusted to preserve equal horizontal (X or  Z)
 and vertical (Y or R) scales.

 Natural sets  minimum visible  region large  enough  to contain  the  whole
 model. Resulting  region  is displayed  in  both windows  and  becomes  the
 default.

 Default sets visible region  dimensions to the  default values. The  region
 visible in the large window becomes the same as in the small one.

 Large Window controls the  dimensions of  the visible  region using  rubber
 band rectangle  in the  large window.  The rubber  rectangle is  controlled
 using mouse or cursor keys. First,  choose position of the lower left  hand
 corner, then of the upper right hand one.

 Small Window does the same, but rubber band rectangle appears i n the small
 window. This mode is recommended when whole or part of the required  region
 lies outside the large window.

       6.2.7 Obtaining Model Information

 You can get detailed information on  the current model using Info  submenu.
 In this submenu  choose the  object type  (vertices, edges  or blocks)  and
 complete information corresponding to that  type will be displayed  (amount
 of objects, presence of labels, mesh parameters, etc.). Then you can pick a
 specific object within that group to  get more local information.  Pressing
 ESC returns to  the menu. This  mode is used  to get total  number of  mesh
 nodes, to check labels, to examine the mesh spacing values and so on.

            6.3 Additional Options

       6.3.1 Saving Model

 The Save command of File menu saves the model to disk. The Save As does the
 same but lets you change the name of output  file. It is wise to save  mesh
 not only when editing  is over, but regularly  during the session to  avoid
 troubles due to errors or power failure.

     Note. When the Save  As command changes name  of the model file  it
     automatically updates  reference  to  the  model  file  in  problem
     description.


       6.3.2 Opening Model File

 To create new empty  model choose New  in the File  menu. To open  existing
 model file choose Open in the same menu,  and then type or select the  file
 name. If the  active model  was changed  you will  be prompted  to save  it
 before transition to the new one.

 With Open, you can import old  geometry model files created with the  first
 or second versions of QuickField and  having .TRI extension. To do so,  you
 need only to specify .TRI extension when selecting the file.

     Note. While loading old-formatted  model, all numerical labels  are
     transferred to literal form automatically.


       6.3.3 DXF File Import

 You can import model geometry or  its fragments from the DXF file  produced
 with any major CAD system. To do so, choose Import DXF in the File menu and
 then type or select required file name. The visible region is automatically
 extended if needed to assure visibility of all imported geometric  objects.
 If the model is not empty when reading  the DXF file, it is recommended  to
 save the current  model state before  the operation. This  will give you  a
 chance to return to the initial stage if the imported objects  incidentally
 overlap the existing part of model.

       6.3.4 Discretization Visibility Options

 There  are  four  switches   Show Mesh,  Show Domain,  Show  Breaking,  and
 Show Spacing which affect  the discretization visibility  level. These  are
 accessible through Options menu. When all these switches are off, region is
 displayed without discretization. This mode  is useful for region  geometry
 description and label setting. If the Show Spacing mode is switched on, all
 explicitly set spacing  values are shown  as circles  with the  appropriate
 radii.

 When Show Breaking switch is on, the mesh size is shown as tic marks on the
 edges. It is  convenient to use  both Show  Spacing and Show  Breaking when
 specifying the mesh  spacing values. Show  Mesh lets you  see the  complete
 triangular mesh. Turn it on to check the mesh building process. Show Domain
 without Show  Mesh displays  the  domains  due to  geometric  decomposition
 process.

 The state of these switches is remembered between sessions.

       6.3.5 Attraction Distance Parameter

 To avoid  small unrecognizable  inaccuracies  in geometry  definition,  new
 vertices or edges cannot  be created very close  to the existing ones.  The
 creation of new geometric  objects is controlled  by the epsilon  parameter
 also called the attraction distance.

 The following rules concern creating new vertices and edges.
 *    Creating a new vertex  is prohibited within 2*epsilon-neighborhood  of
      the existing one.
 *    A new edge  cannot be added  if it joins  the same vertices  as of  an
      existing edge  and  the  maximum gap  between  them  does  not  exceed
      epsilon.
 *    If the distance between a vertex to add and some edge is less than  or
      equal epsilon, the  vertex is attracted  by the edge  and the edge  is
      automatically split into pair of new edges to incorporate the  vertex.
      The same is true when new edge is added, but in this case the new edge
      may be attracted by existing vertex.

 The default value of epsilon  is 0.5 per cent  of the visible region  size.
 You can set different value by choosing Epsilon in Options menu. Decreasing
 epsilon would allow you to describe very fine details of the model. But the
 most convenient way to get the same result is to zoom in the window.


                      7. PROBLEM PARAMETERS DESCRIPTION

 To solve the  problem it  is needed  to describe  the material  properties,
 field sources and boundary conditions. These  parameters are stored in  the
 property description  file. The  correspondence  between records  of  these
 files and subdomains  or boundaries  of the  region is  established by  the
 labels assigned to geometrical objects  during editing the model.  Labeling
 blocks, edges and vertices is described in "Model Geometry Definition".

 Physical values for  a problem  may be  defined in  one or  two data  files
 attached to the problem.  Both files have the  same format and  distinguish
 only in purpose. The first file is the  basic data file of the problem  and
 is assumed to contain the data specific to that problem. The second is  the
 library  file,  that  contains  common  material  properties  and  standard
 boundary conditions for a class of problems.

 To edit the basic  data file, choose Data  in the Edit  menu (ALT+E, D)  to
 edit the library file, choose  Library (ALT+E, L.) The alternate method  to
 start editing data is to select  the name of one of  the data files and  to
 choose the Open button  while editing the problem description.

 When entering data file  editing mode, the  dialog box appears,  containing
 three lists of labels, which correspond to blocks, edges and vertices.

 Option buttons above the  list boxes, allow you  to choose the label  group
 type. One you pick a label  from the available lists, it gets  highlighted.
 In this case  it appears also  in the text  box below the  list boxes.  The
 label in the text box  is the current label,  so all the immediate  actions
 are done to this label.

 The labels with no specified data are marked with asterisks. Labels of  the
 blocks which are excluded from  consideration (i.e., having empty  material
 properties,) are marked with double exclamation mark.

 Options for editing the data file  could be divided into three groups.  The
 first group considers actions on creating  new labels and editing data  for
 existing ones. Operations on copying, renaming and removing some data  set,
 which corresponds to  some label,  belong to  the second  group. The  third
 group assumes the actions  on saving the current  state of data file  under
 another file name and merging two data files.

 To exit from data  file editing, choose the  Close command button or  press
 the ESC key. You will be prompted to save the changes to file.


           7.1 Creating a New Label

 To create new label:
 *    choose appropriate type of geometrical object-block, edge or vertex;
 *    type the name of the label in the  text box titled Label. You may  use
      the ins key in addition to usual methods  to move to the text box.  If
      the label's  name already  exists  in the  list,  but is  marked  with
      asterisk (which means that the data for the label is not defined  yet)
      you need not type  the name, but  simply select it  in the list  using
      keyboard or mouse;
 *    and choose Add button or press ENTER to start editing the data.

 After you  define the  data, new  label  appears in  the list  of  existing
 labels. If data editing was canceled, new label is not created.


           7.2 Editing Label Data

 To edit the data assigned to some label, select that label and choose  Edit
 button or press  ENTER. The  dialog box appears,  its view  depends on  the
 class of current problem  and on the type  of geometrical object which  the
 label corresponds to.

 To finish label data editing, choose OK button. Choosing Cancel button will
 end the editing and discards all changes to the values.

       7.2.1 Editing Data in Electrostatics

 Block label  data  for electrostatics  problem  contain two  components  of
 electric permittivity and possibly distributed charge density.

 When  creating  data  for  a  new  label,  the  text  boxes  for   electric
 permittivity components contain None instead of  numbers. The word None  in
 these boxes or absence  of value means  that the block  with such label  is
 excluded. If  you want  to define  the material  properties (and  therefore
 include the block into consideration), simply type in the value of electric
 permittivity, which will replace the highlighted None.

 If you need to define two components different from each other, first check
 the Anisotropic box.

 The data  for the  edge label  allow  to assign  one of  possible  boundary
 conditions. Select the type of condition and then type in the values.

 The vertex in  the problem of  electrostatics may have  known potential  or
 concentrated charge. Check one of these options and then enter a value.

       7.2.2 Editing Data in Magnetostatics

 With problems of magnetostatics, block label data contain two components of
 magnetic permeability tensor,  the current  density and  two components  of
 coercive force, if the subregion is the permanent magnet.

 With nonlinear  materials,  you need  to  define the  magnetization  curve,
 instead of magnetic permeability. In this  case check the Nonlinear box  to
 get into the B-H curve editor. If a B-H curve had already been defined, the
 dialog box would contain a B-H Curve button which can be chosen to get into
 the curve editor. Editing the magnetization curve is discussed in  "Editing
 the Curves" section later in this chapter.

 When  creating  data  for  a  new  label,  the  text  boxes  for   magnetic
 permeability components contain None instead of  numbers. The word None  in
 these boxes or absence  of value means  that the block  with such label  is
 excluded. If  you want  to define  the material  properties (and  therefore
 include the block into consideration), simply type in the value of magnetic
 permeability, which will replace the highlighted None.

 If you need to define two components different from each other, first check
 the Anisotropic box.

 The data  for the  edge label  allow  to assign  one of  possible  boundary
 conditions. Select the type of condition and then type in the values.

 The vertex in the problem of magnetostatics may have known potential or the
 concentrated current may flow through the vertex. Check one of the  options
 and then enter a value.

       7.2.3 Editing Data with Current Flow Problems

 Block label data for the problem of current flow contain two components  of
 electric resistivity.

 When creating data for a new label, the text boxes for electric resistivity
 components contain None instead of numbers. The word None in these boxes or
 absence of value means that the block containing such label is excluded. If
 you want to define the material properties (and therefore include the block
 into consideration),  simply type  in the  value of  electric  resistivity,
 which will replace the highlighted None.

 If you need to define two different components of resistivity, first  check
 the Anisotropic box.

 The data for the edge  label allow you to  assign one of possible  boundary
 conditions. Select the type of condition and then type in the values.

 The vertex  in the  problem of  current flow  may have  known potential  or
 external current. Check one of these options and then enter a value.

       7.2.4 Editing Data with Heat Transfer Problems

 The data for  block label contain  two components  of thermal  conductivity
 tensor and, possibly, the volume power of heat source.

 To describe the thermal  conductivity as a  function of temperature,  check
 the  Nonlinear  box   and  the  temperature   curve  editor  for   defining
 lambda = f(T) will be displayed. Curve editing is discussed in "Editing the
 Curves" section later in this chapter.

 Also the volume power of  heat source could be  described as a function  of
 temperature. To do so, check the Function of Temperature box related to the
 heat source field. The templates for editing the dependencies are described
 in "Editing the Curves".

 When creating new label, the text boxes for thermal conductivity components
 contain None instead of numbers. The word None in these boxes or absence of
 value means that the block containing  such label is excluded. If you  want
 to define the  material properties (and  therefore include  the block  into
 consideration), simply type  in the  value of  thermal conductivity,  which
 will replace the highlighted None.

 If you need  to define two  different components  of thermal  conductivity,
 first check the Anisotropic box.

 The data for edge  label allow you to  describe boundary conditions.  Check
 the condition  which  you  need,  and then  type  in  the  parameters.  The
 condition of the  second kind and  the convection  and radiation  condition
 could be  combined together  which means  that the  heat flow  through  the
 surface is compounded from several components.

 The vertex in heat transfer problem  may have known temperature or  string-
 like heat source.  Check one  of these  possibilities, and  then enter  the
 numeric parameter.

        7.2.5 Editing Data with Stress Analysis Problems

 When editing the  data for the  block label with  stress analysis  problem,
 there are two  sets of properties  to be edited  simultaneously. To  switch
 from one set to  another, use option buttons  at the top  of dialog box  or
 press page up or page down keys.

