Copyright © 1998 by MSTR Technology
Introduction
This document explains how to create 2D (and simple 3D) geometric models for the MSTR Technology FEWaves program. The purpose of creating a geometric model is not only to draw an object on the screen as with a drafting-oriented CAD package, but also to define the geometric boundaries of the problem efficiently and uniquely so that other modules in the MSTR Technology analysis system can use the geometric information to attach properties, drive the finite element mesh generation process, and display results. Therefore, creating a geometric model is the foundation of the entire analysis process. Prior thought into the geometric model is necessary to properly define the "real" model to solve.
Any geometric model contains two types of data: coordinate mapping functions and topology, Coordinate mapping functions describe where the geometric objects are located in space. The simplest example is a geometric vertex, which is simple a point in space with three real values giving its (X,Y,Z) coordinates. A more complex example would be a geometric edge (or, in our nomenclature, a "g_edge") for which there are three mapping functions: FX(u), FY(u), and FZ(u). As the dimensionless parameter, u, varies from 0 (the beginning of the g_edge) to 1 (the end of the g_edge), these three functions trace a trajectory in space. Depending on the function, the g_edge can be a straight line, cubic spline, rational cubic, conic arc, or any other curve.
If displaying the objects on a computer screen or paper was the only consideration, the coordinate mapping functions would be sufficient. However, for analysis we need to know more about the geometric model in order to answer questions like these: For a given point in space, (X,Y,Z), which geometric object is the point inside? Or, what geometric entities are on the outer bounder of the problem? To answer these and similar questions, we need to know how the geometric objects are connected to define the regions of interest to our analysis problem. These connections are known as topology and we use the connections to build the geometric model from objects of lower dimension to objects of higher dimension. For example, two vertices (0 dimension define the end points of a g_edge (1 dimension). Several g_edges together form the boundary of a geometric face (or "g_face" = 2 dimensions). Finally, several g_faces together form the boundary of a geometric volume (3 dimensions). Because the focus of this document is on building 2D geometric models, we will concentrate on vertices, g_edges, and g_faces.
Before we begin a detail discussion of how to build models, we should note that the best results will be obtained when geometric models are built using the ability of the MSTR Technology "s_parser" to evaluate input lines in terms of user-defined constants and functions, rather than hard-coding the numerical data directly, enabling you to change the dimensions of the model easily. This is discussed in a companion document, "Symbolic Parser for CAE Applications." If you have not yet read this document, please take a few minutes now to scan it before continuing.
The Geometric Definition File
All geometric model building in the MSTR Technology analysis system is controlled by the geometric definition file. This is an ASCII (text) file that you can create or modify with any text editor on your computer. The default file name extension is ".geo". For our present purposes, this file contain only two types of information. First, it it an ideal place to define the constant and functions that will be used when building the model. Second, it contains one line (the last line in the file) that directs the MSTR Technology analysis system to build a geometric model in "2D style" from two additional input files. (Other commands will be used for building full 3D models.) These two files, respectively, define the vertex locations and the g_edges. In "2D style," creation of g_faces is implicit in the creation of g_edges, as will be discussed below.
As an example, consider a simple 2D model of a square box. You create a geometric definition file called "box.geo" as follows:
x0 = 0 # X value of center of box
y0 = 0 # Y value of center of box
side = 1 # length of a size of the box
half = side/2 # half of the length
@2d_style "box.pts" "box.edg"
The first four lines define the parameters that will be used to build the model. The fifth line tells the MSTR Technology geometry builder module to use the "2D_Style" to create the model from two files, the vertex ("points") definition file and the g_edges definition file, respectively. Note that the file names defined on the last line are enclosed in quotes. Although by convention they have the same root name as the geometry definition file and the respective extension, ".pts" and ".edg", the actual names can be any valid file names.
The Vertex ("Points") File
The vertex file contains the ID numbers and location of vertices. Although the vertex locations are normally given in order, it is permissible to list the vertices out of order. A vertex definition line consists of a positive ID number followed by zero, one. two, or three coordinates. Coordinates not given on the line are assumed to be zero. Note that although the focus of this document is 2D, all vertices have 3D location. Normally, in a 2D model all Z coordinates will be omitted and will therefore default to zero.
In addition to vertex definition lines, the vertex file can contain constant/function definitions. One reason to place some definitions in the vertex file rather than the geometry file would be to define those parameters that only affect the vertex locations. Once a parameter is defined, its value is available for all subsequent inputs, even those in another file.
Here is an example of a four-line vertex file for our box model:
1, x0-half, y0-half
2, x0+half, y0-half
3, x0+half, y0+half
4, x0-half, y0+half
There are special command lines that can be inserted into the vertex file to aid in defining vertex locations. These consist of a "@" character followed (no space) by a command keyword (upper or lower case) and, possibly, some parameters.
@OFFSET
The first type of command line is @offset, followed by zero, one, two or three Cartesian offset coordinates. Offsets not included on the line are assumed to be zero. These offsets are added to subsequent vertex locations until canceled by another @offset command. Note that offsets are always in Cartesian coordinates (X,Y,Z). The our box example, we could change the file as follows:
@offset x0,y0
1, -half, -half
2, +half, -half
3, +half, +half
4, -half, +half
@CARTESIAN
@CYLINDRICAL
@SPHERICAL
The default for entering coordinates is to use the Cartesian (X,Y,Z) system. You can switch to cylindrical coordinates
with the command line, @cylindrical. You can
also switch to spherical coordinates 
with
the command line, @spherical. (This is mostly useful for 3D points.) You can switch back to Cartesian coordinates
with the @cartesian command. Here is the above example in cylindrical coordinates:diag2 = sqrt(2)*half
@offset x0,y0
@cylindrical
#degrees
1, diag2, -135
2, diag2, -45
3, diag2, +45
3, diag2, +135
Note that angles for cylindrical and spherical coordinate systems are in radians unless overridden by one of the commands listed below.
Angle Units