OOF: Finite Element Analysis of Microstructures

Example 1: Homogeneous Material Under Uniaxial Loading next up previous contents
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Example 1: Homogeneous Material Under Uniaxial Loading

This is a simple example that will hopefully give you a quick introduction to OOF and its general utilities. We will create a grid (finite element mesh) within OOF and perform a virtual uniaxial mechanical test on it.

. Start OOF:
Start up the OOF graphical interface: oof. This should create and display the main OOF menu, with the word ``OOF'' prominently in the upper left hand corner. (If this doesn't happen, then something is dreadfully wrong. Make sure that the compiled version of OOF matches your architecture.)

. Initialize:
Launch the Initialize Menu by clicking on the word initialize in the Menus subwindow. The /initialize menu should occupy the real estate vacated by the main OOF menu.2.2

. Uniform:
You will see that there is currently only one type of grid -- a uniform grid. Launch the /initialize/uniform menu by clicking on uniform in the /initialize menu.

. Mesh Parameters:
Set the height of the grid by clicking on height in the Variables list. A variable dialog box appear at the bottom right corner of the menu, with some explanatory text. You can type in the desired height in the dialog box; Let's make the sample taller than it is wide by setting the height equal to Hit the $\langle$return$\rangle$ key or click on the Set button to tell OOF that you're done changing the height variable. Notice that a new window pops up; this is the message box where information is stored and reported about the current state of OOF. Also notice that the new value of height appears in the Variable list. The values of nx and ny specify the number of triangular elements in the $x$-direction (width) and the $y$-direction (height). nx and ny of about 20 are about right if you want nearly instantaneous solutions, although you might try different values to see how they affect the mesh and the computation time.

. Function Window:
Click once on isotropic to launch a Function Window indicating that you want finite elements for a isotropic material to fill the grid. (If your X-Windows manager is putting a frame around the windows, then the words ``initialize uniform isotropic'' appear on the window frame. This is the path to this command from the main OOF Menu.)

. Set Material:
The Function Window for the isotropic element provides a table to fill out attributes for that particular type of element. The isotropic element has three thermoelastic parameters and the table allows you to specify the Young's modulus, the Poisson's ratio and the thermal expansion coefficient. Note that if you hit a return in any of the function subwindows, it causes execution of that function. Use the mouse or the $\langle$tab$\rangle$ key to set more than one parameter. Set the Young's modulus to 2 and the Poisson's ratio to 0.25. Let's imagine that we are doing the virtual experiment on a thin material and set the two-dimensional stress state to be plane stress by clicking on the false button in the planestrain row. We won't be changing temperature in this example so the thermal expansion coefficient alpha does not matter. The value of gray controls how the mesh will be drawn; gray takes values between 0 and 1 inclusive, where 0 is black and 1 is white.

. Create the Mesh:
After all the information for the element has been entered, initialize the mesh by executing the function by clicking on the function name isotropic button at the top of the function window. Notice that the function execution is recorded in the message window. (Don't worry if you execute this function before you had intended, you can always recall the function and re-execute it.) The finite element mesh should now be ready.

. Graphics:
Look at the graphical representation of the mesh. Get to the main OOF Menu by either clicking on the Home button at the top of the /initialize/uniform submenu, or by backtracking by clicking on the Back button. From the main OOF Menu, open the graphics submenu. From the /Graphics Menu, open a Drawer by executing the open function by clicking on it twice quickly. (Clicking on it once would open a Function Window.) A Drawer should appear with a gray rectangle representing the isotropic material.

. Drawing Control:
Turn on the element edges so that the grid becomes apparent. The Coordinates Dashboard is currently visible. Switch to the Attributes Dashboard by clicking and holding the left mouse button on the Dashboard Selector and selecting Attributes from the pop-up menu. The controls visible in the Dashboard should change. Turn on the element edges by clicking on the button next to Elements. The mesh should be redrawn with edges turned on. The height, width and number of elements in the mesh were determined by the values you chose in the /initialize/uniform Menu.

. Pick Nodes:
Verify that the mesh has the height and width that you specified. Open the Node Info Dashboard on the Drawer. Move the mouse into the image region of the Drawer and place the hook of the ``?'' cursor over the top-right node and click with any button. (In this case, nodes are the vertices of the triangular elements.) You should see information appear in the Message Window reflecting the state of the Dashboard and the node which you queried. If you picked correctly, the node coordinates should be equal to width and height. The node type should be xy meaning that the node has an x- and a y- degree of freedom.

. BCs:
Set the boundary conditions. This is done by removing degrees of freedom from nodes. Note tha this operation only affects the behavior of the equilibration stage of the solution. We will still be able to displace these nodes when distorting the mesh. From the main OOF Menu, open the submenu bc. Fix the spatial degrees of freedom by picking the fix submenu. Let's fix both the x- and y- coordinates, by picking on the both submenu. The /bc/fix/both submenu will have names of groups of nodes in the Function column. We will stretch the material in the vertical direction with fixed grips. Select top to remove the x- and y- degrees of freedom from the top row of nodes; do the same for the bottom nodes.

. Set Distortion:
Distort the mesh into the configuration for which you want a solution. From the main OOF Menu, open the distort submenu. Open the set submenu. There are a number of choices in the Variables column. Prepare to stretch the material by setting a ystrain of 0.20 (a strain of 20 percent in the vertical direction.) Now you have to specify which nodes you want to be distorted: click on the nodegroup top. Notice that in the graphics Drawer that nothing has happened; this is because the distortion has yet to be applied.2.4

. Apply Distortion:

Move Back one menu to /distort. Keep one eye on the graphics Drawer while you click on the increment function. You will see that the top elements have been distorted. To get the entire picture back into the Drawer either click the middle mouse on the z(oom) button at the top-left corner of the image subwindow of the Drawer or open the Coordinates dashboard and click on Show Entire Image.

. Solution:
From the main OOF Menu, click on the equilibrate function. Information about the solution will appear in the Message Window and the current graphical representation will appear in the image subwindow of the Drawer.

. Stresses:
Get a graphical picture of the stresses for the current solution. On the Drawer, hold down the left button on the top (wide) selector to bring up the list of Drawer types. Select Stress invariant 1. This will display the trace of the two-dimensional stress matrix: $\sigma_{xx} + \sigma_{yy}$.

. Numerical Values:
Change to the Element Info Dashboard on the Drawer. Turn on the stress button as well as several of the components of stress listed below it. Move the mouse onto the image and click on an element. The numerical values of the requested stress components in the element will appear in the message window.

. Statistics:

Switch the Drawer back to the Mesh display and open the Attributes Dashboard. We will be selecting elements so turn on the Hot Elements option, so that the selected elements are visible. Turn on the Click to Select$\ldots$ Elements option. In the image subwindow, drag a rectangle by holding down the mouse button as you move the mouse. The selected elements should change color. From the main OOF Menu, select the /output/stress/statistics submenu. Change the type variable to invariant (Click once on the word type in the Variables list. A pull-down menu of different statistics types appears at the bottom of the Menu. Use the left mouse button on the pull-down menu to see all the choices, or use the right or middle buttons to cycle through the choices.) Use the function selected to gather statistics on the selected elements. Output appears in the message window.

. Play, Quit:
You might want to play with various menus and see what's available. When you want to quit, go back to the main OOF Menu and click on the quit option in the Function list, or the Quit button at the top of the window.

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Next: Example 2: Using Data Up: Examples Previous: Examples   Contents
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