 When creating new  label, the text  boxes for Young's  moduli contain  None
 instead of numbers. The word None in these boxes or absence of value  means
 that the block containing such label is excluded. If you want to define the
 material properties (and therefore  include the block into  consideration),
 simply type in  the value of  the Young's modulus,  which will replace  the
 highlighted None.

 The Anisotropic boxes, which applied to  elastic moduli or coefficients  of
 thermal expansion, allow you to describe anisotropic properties in each set
 independently.

 The data for  thermal stress analysis  is slightly  different for  thermal-
 stress coupled and non coupled problems:
 *    With an uncoupled problem, you  define the difference of  temperatures
      between strained  and  strainfree  states,  which  is  assumed  to  be
      constant within all blocks with the corresponding label.
 *    With thermal-stress coupling,  you need to  define the temperature  of
      strainfree state for each block subjected to temperature loadings.

 The values for  allowable stresses do  not affect the  solution. Those  are
 only used  in  postprocessing  stage  to  calculate  the  Mohr-Coulomb  and
 Drucker-Prager criteria. You don't need define allowable stresses, if these
 criteria are of no interest to you.

 The data defined  for an edge  label may include  constraints along one  or
 both coordinate axes and the surface forces are described either as  normal
 pressure or  by their  Cartesian components.  To apply  fixed  displacement
 along an  axis,  check  the appropriate  box  and  then enter  a  value  of
 displacement.

 The node label data may define rigid  or elastic support along one or  both
 coordinate  axes,  or  concentrated  external  force.  To  describe   rigid
 constraint along some axis, check the  appropriate box, and then enter  the
 value of fixed displacement.

       7.2.6 Editing the Curves

 Curve functions,  which  describe  some  field  dependent  parameters,  are
 implemented as tables containing two columns:  an argument and a  function,
 e.g., magnetic field intensity and flux density or temperature and  thermal
 conductivity. Editing the table is supported with graphical presentation of
 the dependency, which is interpolated with  cubic spline among the  entered
 points. The solver uses just the same curve as you see on your screen.

 To add the  new point to  the dependency, type  in two values  (B and H  in
 shown example) and press ENTER key or choose Add button. If the argument of
 a new point coincides with the argument of existing one, new point replaces
 the old one.

 To remove the point, select it in the table and choose the Delete button or
 press the del key.

 You may control the scaling of  the graph with use of  the Zoom In or  Zoom
 Out buttons.

 To exit from editing the curve, choose the Close button or press ESC.  Note
 that subsequent canceling of label data editing with ESC key or the  Cancel
 button will discard all changes including the curve editing.

            7.3 Copying, Renaming and Deleting the Label

 In order to copy or rename the label  (to be precise, the data set  related
 to the label), select the label in the  list and choose the Copy or  Rename
 button. The new name  is entered in  a dialog box,  which appears when  you
 choose the button.

 To remove the label, select it and choose Delete or press del.


           7.4 Merging and Copying Data Files

 The Merge command button allows you to expand the contents of the data file
 being edited with the labels contained in some other data file for the same
 type of problems. The labels with coinciding names will not be replaced.


                            8. SOLVING THE PROBLEM

 This chapter  describes, how  to solve  the prepared  problem, and  methods
 QuickField uses to solve.

 Several conditions have  to be met  to solve a  problem. The problem  type,
 plane, required precision and other parameters have to be specified in  the
 problem description file.  The model  geometry file  must contain  complete
 model with mesh and labels. Each label referred by the model file is to  be
 defined in the problem's private or library data file.

 To obtain the problem solution, choose Solve  Problem from the Results menu
 (ALT+R, S). You may  skip this action and  directly proceed to the  results
 analysis by  choosing Analyze  from the  Results menu  (ALT+R, A).  If  the
 problem has not been solved yet or its results are out of date, the  solver
 will be invoked automatically.

 Special bar indicator lets  you see the progress  of the solution  process.
 Linear problems are  solved by  using a  powerful preconditioned  conjugate
 gradients method. The preconditioning based on the geometric  decomposition
 technique guaranties a  very high speed  and very  weak dependence  between
 number  of  nodes  and  the  required  number  of  the  conjugate  gradient
 iterations. Nonlinear problems are solved using the Newton-Raphson  method.
 The Jacobian matrix arising  at each step of  the Newton-Raphson method  is
 inverted the same way as it is done for linear problems.


                            9. ANALYZING SOLUTION

 This chapter  explains  the  procedures for  detailed  examination  of  the
 results using  the  QuickField postprocessing  utility.  The  Postprocessor
 provides various ways of results presentation:
 *    field pictures,
 *    local field values,
 *    integral quantities,
 *    X-Y plots.

 Field pictures and X-Y plots can be saved in vector-formatted file for  use
 with any word-processing or desktop publishing utility. Local field  values
 and sequences of points  from X-Y plots  can be stored  in table files  for
 subsequent use by spreadsheet or user-written programs.


           9.1 Starting and Quitting the Postprocessor

 To examine the results, choose Analyze from the Results menu (ALT+R, A).

 Screen layout when working with the Postprocessor is very similar to one of
 the Model Editor. There  are two graphic windows  displayed on the  screen.

 The small one presents general view of the model, while the large one shows
 detailed field picture  or a X -Y plot. The  message bar  is at the  screen
 bottom. Upper right screen area is  normally occupied by menu, legend  box,
 or a temporary window used to display text information.


           9.2 Building the Field Picture on the Screen

       9.2.1 Interpreted Quantities

 The  set  of  the  physical  quantities  which  can  be  displayed  by  the
 Postprocessor depends on the problem type.

 For the electrostatic problem these quantities are:
 *    scalar electric potential (voltage);
 *    vector of electric field intensity;
 *    vector of electrostatic induction;
 *    electric permittivity (or its largest component in anisotropic media);
 *    electrostatic field energy density.

 For the magnetostatic problem:
 *    vector magnetic potential A in plane-parallel problem or flux function
      in axisymmetric case;
 *    vector of magnetic flux density;
 *    vector of magnetic field intensity;
 *    magnetic permeability (its largest component in anisotropic media);
 *    magnetic field energy density in both linear and nonlinear media

 For the problem of current flow:
 *    scalar electric potential
 *    vector of electric field intensity;
 *    vector of current density;
 *    electric resistivity (its largest component in anisotropic media);
 *    ohmic losses per volume unit.

 For heat transfer problem:
 *    temperature;
 *    vector of heat flow;
 *    thermal conductivity (its largest component in anisotropic media).

 For stress analysis problems:
 *    displacement vector;
 *    strain tensor and its principal values;
 *    stress tensor and its principal values;
 *    von Mises criterion (stored energy of deformation);
 *    Tresca criterion (maximum shear);
 *    Mohr-Coulomb criterion;
 *    Drucker-Prager criterion;
 *    Hill failure criterion (failure index).
      The Hill failure  criterion is  calculated only  for those  materials,
      where allowable stresses were defined  (while editing the block  data,
      see " Problem Parameters  Description "). If  any  pair  of  allowable
      stresses is not given, the corresponding term is excluded from account
      while calculating the Hill Index.

       9.2.2 Field Presentation Methods

 Several methods are available for displaying the field picture:
 *    Color map for distribution of a chosen scalar quantity. The color  map
      is accompanied by the legend showing the correspondence between colors
      and numerical values.
      You can adjust  the color  scale, changing  the range  limits for  the
      chosen quantity.
 *    Field lines.  Those are  isotherms for  temperature fields,  lines  of
      equal potential  in electrostatics  and flux  lines for  magnetostatic
      problems.
      You  can  manipulate  the  picture,  changing  the  distance   between
      neighboring lines.  This  distance  is measured  in  units  of  chosen
      quantity.
 *    Vectors-family of line segments showing magnitude and direction of the
      vector quantity. The  base point of  each vector is  marked by a  dot.
      Vectors are drawn in the nodes of the regular rectangular grid.
      You can change the grid cell  size and the scaling factor for  desired
      vector quantity.

 The following methods are specifically for stress analysis problems:
 *    Deformed boundary  and  shape  indicated  by  means  of  deformed  and
      original rectangular grid.
 *    Stress tensor  display  as  a  pair  of  eigenvectors  reflecting  the
      direction  of  principal  axes,  magnitudes  and  signs  of  principal
      stresses (blue color denotes tension, red color-compression);

 With these  methods, you  can change  the grid  cell size  and the  scaling
 factors in order to manipulate the appearance.

 It is possible to combine several visualization methods in the same picture
 to obtain the most expressive result.

       9.2.3 Field Picture Constructing

 When entering  the Postprocessor,  the default  form of  the field  picture
 appears on the  screen. You may  use Field View  from main  menu to  select
 other display methods or quantities.

 Shown dialog box corresponds to the problem of magnetics.

 To choose desired visualization method, select corresponding check box. You
 can select any combination of  methods at once. If  none of the methods  is
 selected, only the model's geometry is shown.

 This dialog  box also  allows to  change  scaling parameters  for  selected
 methods of presentation.  When you  select some  edit box,  you can  choose
 Suggest button to obtain suggested  value of corresponding parameter.  Note
 that suggested  values  for  Minimum  and  Maximum  fields  are  those  for
 currently visible part of the model.

 The Field  View dialog  box for  the stress  analysis problem  additionally
 allows to select tensor quantity visualization.

 Selecting  the   Deformed  Shape   option   turns  on   Deformed   Boundary
 automatically.

 Sizes  of  the  vector  symbols  of   all  vector  quantities  except   the
 displacement vector  are determined  by  the corresponding  physical  value
 multiplied by the scaling  factor and by the  cell size. Similar method  is
 used for stress tensor components. Unlike other vector quantities, the size
 of the displacement vector on the screen does not depend on the cell  size.
 It is determined  by the dimensionless  scaling factor, the  unit value  of
 which means that the displacement is shown in its natural scale.

 Color map of  temperature difference in stress analysis problem  visualizes
 temperature distribution as it is defined  by user or imported from  linked
 heat transfer problem. In the last case, temperature is shown only in those
 blocks, where it is really taken into account.

 The Failure  Index position  is available,  when  there exist  blocks  with
 correctly defined allowable stresses.

 Choosing the OK button  causes redrawing the field  picture on the  screen.
 Cancel closes the dialog  box without redrawing  the picture and  preserves
 preceding values of all the parameters.

        9.2.4 Window Scaling Management

 To adjust the scale of the field  picture, choose Zoom from the menu.  This
 command is very similar to the  analogous command of the Model Editor,  but
 the default window dimensions cannot be altered, they retain values set  in
 the Model Editor.

 Keyboard allows you to type in dimensions of the visible region. Limits  of
 the  visible  region  can  be  automatically  adjusted  to  preserve  equal
 horizontal (X or Z) and vertical (Y or R) scales.

 Default sets visible region  dimensions to the  default values. The  region
 visible in the large window becomes the same as in the small one.

 Large Window controls the  dimensions  of the visible  region using  rubber
 band rectangle  in the  large window.  The rubber  rectangle is  controlled
 using mouse or cursor keys. First,  choose position of the lower left  hand
 corner, then of the upper right hand one.

 Small Window does the same, but rubber band rectangle appears in the  small
 window. This mode is recommended when whole or part of the required  region
 lies outside the large window.

 Maximize enlarges the large window to the full screen for hard copying  and
 taking photos. Pressing any key returns the Postprocessor to its  preceding
 state. The color  map legend could  be shown in  maximized view. To  switch
 legend on or off, choose Show Legend in Options menu before maximizing.


           9.3 Access to Local Field Data

 The Postprocessor displays local field data in Values mode. Click the point
 where you need to know the values of the field quantities, or press tab and
 then enter the coordinates of the point with the keyboard. Once you  choose
 the point, the values at this point  are displayed on the screen. To  leave
 the Values mode use ESC key, or press right mouse button.

