MATLAB redAnTS TUTORIAL 1 - page 2

Step 2: Geometry

redAnTS generously offers you two different mesh generators:

1. Mapping Mesh Tool
2. CSG Mesh Tool (CSG stands for Constructive Solid Geometry)

Click on the drop-down menu under Mesh. You'll see the following options:

Note that there is also Help available for this menu. Click on Help and scan through it to get an idea of the online information that is available. Dismiss the help window.

In this tutorial, we'll create a new mesh using the Mapping Mesh Tool. Under Mesh, click on Create Mapping . This brings up the MappingMeshTool GUI.

Define Drawing Palette

We'll first create the domain i.e. the rectangle, and then mesh it. Let's define the palette on which we'll draw the domain and overlay grid lines on the palette. This is done using the Grid options on the top, right corner of the GUI. The grid lines are helpful in determining coordinates of points. From the problem statement, the range of the drawing palette is chosen as -0.40<x<1 and -0.2<y<1.2. This will fit the domain within the palette with a little bit of space to spare around the edges. We'll choose the spacing of the grid lines to be 0.1 in x and y directions. Thus, enter Xmin=-0.4, X spacing=0.1, Xmax=1, Ymin=-0.2, Y spacing=0.1, and Ymax=1.2. (As you enter these values, you can jump to the next entry using the Tab key.) Click on Make Grid.

Draw Rectangular Domain

In redAnTS, each domain is composed of one or more subdomains. redAnTSrequires that each subdomain be a four-sided region defined by eight vertices (the corners and midpoints of each side). The vertices must be defined in a counterclockwise direction around the subdomain, starting with any corner. Since our geometry is a nice rectangular shape, we need only one subdomain. The eight vertices for the subdomain are defined starting from the lower, left corner as shown below.

The mid-point vertices v2,v4,v6, and v8 are located half-way along the sides. This will create a mesh of uniform element size. Note that locating the mid-point vertices nearer to one corner would create a mesh of varying element size. You could use this feature to concentrate elements in regions of stress concentration. In general, the three vertices of each side of a subdomain do not need to lie along a straight line; a parabola is fit to them. See the help pages for MappingMeshTool for more details on how to construct your mesh for a general geometry. The help pages can be accessed by clicking on Help in the MappingMeshTool GUI. Sometimes you have to click Help twice before the help pages are pulled up in the MATLAB help window.

From the above figure, the vertex locations (in MATLAB syntax) are as follows:

There are two options for creating the eight vertices: we can use the mouse after pressing the Click SD Points button, or we can enter the coordinates directly into the edit boxes under Vertex positions. We'll use the latter option. Enter the above coordinates in the corresponding edit boxes under Vertex positions as shown below. You can use MATLAB expressions within these boxes. For instance, for the x coordinate of the fifth vertex, enter cosd(30)-0.5*sind(30) under Xpos. Remember to use the correct trig function for how you express your angles: if you enter the angle in degrees, you must use the MATLAB functions sind and cosd, if you enter the angle in radians you must use the MATLAB functions sin and cos.

Now that the geometry has been created in redAnTS, we now need to proceed to Step 3

Go to Step 3: Mesh

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