 The local values of physical quantities obtained in the Values mode can  be
 logged to the table file. This file has self explaining ASCII format,  with
 values separated with  spaces or  commas. The table  file can  be used  for
 printing numerical results, or to pass  them to other application  program,
 e.g., a spreadsheet program to produce  the report. To open the table  file
 choose Open Table from the Options menu. See "Exporting Local Values to the
 Table File" for further explanation.


           9.4 X-Y Plots

 With  QuickField   Postprocessor,   you  can   analyze   field   quantities
 distribution  along  user-defined  paths  of  arbitrary  shape  (contours).
 Contours  are   also  used   for  calculating   integral  quantities   (see
 "Calculating Integrals" later in this chapter) and  for saving local field
 values to the table file (see "Error! Bookmark not defined.").

 To start  this mode,  choose X-Y  Plot from  the menu.  If the  contour  is
 already defined,  X-Y  plot  is immediately  shown  in  the  large  window.
 Otherwise you should  define the contour,  choosing Edit  Contour from  the
 menu.

       9.4.1 Editing Contours

 The contour is a directed curved line consisting of line segments and  arcs
 (including the edges of the model). Some rules are applied to the contours:
 *    The contour may not intersect itself.
 *    Open and closed contours are discerned.
 *    Multiply connected contours have  sense only for calculating  integral
      quantities.

 Contour is shown in the window as  a set of directed lines or  color-filled
 interior (closed counter-clockwise-directed contours).

 To edit  the contour,  choose Edit  Contour from  the menu.  The  following
 operations change the current contour state:

 Add Line     - attaches a line segment or an arc to the contour. The arc is
                specified by its  degree measure (zero  means line  segment)
                and two  end points.  The contour  may  be initiated  by  an
                arbitrary line, but only adjacent lines are accepted  later.
                The line cannot be added to the closed contour. Adding lines
                is terminated by  pressing ESC or  when the contour  becomes
                closed.

 Close Contour- closes an open contour  by connecting its  open ends with  a
                straight line or an arc.

 Add Edge     - append the contour with  an edge of  the model. The  contour
                may be initiated  by an  arbitrary edge,  but only  adjacent
                edges are accepted later.  The edge cannot  be added to  the
                closed contour. Adding edges  is terminated by pressing  ESC
                or when the contour becomes closed.

 Add Block    - considers the current  closed contour as  a frontier of  the
                plane  region  and  updates   this  region  by  adding   (or
                subtracting) a  block  of the  model  in the  sense  of  set
                theory. Adding blocks is terminated by pressing ESC.

 Undo         - reverses the last action done with the contour.

 Clear        - deletes the entire contour.

 Change Direction    -    alters the  contour  direction. The  direction  is
                shown by the arrows at the contour elements.

 Once edited,  the  state  of  the  contour  is  preserved  until  the  next
 modification or the  end of  postprocessing session.  Depending on  current
 state of the contour, some editing operations may be prohibited.

 The direction of the contour is significant in the following cases:
 *    for volume integrals the domain of integration lies to the left of the
      contour.
 *    for surface integrals the positive normal  vector points to the  right
      relative to the contour direction.
 *    the starting point  of the contour  corresponds to zero  point at  the
      x-axis of the X-Y plot.
 *    if the plotted or the integrated function has different values to  the
      left and to the right of the contour, the right-hand value is used.

       9.4.2 X-Y Plot Management

 Once  the  contour  has  been  defined,  the  X-Y  plot  is  drawn  showing
 distribution of  the  default field  quantity.  In order  to  change  shown
 quantity, choose View from X-Y Plot menu.

 The Postprocessor is capable of showing multiple quantities simultaneously,
 having the same unit of measurement. According to this, all quantities  are
 separated into groups. Full list of quantities includes all those available
 for  color  map  (see  "Interpreted  Quantities"),  and  also  normal  and
 tangential components of vector and scalar quantities.

 When you select the appropriate group  of quantities, the list titled  Show
 contains the  quantities  selected for  display,  and the  Quantities  list
 contains available but not selected quantities. You can use buttons located
 between the  lists, or  simply  double-click in  the  lists, to  move  some
 quantity from one list to another.

 In the  dialog box,  you can  also modify  the range  of y  coordinate.  By
 default, it fits all currently selected  curves. You can get the  suggested
 value of lower or upper limit by selecting corresponding text box  (Minimum
 or Maximum) and choosing Suggest button.

 You can switch  on and off  displaying coordinate grid  and markers on  the
 curves. The last mode allows to distinguish the coinciding curves.

       9.4.3 Zooming the X-Y Plot

 Zoom In position in X-Y  Plot menu allows you  to change the plot  scaling,
 using the rubber rectangle. Then you  can return to the default ranges  for
 both axes, choosing Zoom Out.

 Choosing  Maximize  enlarges  the  X-Y  plot  window  to  the  full  screen
 dimensions without  changing axes  ranges. Then  press  any key  to  return
 Postprocessor to its normal state. The  legend is shown in maximized  view,
 if Show Legend in Options menu has been switched on earlier.


           9.5 Calculating Integrals

 A postprocessing calculator  is available for  evaluating integrals in  the
 Integrals menu.  Integrals  are  calculated with  respect  to  the  contour
 defined in  Edit  Contour mode.  QuickField  calculates line,  surface  and
 volume integrals. In plane-parallel problem, a contour defines  cylindrical
 (in generalized  sense)  surface  of infinite  depth,  or  volume  of  that
 cylinder for  volume  integral. Therefore,  in  plane-parallel  formulation
 surface and volume integrals are calculated per unit depth. In axisymmetric
 problem, a contour defines toroidal surface, or toroid for volume integral.

 Positive direction of a contour is counter-clockwise. The direction of  the
 contour is accounted as follows:
 *    for volume integrals the domain of integration lies to the left of the
      contour.
 *    for surface integrals the positive normal  vector points to the  right
      relative to the contour direction.
 *    if the plotted or the integrated function has different values to  the
      left and to the right of the contour, the right-hand value is used.

 Force, torque  and electric  charge have  sense only  when the  contour  is
 closed. However, they are calculated  for unclosed contours too,  commented
 as partial.

 The quantities available for electrostatic problems are:
 *    total electric charge in a particular volume
 *    total electrostatic force acting on  bodies contained in a  particular
      volume
 *    total torque of electrostatic forces acting  on bodies contained in  a
      particular volume
      The torque  vector  is parallel  to  z-axis in  planar  case,  and is
      identically  equal  to  zero  in  axisymmetric  one.  The  torque   is
      considered relative to the origin of the coordinate system. The torque
      relative to any other arbitrary point can be obtained by adding  extra
      term of cross product [F , r], where F is the total force and r is the
      radius vector of the point.
 *    electric field energy For magnetostatic problems:
 *    total magnetostatic force acting on  bodies contained in a  particular
      volume
 *    total torque of magnetostatic forces acting  on bodies contained in  a
      particular volume
      The torque vector  is parallel to  z-axis in the  planar case, and  is
      identically equal  to zero  in the  axisymmetric  one. The  torque  is
      considered relative to the origin of the coordinate system. The torque
      relative to any other arbitrary point can be obtained by adding  extra
      term of cross product [F, r], where F is the total force and r0 is the
      radius vector of the point.
 *    magnetic field energy
 *    flux linkage per one turn of the coil

 For problems of current flow:
 *    electric current through a given surface
 *    power losses in a volume

 For heat transfer problems:
 *    heat flux through an arbitrary closed or unclosed surface

 No integral quantities are available for stress analysis.

 To get the  integral quantities, choose  Integrals from the  menu. In  this
 mode you can edit the contour  and select the required quantity from  menu.
 Some integrals require closed counter-clockwise oriented contour, otherwise
 they have no physical sense.

 Apart from the main list of  integral quantities some additional  integrals
 are available in Line/Surf.  Int. menu (line and surface  integrals) and in
 Volume Int. menu (volume  integrals). All  these integrals  are defined  by
 equations shown in the menu.

 When the electrostatic or magnetic force, torque, electric charge, electric
 current or heat flux are to be calculated, the domain of integration may be
 chosen by many  different ways.  The only  requirement for  the surface  of
 integration is to contain all the necessary bodies, but to avoid any  extra
 bodies or field sources. It is significant to understand that the precision
 will be the best if you choose  the integration surface as far as  possible
 from the places with strong inhomogeneity of field, e.g., field sources  or
 boundaries of conducting or ferromagnetic bodies.

 When calculating the flux  linkage the domain  of integration must  exactly
 fit the cross section of the coil.


           9.6 Saving Prepared Results to Files

       9.6.1 Saving the Screen Picture

 The postprocessor is capable of storing  current field picture or X-Y  plot
 in widely supported graphics file formats. Graphics objects in these  files
 are stored in vectorial form, independent  of output device resolution.  It
 allows to  obtain maximum  quality pictures  on different  printers.  These
 files could be as well directly printed, as included into other  documents.
 There is a  lot of word  processors and desktop  publishing systems,  which
 could import vector-formatted graphics files for editing and printing.

 The postprocessor supports following graphics formats:
 *    Computer Graphics Metafile-CGM (ISO 8632-3:1992 compliant).
 *    PostScript(R) language  by  Adobe(R) System  Incorporated.  PostScript
      file created by QuickField  could be directly  sent to any  PostScript
      printer.
 *    Encapsulated PostScript-EPS.  An EPS  file  is a  standard  PostScript
      language file,  destined  for  including  in  other  documents  as  an
      illustration. EPS  file  created  by QuickField  also  conforms  Adobe
      Illustrator(R) format, that in many cases allows not only to print but
      also to edit graphics image.

 To save the field picture to file, choose Export in the File menu.

 The Line Styles box allows you to select appropriate line styles and widths
 for separate field picture elements. The line width is measured in  points-
 typographic unit equal to 1/72 inch. Hair line means line of minimum  width
 allowed for printing device.  Dot means dotted line  of the same width.  To
 revert line styles to default settings, choose Reset.

     Note:  Appearence  of  imported  field  picture  elements  in  some
     application depends on the features of graphics import filter  used
     by that applications, e.g., several  filters do not support  dotted
     line style.


 The Color Grades text box allows to switch to greated (or lower) number  of
 colors in color map,  than default 10  grades used to  draw the picture  on
 screen. If the exporting color mode is black and white, grey scale is  used
 instead of colors.

 We recommend exporting in Full Color mode only when you are really planning
 to use the color printer.

 To export the X-Y plot currently drawn on the screen, choose Export in  the
 File menu. The dialog box that appears is similar to Export Picture  dialog
 box.

       9.6.2 Exporting Local Values to the Table File

 The local values of  physical quantities obtained in  the Values mode  (see
 "Access to Local Field Data ") can be logged  to the table file.  This file
 has self  explaining ASCII  format, with  values separated  with spaces  or
 commas. The table file  can be used for  printing numerical results, or  to
 pass them  to other  application program,  e.g., a  spreadsheet program  to
 produce the report.

 To open the table file choose Open  Table from the Options menu. The dialog
 box will appear, asking for the name of the table file, its format and  the
 set of the field quanitites to be included in the table. The table also may
 contain optional header.  Existing files  may be  appended or  overwritten.
 Once this option  is activated,  for every point  you click  in the  Values
 mode, a line is written to the table file.

 If you wish other filename, than that's  suggested, you can type it in  the
 File text box, or choose Browse to pick the filename from the directory.

 The list of currently selected quantities is displayed in the Columns  list
 box. To add some quantity to the list:
 *    Select the option  button corresponding to  the group,  to which  that
      quantity belongs. The list of available quantites will be  redisplayed
      in accordance to the group chosen.
 *    Select needed quantity  from the list  box and choose  Add or  double-
      click in the list. That quantity will appear in the Columns list box.

 To delete some  quantity from the  list of  currently selected  quantities,
 select that quantity in the Columns  list box and choose Delete or  double-
 click in the list.

 Values in the  table can be  separated with spaces  or commas (the  default
 extensions are .TXT and .CSV, respectively). In some cases, comma-separated
 tables are better understood by spreadsheet applications.

 To close output  to the  table file,  choose Close  Table from  the Options
 menu.

        9.6.3 Exporting Field Values along the Contour to the Table File

 You can save  field data  in the  points, distributed  along the  currently
 selected contour, to the table  file of the same  format with that is  used
 for exporting local field values, described  in "Exporting Local Values to
 the Table File". To save the data,  choose Tabulate in X-Y  Plot menu. The
 dialog box appears, allowing you to  manage the format and contents of  the
 table.

 In addition to the controls in  the Open Table dialog box, this dialog box
 allows you to control the number  of rows in the  table. You can enter  the
 value in the  Rows Number text  box. Its meaning  depends on option  button
 selection below the text  box. If At Whole  Contour is selected, the  table
 will contain that number of rows, equally distributed along the contour and
 accounting its ends. If selected is In Each Segment, given number of points
 will be equally distributed along  each segment, constituting the  contour.
 The total namber of rows in the table will be that number multiplied by the
 number of segments (plus one additional row, if the contour is unclosed).

 Also, some  additional  quantities are  available:  the distance  from  the
 contour start,  and normal  and tangential  components  of the  vector  and
 tensor quantities, with respect to local contour direction.

       9.6.4 Fast Printing the Results

 If you do not need high quality printing, or if you want to get hardcopy to
 the printer, that does not support PostScript language, QuickField offers a
 special capabilities.

 QuickField supports  special mode  for screen  hardcopies, when  the  field
 picture or X-Y plot is enlarged to entire screen (Maximize position in  the
 menu). There is also a color  scheme suited for creating monochrome  screen
 hardcopies. You can select this color  scheme with Options Colors  command,
 which is available in main QuickField and Postprocessor menus.

 If you are running MS-DOS 5.0 and the GRAPHICS program is resident you can
 obtain the screen hardcopy by pressing shift+print screen on the keyboard.

 If you  run QuickField  under windows,  pressing  PRINT SCREEN  copies  the
 QuickField screen image to the clipboard which allows you to use this image
 in another application.

 Many word  processing programs,  e.g., Microsoft  Word,  provide a  way  to
 obtain screen image in a file, and then include it into the text  document.
 This is  the most  convenient  and common  way  of producing  high  quality
 reports.


           9.7 Additional Options

       9.7.1 Saving the Postprocessor State

 Current state of the  Postprocessor can be saved  to the special .SST  file
 and restored from it  later. The current state  includes: chosen method  of
 presentation, selected  quantity, scales,  ranges, current  contour  state,
 color table, etc. If you analyze several similar problems or the results of
 the same problem several times, you can save  a lot of work by reusing  the
 same Postprocessor parameters once saved in the .SST file.

 Choose Save Setup from the Options menu to save current Postprocessor state
 and Load Setup from the same menu to restore  this state from the file. In
 both cases you will be inquired to  supply the file name. The default  file
 name is constructed from the current problem name and .SST extension.

        9.7.2 Dispaying the Legend for the Field Picture and X-Y Plot

 The legend for the  color map shows the  correspondence between colors  and
 number; and for X-Y plot-between curves and quantities.

 The legend appears  in special  window after  each redrawing  of the  field
 picture or X -Y plot until any  key pressed. It  can be displayed  again by
 choosing Legend from the menu.

 To control  the legend  visibility in  maximized view,  choose Show  Legend
 trigger in Options menu.

       9.7.3 Changing the Color Scheme

 The QuickField  package  has several  alternative  color schemes.  You  can
 switch between these schemes from the main  menu of the package as well  as
 form the main menu of the postprocessor. In both cases, choose Colors  from
 Options menu.

 QuickField stores chosen scheme in QFIELD.INI file.


                                 10. EXAMPLES


           10.1 MAGN1: Nonlinear Permanent Magnet

 A permanent magnet and a steel keeper in the air.

 Problem Type:

 A nonlinear plane-parallel problem of magnetostatics.

 Geometry:

    +------------------------------------------------------+
    !Q                                                  R  !
    !                                                      !
    !                                                      !
    !      M  +----------------------------------+ N       !
    !         !                                  !         !
    !         !                                  !         !
    !         !              Iron                !         !
    !         !                                  !         !
    !         !                                  !         !
    !      K  +----------------------------------+ L       !
    !                                                      !
                                                           !
    !      G  +------+H                I ------- + J       !
    !         !      !                   !       !         !
    !         !Alnico!                   !Alnico !         !
    !         !      !D                E !       !         !
    !      C  +------+------------------ +------ + F       !
    !         !                                  !         !
    !         !                Iron              !         !
    !         !                                  !         !
    !         +----------------------------------+         !
    !         A                                  B         !
    !                                                      !
    !O                                                  P  !
    +------------------------------------------------------+


 The permanent magnets are made of ALNICO, coercive force is 147218 A/m. The
 polarizations of  the magnets  are along  vertical  axis opposite  to  each
 other. The demagnetization curve for ALNICO:

  H (A/m)  -147218 -119400  -99470  -79580   -53710  -19890   0
  B (T)    0.      0.24     0.4     0.5      0.6     0.71     0.77

    The B-H curve for the steel:

  H (A/m)  400   600   800   1000   1400    2000   3000    4000   6000
  B (T)    0.73  0.92  1.05  1.15   1.28    1.42   1.52    1.58   1.60


 Comparison of Results

 Maximum flux density in Y-direction:


      ANSYS          0.42

      Students'      0.40
      QuickField

      Professional   0.417
      QuickField


 See the MAGN1.PBM problem in the EXAMPLES directory.

 Step-by-step Description

 Let us learn,  how to  solve this problem  from scratch.  We'll forget  the
 solution made in MAGN1.PBM, and start a new problem, MAGNET.PBM.

 To create a new problem:
      Choose New  in the  Files menu  (ALT+F, N);  the dialog  box  appears,
 *
      asking for the filename for new problem.
      Change, if needed,  the drive and  directory in  the Directories  list
 *
      box.
 *    Type magnet in the Filename box.
 *    Choose OK.

 The extension .PBM will be added automatically.

 To select convenient length measurement units (millimeters):
 *    Choose Length Units in the Options menu. A dialog box appears.
 *    Select Millimeters.
 *    Choose OK.

 To assign the problem with appropriate features:
 *    Choose Problem in the  Edit menu (ALT+E,  P). The Problem  Description
      dialog box appears.
 *    Select Magnetostatics in the Problem Type drop-down list box.
      Select XY Plane.
 *    We'll agree with  suggested model and data file names (MAGNET.MOD  and
      MAGNET.DMS.)

 If  the  Library  Data  filename  box  is  not empty, clear it, since we'll
 define all the labels in the local data file (MAGNET.DMS.)

 We can  start  editing  the model  or  the  data directly  in  the  Problem
 Description dialog box. To edit the model:
 *    select the Geometry text box (click anywhere in the box with a  mouse,
      or press Alt+G, or press TAB until the selection reaches the box.)
 *    choose the Open button.

 The Model Editor starts.

 First, we should  make a decision  concerning dimensions  of the  problem's
 region. Since  the  given problem  is  physically unbounded,  the  magnetic
 system must be surrounded with a layer  of air thick enough to neglect  the
 influence of the boundary. We suppose that three times the width of the air
 gap between  the  magnet  and  the steel  keeper  will  be  a  satisfactory
 thickness of the air layer around  the magnet, so the rectangle 100 '100 mm
 will fit our region's geometry.

 The first step  with the  new model  in Model  Editor is  to adjust  window
 dimensions fitting the  problem's region.  Since the  problem has  vertical
 axis of symmetry, it  is convenient to set  zero of x-axis  at the axis  of
 symmetry. So the region fits the square (-50 < x < 50, 0 < y < 100).

 To assign these values to the window limits:
 *    Choose Keyboard in the Zoom menu.
 *    Type the values in appropriate text boxes.
 *    Press ENTER  or  click  the dialog  box  background  anywhere  outside
      options.

 Now we  can  proceed with  defining  the  geometry itself.  To  define  the
 vertices which correspond to points labeled with letters A through R in the
 sketch:
 *    Enter Add Vertex  mode in  the Model menu.  The plus  sign cursor  (+)
      arises in the large window indicating the point locating mode.
 *    Use DIRECTION keys or a mouse to  move cursor from point to point  and
      press ENTER or click left mouse button where you want the vertex to be
      located. New vertices immediately appear in the window.
 *    Or, press TAB, type coordinates, and press ENTER for each new  vertex.
      Don't worry about  making mistakes-you can remove  erroneous vertices
      later.
 *    Press ESC to return to the Model menu.

 If you have created excess points, you can remove them now:
 *    Choose Delete  Vertex. The  X-shaped cursor  appears to  indicate  the
      picking mode.  Consequently pick  excess vertices,  which  immediately
      disappear.
 *    Press ESC to return to the Model menu.

 Now we can create edges connecting the vertices:
 *    Choose Add Edge.  A dialog box  appears asking the  arc angle for  new
      edges.
 *    Press ENTER (or click gray background of the dialog box) to agree with
      suggested zero value,  which means  creating the  straight lines.  The
      picking mode (X-shaped) cursor appears in the window.
 *    Pick points  A,  B,  F,  C, A  consequently  to  create  edges,  which
      constitute the rectangle  ABFC. The  edges immediately  appear on  the
      screen. In fact, we created six  edges, not four, because edge FC  was
      split into three (FE, ED and DC) while creating.
 *    Press ESC to break the chain of edges and start a new one.
 *    Repeat last two positions to create chains CGHD, EJGF, rectangle  KLNM
      and bounding rectangle OPRQ.
 *    Press ESC to return to the Model menu.

 You can remove erroneous edges, using the Delete Edge command.

 We are  done  with  the model's  geometry.  Now  we can  assign  labels  to
 geometrical objects to describe  material properties, sources and  boundary
 conditions.

 The problem contains four materials  having different properties: the  air,
 the steel and two pieces of permanent magnet, which differ in direction  of
 magnetization vector.  To be  clear,  we can  use  the labels  Air,  Steel,
 ALNICO Up and ALNICO Dn to label appropriate blocks.

 To assign these labels to blocks:
 *    Press ESC to close the Model menu and  return to the main menu of  the
      Model Editor.
 *    Choose Label Blocks in the Label menu. The picking mode cursor arises.
 *    Pick inside the CDHG rectangle. The block becomes highlighted and  the
      dialog box appears asking for the label value.
 *    Type ALNICO Dn and press ENTER. The X-shaped cursor appears again.
 *    Repeat the last two  positions to label the  CDJI rectangle as  ALNICO
      Up, the ABFC rectangle as Steel and the OPRQ as Air.
 *    Pick inside  the  KLNM  rectangle. Because  the  Steel  label  already
      exists, you can simply pick it in the list of existing labels  instead
      of typing and then press ENTER.  (You can also use the Select  command
      to assign some label to several blocks at once.)
 *    Press ESC to return to the label menu.

 Edge labels are used  to define specific boundary  conditions on inner  and
 outer boundaries  of the  region. In  our  case, we  need to  specify  zero
 Dirichlet boundary condition for the outer boundary (rectangle OPRQ).

 To assign labels to edges:
 *    Choose Select Edges from the Select  menu (we'll select several  edges
      to assign a label to them at once.) The picking mode cursor arises.
 *    Pick consequently  four edges,  which constitute  the rectangle  OPRQ.
      Those edges become  highlighted that indicates  the selection. If  you
      have selected excess edge, pick it once more to unselect it.
 *    Press ESC to cancel selection mode.
 *    Choose Label  Selected. A  dialog box  appears  asking for  the  label
      value.
 *    Type Zero and press Enter to assign the label to selected edges.

 Now we have finished with assigning labels to geometrical objects. You  can
 check their values in the Find Label mode.

 We can proceed with building a mesh of finite elements. To define the  mesh
 density, we need to define mesh  spacing parameters in several vertices  of
 the model. We  suppose that the  field is most  non-homogeneous around  the
 magnets, so the mesh there must  be maximum dense. Therefore, we'll  assign
 the spacing value of 4 mm to the vertices A-N and the value of 8  mm to the
 vertices O, P, R and Q to build the mesh of approximately 430 nodes.

 To define spacing values:
 *    Press ESC to return from the Label menu to the main menu.
 *    Choose Mesh to open the mesh building menu.
 *    Choose Select Blocks from the Select menu, which allows to assign  one
      spacing value to several vertices at once.
 *    Select block OPRQ (outside of magnets and steel keepers) and press ESC
      to return to the Mesh menu.
 *    Choose Set Spacing. A dialog box appears asking for the spacing value.
 *    Type 4  and  press ENTER.  This  value  is now  assigned  to  selected
      vertices.
 *    Choose Select  Vertex from  the Select  menu  to select  bounding  box
      vertex.
 *    Select vertices O, P, R and Q.
 *    Choose Set Spacing, type 8 and press ENTER. The model is now ready  to
      build the mesh.
 *    Choose Build Mesh. A dialog box appears asking, which blocks you  want
      to mesh.
 *    Choose In All Blocks to build the meshes for all blocks at once.

 Now the model is ready.

 To exit the Model Editor with saving the file:
 *    Press ESC  twice to  close the  Mesh menu  and quit.  The box  appears
      prompting you to save the model file.
 *    Choose Yes  to confirm  saving operation.  ption  dialog box.  Let  us
      continue with defining data for material properties

 You have returned to the Problem Descri and boundary conditions.

 To start editing data file:
 *    Select the Data text box.
 *    Choose the Open button. A dialog box appears warning you that the file
      MAGNET.DMS does not exist.
 *    Choose OK to create new data file.

 The Properties Description  File dialog  box appears.  It contains  labels,
 which you have just defined in the  model. The label names are marked  with
 asterisks to outline the fact, that the  data for these labels are not  yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label Air:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      double-click on the name's field.)

 A  dialog  box  appears,  prompting   to  enter  material  properties   and
 distributed source for block label Air.

 To assign values:
 *    Type 1 in any text box for components of magnetic permeability tensor.
 *    Choose OK.

 Now we'll learn how to describe  nonlinear magnetic properties by means  of
 editing the B-H curve. To start editing for block label Steel:
 *    Select its name in the list  box and choose Open button. The  property
      editing dialog box appears.
 *    Select the Nonlinear box. This causes starting the B-H Curve Editor.

 With the Curve  Editor, you  can simply enter  the values  from the  table,
 point by point, checking the curve in the  graph to the left of the  table.
 The point (0; 0) is always presented  in the table, which cannot be  edited
 nor deleted. Since the cursor is  already in the box  for new B value,  you
 can start  entering new  points. To  create  the first  point  (B = 0.73 T,
 H = 400 A/m, see the table at page 35):
 *    Type 0.73 and  press ENTER.  The cursor  will move  to the  box for  H
      value.
 *    Type 400 and press ENTER. The new point will be added to the table and
      immediately displayed in the graph. The cursor will return back to the
      box for B value.
 *    Repeat these actions  for other  points of  the table.  Points may  be
      entered in any order.

 In case  of mistyping,  the  erroneous point  would  in general  produce  a
 noticeable anomaly in the displayed curve. You can select this point in the
 graph or in the table and then delete it or correct its coordinates.

 When you are done  with entering points, and  the curve looks like  classic
 B-H curve, choose the  Close button to finish  curve editing and return  to
 property editing dialog. Since  we do not want  to change any more  values,
 choose OK button to finish editing data for label Steel.

 Describing data for  the permanent  magnet is  a bit  more complicated.  In
 addition to demagnetization curve, the direction of resistant magnetization
 should be specified  by means of  the vector of  coercive force. Now  we'll
 define the demagnetization curve for label ALNICO Up:
 *    Select its name in the list  box and choose Open button. The  property
      editing dialog box appears.
 *    Type 1 in any text box for components of magnetic permeability tensor.
      This is void action, the only purpose of which is to specify that  the
      data for the label is not empty, so that other text boxes will  become
      available.
 *    Select the text box for y-component of coercive force and type 147218.
 *    Choose the Nonlinear box. This starts the B-H Curve Editor.

 Note that  the predefined   point is  now at   (-147218, 0).  It is exactly
 the first point from the table.  Now we can continue with adding  all other
 points from the table.  When this job is  done, choose the Close  button to
 finish curve editing  and return to  property editing dialog.  Then  choose
 OK button to finish editing data for label ALNICO Up.

 To define data for label ALNICO Dn, we need not repeat all this actions. We
 can simply copy the  data from ALNICO  Up, and change the  direction of the
 coercive force. To do this:
 *    Select ALNICO Up in the list box.
 *    Choose Copy. The dialog box appears asking for destination label name.
 *    Change ALNICO Up to ALNICO Dn and choose OK. The data for these labels
      are now the same.
 *    Select ALNICO Dn in the list box and choose Open.
 *    Select the text box for y-component of coercive force and insert minus
      sign before digits to  change the direction of  coercive force to  the
      opposite one.
 *    Choose OK.

 Now we'll continue with edge labels'  data. We'll define the label Zero  as
 homogeneous Dirichlet boundary  condition (A = 0). To define  the data for
 edge label Zero:
 *    Select its name  and choose Open.  A dialog box  appears, allowing  to
      assign to edge label any of possible boundary conditions.
 *    Select  the  Dirichlet  Condition  box.  Zero  value  of   pre-defined
      potential will be suggested.
 *    Choose OK.

 All the data needed to solve the problem is now defined. To exit from  data
 editing mode:
 *    Choose Close button in the Properties  Description File dialog box.  A
      dialog box appears, prompting you to save changes to data file.
 *    Choose Yes to save changes. Now you return to the Problem  Description
      dialog box again.
 *    Choose OK.

 At last, we can solve the problem and  analyze the solution. To do this  in
 one step:
 *    Choose Analyze from the Results menu.  You will be suggested to  solve
      the problem first, as the results are absent.
 *    Choose OK.


           10.2 MAGN2: Solenoid Actuator

 A solenoid actuator  consists of a  coil enclosed in  a ferromagnetic  core
 with a plunger.  Calculate the magnetic  field and a  force applied to  the
 plunger.

 Problem Type:

 A nonlinear axisymmetric problem of magnetics.

 Given:
   Relative permeability of air and coil m = 1;
   Current density in the coil j = 1*10+6 A/m2;

 The B-H curve for the core and the plunger:

  H, A/m    460    640    720    890    1280   1900   3400   6000
  B, T      0.80   0.95   1.00   1.10   1.25   1.40   1.55   1.65


 Problem:

 Obtain the  magnetic field  in the  solenoid  and a  force applied  to  the
 plunger.

 Solution:

 This magnetic system is  almost closed, therefore  outward boundary of  the
 model can be put relatively close to the solenoid core. A thicker layer  of
 the outside air  is included  into the model  region at  the plunger  side,
 since the magnetic field in this area cannot be neglected.

 Mesh density is chosen  by default, but to  improve the mesh  distribution,
 three additional  vertices are  added to  the  model. We  put one  of  this
 vertices at the  coil inner  surface next to  the plunger  corner, and  two
 others next to the corner of the core at the both sides of the plunger.

 A contour for the force calculation encloses the plunger. It is put in  the
 middle of the air gap between the plunger and the core. While defining  the
 contour of integration,  use a strong  zoom-in mode to  avoid sticking  the
 contour to existing edges.

 The calculated force applied to the plunger F = 374.1 N.

 See the MAGN2.PBM problem in the EXAMPLES directory. Load the Postprocessor
 setup from the MAGN2.SST file to  get the predefined contour for the  force
 calculation.

 Comparison of Results

 Maximum flux density in Z-direction in the plunger:


                Bz (T)

    Reference   0.933

    QuickField  1.0183

 Reference

 D. F.  Ostergaard,  "Magnetics  for static  fields",  ANSYS  revision  4.3,
 Tutorials, 1987.


           10.3 MAGN3: Ferromagnetic C-Magnet

 A permanent C-magnet  in the  air. The  example demonstrates  how to  model
 curved permanent magnet using the equivalent surface currents.

 Problem Type:

 Plane problem of magnetics.

 Geometry of the magnet:
   Height: h = 7.5 cm;
   Width: w = 5 cm;
   Thickness: t = 1 cm.

 Given:
   Relative permeability of the air mu = 1;
   Relative permeability of the magnet mu = 1000;
   Coercive force of the magnet Hc = 10000 A/m.

 The polarization of the magnet is along its curvature.

 Solution:

 To avoid  the influence  of the  boundaries  while modeling  the  unbounded
 problem, we'll  enclose the  magnet  in a  rectangular  region of  air  and
 specify zero Dirichlet boundary condition on its sides.

 Magnetization of straight  parts of  the magnet  is specified  in terms  of
 coercive force vector. Effective surface currents simulate magnetization in
 the middle curved part of the magnet.

 See the MAGN3.PBM problem in the EXAMPLES directory.

           10.4 ELEC1: Microstrip Transmission Line

 A  shielded  microstrip  transmission  line  consists  of  a  substrate,  a
 conducted strip, and a shield.

 Problem Type:

 Plane-parallel problem of electrostatics.

 Geometry:

                        Shield
                       -------
                      /
                     /
    D +----------------------------------------- + C
      !                                          !
      !                                          !
      !       Air                 Conductor      !
      !                          -----------     !
      !                         /                !
      !                        /                 !
      !                       /                  !
    G !              E       / F                 ! H
      +---------------=========----------------- +
      !                                          !
      !         Substrate                        !
      !                   J                      !
    A +-------------------o--------------------- + B


 The transmission line is directed along z-axis, its cross section is  shown
 in the sketch. The rectangle ABCD is a  section of the shield, the line  EF
 represents a conductor strip.

 Given:
   Relative permittivity of air epsilon = 1;
   Relative permittivity of substrate epsilon = 10;
   Dimensions: Shield height and width = 10 cm, substrate height = 1 cm,
   conductor width = 1 cm.

 Problem:

 Determine the capacitance of a transmission line.

 Solution:

 There are several different approaches to calculate the capacitance of  the
 line:
 *    To apply some distinct potentials to  the shield and the strip and  to
      calculate the charge that arises on the strip;
 *    To apply zero  potential to the  shield and to  describe the strip  as
      having constant but  unknown potential  and carrying  the charge,  and
      then to measure the potential that arises on the strip.

 Both these approaches make use of the equation for capacitance:

      C = q / U.

 Other possible  approaches are  based on  calculation of  stored energy  of
 electric field. When the voltage is known:

      C = 2 * W / (U * U), and when the charge is known:

      C = q*q / (2 * W)

 Experiment with this example shows that energy-based approaches give little
 bit less precision than  approaches based on charge  and voltage only.  The
 first approach needs to get  the charge as a  value of integral along  some
 contour, and the  second one  uses only a  local value  of potential,  this
 approach is the simplest and in many cases the most reliable.

 The first and third approaches are  illustrated in the ELEC1_1.PBM  problem
 in the EXAMPLES directory, and the ELEC1_2.PBM explains the second and  the
 fourth approaches.

 Results (obtained using Professional QuickField):

 Theoretical result:      C = 178.1 pF/m.

 Approach 1:    C = 177.83 pF/m (99.8%).

 Approach 2:    C = 178.47 pF/m (100.2%).

 Approach 3:    C = 177.33 pF/m (99.6%).

 Approach 4:    C = 179.61 pF/m (100.8%).

 Step-by-step Description

 Let us learn,  how to  solve this problem  from scratch,  using the  second
 approach. We'll forget the  solution made in ELEC1_2.PBM,  and start a  new
 problem, STRIP.PBM.

 To create new problem:
 *    Choose New  in the  Files menu  (ALT+F, N);  the dialog  box  appears,
      asking for the filename for new problem.
 *    Change, if needed,  the drive and  directory in  the Directories  list
      box.
 *    Type strip in the Filename box.
 *    Choose OK.

 The extension .PBM will be added automatically.

 To select convenient length measurement units (centimeters):
 *    Choose Length Units in the Options menu. A dialog box appears.
 *    Select Centimeters.
 *    Choose OK.

 To assign the problem with appropriate features:
 *    Choose Problem in the  Edit menu (ALT+E,  P). The Problem  Description
      dialog box appears.
 *    Select Electrostatics in the Problem Type drop-down list box.
 *    Select XY Plane.

 We'll agree  with  suggested  model and  data  file  names  (STRIP.MOD  and
 STRIP.DES.) If the Library Data filename box is not empty, clear it,  since
 we'll define all the labels in the local data file (STRIP.DES.)

 We can  start  editing  the model  or  the  data directly  in  the  Problem
 Description dialog box. To edit the model:
 *    select the Geometry text box (click anywhere in the box with a  mouse,
      or press ALT+G, or press TAB until the selection reaches the box.)
 *    choose the Open button.

 The Model Editor starts.

 The first step  with the  new model  in Model  Editor is  to adjust  window
 dimensions fitting the  problem's region.  Since the  problem has  vertical
 axis of symmetry, it  is convenient to set  zero of x-axis  at the axis  of
 symmetry. So the region fits the square (-5 < x < 5, 0 < y < 10.) To assign
 these values to the window limits:
 *    Choose Keyboard in the Zoom menu.
 *    Type the values in appropriate text boxes.
 *    Press ENTER  or  click  the dialog  box  background  anywhere  outside
      options.

 Now we  can  proceed with  defining  the  geometry itself.  To  define  the
 vertices which correspond to points labeled with letters A through F in the
 sketch:
 *    Enter Add Vertex mode in  the Model  menu. The  plus sign  cursor ( +)
      arises in the large window indicating the point locating mode.
 *    Use DIRECTION keys or a mouse to  move cursor from point to point  and
      press ENTER or click left mouse button where you want the vertex to be
      located. New vertices immediately appear in the window.
 *         Or, press TAB,  type coordinates, and  press ENTER  for each  new
      vertex. Don't  worry about  making mistakes -you can  remove erroneous
      vertices later.
 *    Press ESC to return to the Model menu.

 If you have created excess points, you can remove them now:
 *    Choose Delete  Vertex. The  X-shaped cursor  appears to  indicate  the
      picking mode.  Consequently pick  excess vertices,  which  immediately
      disappear.
 *    Press ESC to return to the Model menu.

 Now we can create edges connecting the vertices:
 *    Choose Add Edge. A dialog  box appears asking  the arc angle  for new
      edges.
 *    Press ENTER (or click gray background of the dialog box) to agree with
      suggested zero value,  which means  creating the  straight lines.  The
      picking mode (X-shaped) cursor appears in the window.
 *    Pick points  A,  B,  C,  D, A  consequently  to  create  edges,  which
      constitute the rectangle  ABCD. The  edges immediately  appear on  the
      screen.
 *    Press ESC to break the chain of edges and start a new one.
 *    Pick point E and then F to create the corresponding edge.
 *    Press ESC twice to return to the Model menu.

 You can remove erroneous edges, using the Delete Edge command.

 We need  some  additional  constructing  to  create  edges  which  separate
 substrate from the air. The easy way to create them is to copy the edge  AB
 shifting it 1  cm upper. No doubt  that new edge will partly coincide with
 the already created edge EF-while creating, the coincidence is checked out,
 and only non-existent parts of new edge are really created. To make a copy:
 *    Choose Copy Edge. A  dialog box appears asking  for the components  of
      the shift vector.
 *    Press TAB  or DOWN  ARROW to  move to  the text  box corresponding  to
      y-component.
 *    Type 1.
 *    Press ENTER. The picking mode (X-shaped) cursor appears in the window.
 *    Pick the edge AB to make its copy. New vertices and edges arise on the
      screen.
 *    Press ESC to cancel copying mode and return to the Model menu.

 We are  done  with  the model's  geometry.  Now  we can  assign  labels  to
 geometrical objects to describe  material properties, sources and  boundary
 conditions.

 The model contains two blocks having different material properties: the air
 and the substrate. To be clear, we can use the word Air to label the  upper
 block and Substrate for the lower one. To assign these labels to blocks:
 *    Press ESC to close the Model menu and  return to the main menu of  the
      Model Editor.
 *    Choose Label Blocks in the Label menu. The picking mode cursor arises.
 *    Pick the  upper  block. It  becomes  highlighted and  the  dialog  box
      appears asking for the label value.
 *    Type Air and press ENTER. The X-shaped cursor appears again.
 *    Pick the lower block, type Substrate and press ENTER.
 *    Press ESC to return to the Label menu.

 Edge labels are used  to define specific boundary  conditions on inner  and
 outer boundaries of the  region. In our case,  we need to specify  boundary
 conditions for the shield (rectangle ABCD) and for the strip (line EF).  To
 assign labels to edges:
 *    Choose Select Edges from the Select  menu (we'll select several  edges
      to assign a label to them at once.) The picking mode cursor arises.
 *    Pick consequently  six edges,  which  constitute the  rectangle  ABCD.
      Those edges become  highlighted that indicates  the selection. If  you
      have selected excess edge, pick it once more to unselect it.
 *    Press ESC to cancel selection mode.
 *    Choose Label  Selected. A  dialog box  appears  asking for  the  label
      value.
 *    Type Shield and press ENTER to assign the label to selected edges.
 *    Choose Label  Edges. The  picking mode  cursor appears.  This mode  is
      convenient for assigning labels edge-by-edge.
 *    Pick the edge EF. A dialog box appears.
 *    Type Strip and press ENTER to assign the label.
 *    Press ESC to return to the Label menu.

 We also need to assign vertex label to any vertex contacting the strip,  to
 specify that the strip is charged.  No matter which vertex you choose,  the
 charge will be distributed through all  the conductor. To assign the  label
 to a vertex:
 *    Choose Label Vertices. The picking mode cursor arises.
 *    Pick any of vertices E or F. A dialog box appears asking for the label
      value.
 *    Type Charge and press ENTER to assign the label to vertex.
 *    Press ESC to return to the Label menu.

 Now we have finished with assigning labels to geometrical objects. You  can
 check their values in the Find Label mode.

 We can proceed with building a mesh of finite elements. To define the  mesh
 density, we need to  define spacing parameters in  several vertices of  the
 model. We suppose that the electric field is most non-homogeneous near  the
 ends of the strip, so  the mesh there must  be very fine. Therefore,  we'll
 assign the spacing value of 0.1  cm to the vertices E  and F, the value  of
 0.5 cm to the  vertices A,  B, H and  G an  d the value  of 1.5  cm to  the
 vertices D and C to  build the mesh of  approximately 400 nodes. To  define
 spacing values:
 *    Press ESC to return from the Label menu to the main menu.
 *    Choose Mesh to open the mesh building menu.
 *    Choose Select Vertices from  the Select menu,  which allows to  assign
      one spacing value to several vertices at once.
 *    Select vertices A,  B, C and  D and press  ESC to return  to the  Mesh
      menu.
 *    Choose Set Spacing. A dialog box appears asking for the spacing value.
 *    Type 0.5  and press  ENTER. This  value is  now assigned  to  selected
      vertices.
 *    Choose Unselect All from  the Select menu  to unselect all  previously
      selected objects.
 *    Select vertices E and F.
 *    Choose Set Spacing, type 0.1 and press ENTER.
 *    Choose Select Edges from the Select menu.
 *    Select edge CD and press  ESC to return to  the Mesh menu. Choose  Set
      Spacing, type 1.5 and press ENTER. The model is now ready to build the
      mesh.
 *    Choose Build All to build the meshes for both blocks at once.

 Now the model is ready. To exit the Model Editor with saving the file:
 *    Press ESC  twice to  close the  Mesh menu  and quit.  The box  appears
      prompting you to save the model file.
 *    Choose Yes to confirm saving operation.

 You have returned to  the Problem Description dialog  box. Let us  continue
 with defining  data for  material properties  and boundary  conditions.  To
 start editing data file:
 *    Select the Data text box.
 *    Choose the Open button. A dialog box appears warning you that the file
      STRIP3.DES does not exist.
 *    Choose OK to create new data file.

 The Properties Description  File dialog  box appears.  It contains  labels,
 which you have just defined in the  model. The label names are marked  with
 asterisks to outline the fact, that the  data for these labels are not  yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label Air:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      click a mouse once more on the name's field.)

 A  dialog  box  appears,  prompting   to  enter  material  properties   and
 distributed source for block label Air. To assign values:
 *    Type 1 in any text box for components of electric permittivity tensor.
 *    Choose OK.

 Repeat last  actions  for  the  label  Substrate.  The  value  of  relative
 permittivity of substrate is 10.

 Now we'll continue with edge labels' data. We'll define the label Shield as
 a homogeneous Dirichlet boundary condition (U = 0) and the label Strip as a
 conductor condition (U = const).

 To define the data for edge label Shield:
 *    Select its name  and choose Open.  A dialog box  appears, allowing  to
      assign to edge label any of possible boundary conditions.
 *    Select  the  Dirichlet  Condition  box.  Zero  value  of   pre-defined
      potential will be suggested.
 *    Choose OK.

 To define the data for edge label Strip:
 *    Select its name and choose Open.
 *    Select the Conductor box.
 *    Choose OK.

 We need to  define the  vertex label  Charge to  assign the  charge to  the
 strip. To determine the capacitance, the exact value of the charge does not
 matter. We'll choose a value of 1.

 To define the data for vertex label Charge:
 *    Select its name  and choose Open.  A dialog box  appears, allowing  to
      specify the charge, or to assign the Dirichlet boundary condition.
 *    Select the Electric Charge box.
 *    Type 1 in the text box for charge value.
 *    Choose OK.

 All the data needed to solve the problem is now defined. To exit from  data
 editing mode:
 *    Choose Close button in the Properties  Description File dialog box.  A
      dialog box appears, prompting you to save changes to data file.
 *    Choose Yes to save changes. Now you return to the Problem  Description
      dialog box again.
 *    Choose OK.

 At last, we can solve the problem and  analyze the solution. To do this  in
 one step:
 *    Choose Analyze from the Results menu.  You will be suggested to  solve
      the problem first, as the results are absent.
 *    Choose OK to start the solver.

 After finishing,  the Postprocessor  starts automatically.  There are  many
 possibilities to analyze the field in the Postprocessor. We will show  only
 those steps needed to determine the capacitance:
 *    Choose Values from the menu. Cross-shaped cursor appears allowing  you
      to pick points to determine the local field data.
 *    Move the cursor to the point  (0.0, 1.0) (exactly; the convenient  way
      is to use  the DIRECTION keys,  or to press  TAB and type  coordinates
      from keyboard.)
 *    Press ENTER.

 The box appears,  showing you the  local field data.  The potential of  the
 strip is 5.251e+9 Volts. The capacitance is

      C = q / U = 1 / 5.251e+9 = 190.4 pF/m

 Note that, with plane-parallel problems, we specify the sources as specific
 values per unit depth (e.g.,  the charge of the  strip), and the result  is
 specific capacitance per unit depth, measured in F/m.

 Since the mesh  is rather  rough, the  solution gives  less precision  than
 provided in ELEC1_2.PBM.

 If you now look through the model provided with ELEC1_2.PBM, ELEC1.MOD, you
 will find some hints for obtaining a more fine mesh near the vertices E and
 F-the points of singularity.

 Since the Model Editor cannot squeeze the mesh spacing inside the edge, but
 only from  one end  to another,  extra vertex  have been  added in  central
 points of edges AB.  This vertex is aimed  to specify manual spacing  value
 for it, which helps to increase the total number of nodes in the mesh. Now,
 the capacitance is

      C = q / U = 1 / 5.444e+9 = 183.7 pF/m


           10.5 ELEC2: Two Conductor Transmission Line

 Problem Type:

 A plane problem of electrostatics.

 Geometry:

 The problem's region is bounded by ground from the bottom side and extended
 to infinity on other three sides.

 Given:
   Relative permittivity of air epsilon = 1;
   Relative permittivity of dielectric epsilon = 2.

 Problem:
    Determine self and mutual capacitance of conductors.

 Solution:

 To avoid the influence  of outer boundaries, we'll  define the region as  a
 rectangle  large  enough  to  neglect   side  effects.  To  calculate   the
 capacitance matrix we set the voltage U = 1 V on one conductor and U = 0 on
 the other conductor.

      Self capacitance: C11 = C22 = q1 / U1;

      Mutual capacitance: C12 = C21 = q2 / U1;

 where charge  Q1  and  Q2 are  evaluated  on  rectangular  contours  around
 conductor 1 and 2 away from their edges. We chose the contours for the  C11
 and C12 calculation to be rectangles  -6 < x < 0, 0 < y < 4 and  0 < x < 6,
 0 < y < 4 respectively.

 Comparison of Results


                 C11 (F/m)      C12 (F/m)

  Reference      9.23e-11        8.50e-12

  Professional   9.43e-11       -8.57e-12
  QuickField

  Students'      9.72e-11       -8.625e-12
  QuickField


 Reference

 A. Khebir, A. B. Kouki, and R. Mittra, "An Absorbing Boundary Condition for
 Quasi-TEM Analysis of Microwave Transmission  Lines via the Finite  Element
 Method", Journal of Electromagnetic Waves and Applications, 1990.

 See the ELEC2.PBM problem in the EXAMPLES directory.

           10.6 HEAT1: Slot of an Electric Machine

 Temperature field in the  stator tooth zone  of power synchronous  electric
 machine.

 Problem Type:

 The plane-parallel problem of heat transfer with convection.

 Geometry:

 Domain is a segment of stator transverse section. Two armature bars  laying
 in the slot release  ohmic loss. Cooling is  provided by convection to  the
 axial cooling duct and both surfaces of the core.
   Slot height: 0.074 m;
   Slot width: 0.02 m;
   Bar height: 0.029 m;
   Bar width: 0.015 m;
   Wedge height: 0.005 m;
   Stator inner diameter: 0.9 m;
   Stator outer diameter: 1.112 m;
   Cooling duct diameter: 0.015 m.

 Given:
   Specific copper loss: 360000 W/m3;
   Heat conductivity of steel: 25 J/K*m;
   Heat conductivity of copper: 380 J/K*m;
   Heat conductivity of insulation: 0.15 J/K*m;
   Heat conductivity of wedge: 0.25 J/K*m;

 Inner stator surface:
   Convection coefficient: 250 W/K*m2;
   Temperature of contacting air: 40 *C.

 Outer stator surface:
   Convection coefficient: 70 W/K*m2;
   Temperature of contacting air: 20 *C.

 Cooling duct:
   Convection coefficient: 150 W/K*m2;
   Temperature of contacting air: 40 *C.

 See the HEAT1.PBM problem in the EXAMPLES directory.


           10.7 HEAT2: Cylinder with Temperature Dependent Conductivity

 A very  long cylinder  (infinite length)  is maintained  at temperature  Ti
 along its internal surface and To  along its external surface. The  thermal
 conductivity of the cylinder is known to vary with temperature according to
 the linear function lambda(T) = C0 + C1*T.

 Problem Type:

 An axisymmetric problem of nonlinear heat transfer.

 Geometry:

                To           Ti
               ----       -----
                   \           \
                    \           \
      +--------------------------\--------- +
      !////////////////////////// \ /////// !
      +------------------------------------ +
      !                                     !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Ri = 5 mm, Ro = 10 mm;
   Ti = 100 *C, To = 0 *C;
   C0 = 50 W/K*m, C1 = 0.5 W/K*m.

 Problem:

 Determine the temperature distribution in the cylinder.

 Solution:

 The axial length of the model is arbitrarily chosen to be 5 mm.

 Comparison of Results

  Radius         Quickfield     Theory

  0.6            79.2           79.2

  0.7            59.5           59.6

  0.8            40.2           40.2

  0.9            20.66          20.8

 See the HEAT2.PBM problem in the EXAMPLES directory.

           10.8 STRES1: Perforated Plate

 A thin rectangular sheet with a central hole subject to tensile loading.

 Problem Type:

 Plane problem of stress analysis (plane stress formulation).

 Geometry of the plate:
   Length l = 240 mm;
   Width w = 180 mm;
   Thickness t = 5 mm;
   Radius of central opening r = 30 mm.

 Given:
   Young's modulus E = 207000 N/mm2;
   Poisson's ratio n = 0.3.

 The uniform tensile loading (40 N/mm2) is applied to the bottom edge of the
 structure.

 Problem:

 Determine the concentration factor due to presence of the central opening.

 Solution:

 Due to  mirror symmetry  one quarter  of the  structure is  presented,  and
 internal boundaries are restrained in X and Y directions respectively.

 The concentration factor may be obtained from the loading stress (40 N/mm2)
 and the maximum computed stress (146 N/mm2) as

      k = 140.8 / 40 = 3.52.

 See the STRES1.PBM problem in the EXAMPLES directory.

           10.9 COUPL1: Stress Distribution in a Long Solenoid

 A very long, thick solenoid has an uniform distribution of  circumferential
 current. The magnetic flux density and stress distribution in the  solenoid
 has to be calculated.

 Problem Type:

 An axisymmetric problem of magneto-structural coupling.

 Geometry:

      +------------------------------------ +
      !///////// Conducting cylinder ////// !
      +------------------------------------ +
      !              Air                    !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Dimensions Ri = 1 cm, Ro = 2 cm;
   Relative permeability of air and coil mu = 1;
   Current density j = 1*10+5 A/m2;
   Young's modulus E = 1.075*10+11 N/m2;
   Poisson's ratio nu = 0.33.

 Problem:

 Calculate the magnetic flux density and stress distribution.

 Solution:

 Since none of physical quantities varies along z-axis, a thin slice of  the
 solenoid could be  modeled. The axial  length of the  model is  arbitrarily
 chosen to be 0.2 cm. Radial component of  the flux density is set equal  to
 zero at the  outward surface  of the  solenoid. Axial  displacement is  set
 equal to zero at the side edges of the model to reflect the infinite length
 of the solenoid.

 Comparison of Results

 Magnetic flux density and circumferential stress at r = 1.3 cm:


                   Bz (T)         Stheta (N/m2)

    Reference      8.796*10-3     97.407

    QuickField     8.798*10-3     96.301

 Reference

 F. A.  Moon, "Magneto-Solid  Mechanics", John  Wiley  & Sons,  N.Y.,  1984,
 Chapter 4.

 See the COUPL1MS.PBM  and COUPL1SA.PBM problems  in the EXAMPLES  directory
 for magnetic and structural parts of this problem respectively.

 Step-by-step Description

 Let us  learn how  to solve  this problem  from scratch.  We'll ignore  the
 solution made in COUPL1MS.PBM  and COUPL1SA.PBM, and  start a new  problem,
 SOLMAG.PBM. We use a suffix "MAG" to underline that this will represent the
 magnetic part of our problem.

 To create new problem:
 *    Choose New  in the  Files menu  (ALT+F, N);  the dialog  box  appears,
      asking for the filename for the new problem.
 *    Change, if needed,  the drive and  directory in  the Directories  list
      box.
 *    Type solmag in the Filename box.
 *    Choose OK.

 The extension .PBM will be added automatically.

 To select convenient length measurement units (centimeters):
 *    Choose Length Units in the Options menu. A dialog box appears.
 *    Select Centimeters.
 *    Choose OK.

 To assign the problem with appropriate features:
 *    Choose Problem in the  Edit menu (ALT+E,  P). The Problem  Description
      dialog box appears.
 *    Select Magnetostatics in the Problem Type drop-down list box.
 *    Select RZ Plane, since our problem is axisymmetric.

 We'll agree with suggested  data file name  (SOLMAG.DMS), but change  model
 file name to SOL.MOD to stress  out the fact, that  the model file will  be
 shared between magnetic and stress analysis  problems. If the Library  Data
 filename box is not empty, clear it,  since we'll define all the labels  in
 the local data file (SOLMAG.DMS.)

 We can  start editing  the model  or  the data  directly from  the  Problem
 Description dialog box. To edit the model:
 *    select the Geometry text box (click anywhere in the box with a  mouse,
      or press ALT+G, or press TAB until the selection reaches the box.)
 *    choose the Open button.

 The Model Editor starts.

 The first step  with the  new model  in Model  Editor is  to adjust  window
 dimensions fitting  the  problem's  region.  Since  none  of  the  physical
 quantities varies along z-axis, we'll model  a thin slice of the  solenoid.
 We'll choose the axial length of this slice to be 0.2 cm, from  -0.1 to 0.1
 along z-axis. The whole model fits in the square ( -1 < z < 1, -0 < r < 2.)
 To assign these values to the window limits:
 *    Choose Keyboard in the Zoom menu.
 *    Type the values (-1, 1, 0, 2) in appropriate text boxes.
 *    Press ENTER  or  click  the dialog  box  background  anywhere  outside
      options.

 Now we can proceed with defining the geometry itself. As the first step  we
 create vertices, which  represent specific  points of  the model  geometry.
 We'll need six vertices with coordinates:

  z      -0.1   -0.1   -0.1   0.1    0.1    0.1
  r      0      1      2      0      1      2

 To define the vertices:
 *    Enter Add Vertex  mode in  the Model menu.  The plus  sign cursor  (+)
      arises in the large window indicating the point locating mode.
 *    Use DIRECTION keys to move cursor from point to point and press  ENTER
      where you  want the  vertex to  be located.  New vertices  immediately
      appear in the window.
 *    Or, press TAB, type coordinates, and press ENTER for each new  vertex.
      Don't worry about  making mistakes-you can remove  erroneous vertices
      later.
 *    Press ESC to return to the Model menu.

 If you have created excess points, you can remove them now:
 *    Choose Delete  Vertex. The  X-shaped cursor  appears to  indicate  the
      picking mode.  Consequently pick  excess vertices,  which  immediately
      disappear.
 *    Press ESC to return to the Model menu.

 Now we can create edges connecting the vertices:
 *    Choose Add Edge.  A dialog box  appears asking the  arc angle for  new
      edges.
 *    Press ENTER (or click gray background of the dialog box) to agree with
      suggested zero value,  which means  creating the  straight lines.  The
      picking mode (X-shaped) cursor appears in the window.
 *    Pick vertices consequently to create two rectangles one on the top  of
      another. Press ESC to break the chain of edges and start a new one.
 *    Press ESC to return to the Model menu.

 You can remove erroneous edges, using the Delete Edge command.

 We are  done  with  the model's  geometry.  Now  we can  assign  labels  to
 geometrical objects to describe  material properties, sources and  boundary
 conditions.

 The bottom  rectangle represents  the air  inside  the solenoid,  so  we'll
 assign the label air to it. The  top rectangle represents the slice of  the
 solenoid coil itself,  so we'll label  it coil. To  assign these labels  to
 blocks:
 *    Press ESC to close the Model menu and  return to the main menu of  the
      Model Editor.
 *    Choose Label Blocks in the Label menu. The picking mode cursor arises.
 *    Pick inside the  bottom rectangle. The  block becomes highlighted  and
      the dialog box appears asking for the label value.
 *    Type air and press ENTER. The X-shaped cursor appears again.
 *    Pick inside the top rectangle. The  block becomes highlighted and  the
      dialog box appears asking for the label value.
 *    Type coil and press ENTER.
 *    Press ESC to return to the Label menu.

 Edge labels  are  used to  define  the boundary  conditions.  For  magnetic
 problem we need to specify only a zero flux condition at outward surface of
 the solenoid, but to make the  model suitable for the stress analysis  too,
 we'll also assign labels to the side edges of the coil. To assign labels to
 edges:
 *    Choose Label Edges. The picking mode cursor arises.
 *    Pick the top  edge. The edge  becomes highlighted and  the dialog  box
      appears asking for the label value.
 *    Type outer and press ENTER. The X-shaped cursor appears again.
 *    Pick one of  the side edges  of the top  rectangle and  type no  axial
      displ.
 *    Pick another side edge of the coil and type no axial displ, or  double
      click the corresponding line in the Existing Labels list box.
 *    Press ESC to return to the Label menu.

 Now we have finished with assigning labels to geometrical objects. You  can
 check their values in the Find Label mode.

 We can proceed with building a  mesh of finite elements. For simplicity  we
 will use  a  homogeneous mesh  with  element size  approximately  equal  to
 0.055 cm. To build the mesh:
 *    Press ESC to return from the Label menu to the main menu.
 *    Choose Mesh to open the mesh building menu.
 *    Choose Set Spacing. The X-shaped pick-mode cursor appears on a screen.
 *    Pick any vertex, a dialog box appears asking for the spacing value.
 *    Type 0.055 and press ENTER. This  value is now assigned to the  vertex
      and will control the mesh density in the whole region.
 *    Choose Build Mesh. A dialog box appears asking, which blocks you  want
      to mesh.
 *    Choose In All Blocks to build the meshes for all blocks at once.

 Now the model is ready. To exit the Model Editor with saving the file:
 *    Press ESC  twice to  close the  Mesh menu  and quit.  The box  appears
      prompting you to save the model file.
 *    Choose Yes to confirm the saving operation.

 You have returned to  the Problem Description dialog  box. Let us  continue
 with defining  data for  material properties  and boundary  conditions.  To
 start editing the data file:
 *    Select the Data text box.
 *    Choose the Open button. A dialog box appears warning you that the file
      SOLMAG.DMS does not exist.
 *    Choose OK to create new data file.

 The Properties Description  File dialog  box appears.  It contains  labels,
 which you have just defined in the  model. The label names are marked  with
 asterisks to outline the fact, that the  data for these labels are not  yet
 defined. Now we need to select the labels one-by-one and to define the data
 for them.

 To define the data for block label air:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      double-click on the name's field.)

 A  dialog  box  appears,  prompting   to  enter  material  properties   and
 distributed source for block label air. To assign values:
 *    Type 1  in  any one  of  two text  boxes  for components  of  magnetic
      permeability tensor.
 *    Choose OK.

 To define the data for block label coil:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      double-click on the name's field.)

 A  dialog  box  appears,  prompting   to  enter  material  properties   and
 distributed source for block label coil. To assign values:
 *    Type 1  in  any one  of  two text  boxes  for components  of  magnetic
      permeability tensor.
 *    Type 1e6 in the Current Density text box.
 *    Choose OK.

 Now we'll  continue with  edge  labels' data.  We'll  specify a  zero  flux
 condition (Bn = 0) for the  outer label. To  define the data  for the  edge
 label outer:
 *    Select its name  and choose Open.  A dialog box  appears, allowing  to
      assign to edge label any of possible boundary conditions.
 *    Select the Zero Flux Condition box.
 *    Choose OK.

 To define the natural boundary condition for the edge label no axial displ:
 *    Select its name and choose Open.
 *    Choose OK, the dialog box by  default represents the natural  boundary
      condition.

 All the data needed to solve the magnetic problem are now defined. To  exit
 from data editing mode:
 *    Choose Close button in the Properties  Description File dialog box.  A
      dialog box appears, prompting you to save changes to data file.
 *    Choose Yes to save changes. Now you return to the Problem  Description
      dialog box again.
 *    Choose OK.

 At last, we can  solve the problem  and analyze the  magnetic field. To  do
 this in one step:
 *    Choose Analyze from the Results menu.  You will be suggested to  solve
      the problem first, as the results are absent.
 *    Choose OK.
 *    Choose Values to get the field values in a particular point. The  plus
      sign cursor  (+) arises  in  the large  window  indicating the  point
      locating mode.
 *    Use DIRECTION keys to move cursor from point to point and press  ENTER
      where you want to see the field values.
 *    Or, press TAB, type coordinates, and press ENTER for each new point.
 *    Press ESC to exit  the Values mode  and another ESC  to return to  the
      main QuickField menu.

 Once we  got the  results for  the magnetic  part of  our problem,  we  can
 proceed with the stress  analysis. To perform the  stress analysis we  will
 need a new problem description.

 To create new problem description:
 *    Choose New  in the  Files menu  (ALT+F, N);  the dialog  box  appears,
      asking for the filename for the new problem.
 *    Type solstr in the Filename box.
 *    Choose OK.

 The extension .PBM will be added automatically.

 To assign the problem with the appropriate features:
 *    Choose Problem in  the Edit menu  (ALT+E, P). The  Problem Description
      dialog box appears.
 *    Select Stress Analysis in the Problem Type drop-down list box.

 We'll agree  with suggested  data file  name (SOLSTR.DMS),  but change  the
 model file name to the existing SOL.MOD.

 To specify the problem coupling:
 *    Choose Imported Data button in the Problem Description dialog box. The
      Data Imported from Other Problems dialog box appears.
 *    Choose Magnetic forces option in Data Type drop-down list box.
 *    Choose Browse button, and double-click a SOLMAG.PBM file.
 *    Choose Add button, a new line will appear in Data Sources list box.
 *    Choose Close button to return to the Problem Description dialog box.

 Next our step is to define material properties and boundary conditions  for
 the structural problem. To start editing the data file:
 *    Select the Data text box.
 *    Choose the Open button. A dialog box appears warning you that the file
      SOLSTR.DMS does not exist.
 *    Choose OK to create new data file.

 The Properties Description  File dialog  box appears.  It contains  labels,
 which you assigned to the model. The label names are marked with  asterisks
 to outline the fact, that  the data for these  labels are not yet  defined.

 Now we need  to select the  labels one-by-one and  to define  the data  for
 them.

 To define data for the block label air:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      double-click on the name's field.)

 A  dialog  box  appears,  prompting   to  enter  material  properties   and
 distributed source for block  label air. The block  labelled air has to  be
 excluded from  stress calculation.  Since the  text boxes  for the  Young's
 moduli already contain word  None, the all we  need to do  is to choose  OK
 button.

 To define data for the block label coil:
 *    Select its name in the list box (click it with a mouse, or press ALT+B
      and use DOWN key to highlight the name's field.)
 *    Choose Open button (or press ENTER  as Open is the default button,  or
      double-click on the name's field.)

 A dialog  box appears,  prompting to  enter material  properties for  block
 label coil. To assign values:
 *    Type 1.075e11 in any one of three text boxes for Young's moduli.
 *    Type 0.33 in any one of three text boxes for Poisson's ratios.
 *    Choose OK.

 Now we'll continue with edge labels' data. To define the data for the  edge
 label no axial displ:
 *    Select its name  and choose Open.  A dialog box  appears, allowing  to
      assign to edge label any of possible boundary conditions.
 *    Check the  Z  check  box  inside  Fixed  Displacement  rectangle.  The
      displacement is zero by default.
 *    Choose OK.

 To define the natural boundary condition for the edge label outer:
 *    Select its name and choose Open.
 *    Choose OK, the dialog box by  default represents the natural  boundary
      condition.

 All the data  needed to solve  the structural problem  are now defined.  To
 exit from data editing mode:
 *    Choose Close button in the Properties  Description File dialog box.  A
      dialog box appears, prompting you to save changes to data file.
 *    Choose Yes to save changes. Now you return to the Problem  Description
      dialog box again.
 *    Choose OK.

 Now we can solve the problem and analyze  stresses in the coil. To do  this
 in one step:
 *    Choose Analyze from the Results menu.  You will be suggested to  solve
      the problem first, as the results are absent.
 *    Choose OK.
 *    Choose Values to get the field values in a particular point. The  plus
      sign cursor  (+) arises  in  the large  window  indicating the  point
      locating mode.
 *    Use DIRECTION keys to move cursor from point to point and press  ENTER
      where you want to see the stress value.
 *    Or, press TAB, type coordinates, and press ENTER for each new point.
 *    Press ESC to exit  the Values mode  and another ESC  to return to  the
      main QuickField menu.


           10.10 COUPL2: Hollow Thick-Walled Cylinder Subject to Temperature
                 and Pressure

 A very long, thick-walled cylinder is subjected to an internal pressure and
 a steady  state temperature  distribution with  Ti and  To temperatures  at
 inner and outer surfaces respectively. Calculate the stress distribution in
 the cylinder.

 Problem Type:

 An axisymmetric problem of thermal-structural coupling.

 Geometry:

                To           Ti
               ----       -----
                   \           \
                    \           \
      +--------------------------\--------- +
      !////////////////////////// \ /////// !
      +------------------------------------ +
      !                                     !
      +-.--.--.--.--.--.--.--.--.--.--.--.- +
      !                                     !
      +------------------------------------ +
      !//////////////////////////////////// !
      +------------------------------------ +


 Given:
   Dimensions Ri =  1 cm, Ro = 2 cm;
   Inner surface temperature Ti = 100 C;
   Outer surface temperature To = 0 C;
   Coefficient of thermal expansion alpha = 1*10-6 1/K;
   Internal pressure P = 1*10+6 N/m2;
   Young's modulus E = 3*10+11 N/m2;
   Poisson's ratio nu = 0.3.

 Problem:

 Calculate the stress distribution.

 Solution:

 Since none of physical quantities varies along z-axis, a thin slice of  the
 cylinder can  be modeled.  The axial  length of  the model  is  arbitrarily
 chosen to be 0.2  cm. Axial displacement is  set equal to zero  at the side
 edges of the model to reflect the infinite length of the cylinder.

 Comparison of Results

 Radial and circumferential stress at r = 1.2875 cm:


                   Sr (N/m2)     Stheta (N/m2)

    Theory         -3.9834*10+6   -5.9247*10+6

    Students'      -3.827*10+6    -5.882*10+6
    QuickField

    Professional   -3.959*10+6    -5.924*10+6
    QuickField

 Reference

 S. P. Timoshenko and Goodier, "Theory of Elasticity", McGraw-Hill Book Co.,
 N.Y., 1961, pp. 448-449.

 See the COUPL2HT.PBM  and COUPL2SA.PBM problems  in the EXAMPLES  directory
 for the corresponding heat transfer and structural parts of this problem.


           10.11 COUPL3: Temperature Distribution in an Electric Wire

 Calculate the temperature distribution in a long current carrying wire.

 Problem Type:

 An axisymmetric problem of electro-thermal coupling.

 Geometry:

      +------------------------------------ +
      +//////////////////////////////////// +
      +////////------> Current //////////// +
      +//////////////////////////////////// +
      +------------------------------------ +


 Given:
   Wire diameter d = 10 mm;
   Resistance R = 3*10-4 Ohm/m;
   Electric current I = 1000 A;
   Thermal conductivity lambda = 20 W/K*m;
   Convection coefficient alpha = 800 W/K*m2;
   Ambient temperature To = 20 *C.

 Problem:

 Calculate the temperature distribution in the wire.

 Solution:

 We arbitrary chose a 10  mm piece of wire  to be represented by  the model.
 For data input  we need the  wire radius r  = 5 mm, and the  resistivity of
 material:

      rho = (PI * d*d * R) / 4 = 2.356e-8 Ohm*m,

 and voltage drop for our 10 mm piece of the wire:

      DU = I*R*l = 3e-3 (V).

 For the  current flow  problem we  specify two  different voltages  at  two
 sections of the wire, and a zero current condition at its surface. For heat
 transfer problem we  specify zero flux  conditions at the  sections of  the
 wire and a convection boundary condition at its surface.

 Comparison of Results

 Center line temperature:


                 T (centigrade)

    Theory       33.13

    QuickField   32.83

 Reference

 W. Rohsenow and H. Y. Choi, "Heat, Mass, and Momentum Transfer",  Prentice-
 Hall, N.J., 1963.

 See the COUPL3CF.PBM  and COUPL3HT.PBM problems  in the EXAMPLES  directory
 for the corresponding current flow and heat transfer parts of this problem.
