Using the J L Analyzer
for Finite Element Analysis
of Wooden Plates - Part II
Simply Supported Plate Deformation
I have finished writing my book "Left-Brain Lutherie: Using Physics and Engineering Concepts for Building Guitar Family Instruments: An Introductory Guide to Their Practical Application". Details can be found here.
In Part I, we modeled free plate frequency distributions and saw the extent to which the model related to my measurements and the math model that Graham Caldersmith created.
We used the data in the
spreadsheet [ CalderPlateModes.xls
(to download double-click or option-click) ] and entered Lx, Ly, h, Ex, Ey, Exy, est. Gxy, est. nuxy and nuyx and density (lbm/in^3) and it took less than a minute for the program to generate modal frequency distributions (up to 50 can be calculated). All the modal frequency estimates were within 2-3 Hz of my actual measurements. There are many different display possibilities but the animated color ones with exaggerated vertical movement gave me the most insight.
We'll now use the same data from the above spreadsheet and do a simple plate deflection model. The instructions below (modified from the JL Analyzer tutorial) give step-by-step instructions for repeating this experiment. Many of these steps are the same as in Part I.
The procedures in the PROCESS menu (upper right screen) include:
1. Geometry modeling
2. Mesh generation
3. Material and geometry properties
4. Boundary condition and loads
Following the building of the model, we then proceed to:
B. Analysis, on the top menu bar
C. Examine results, in the PROCESS menu
Step A: Modeling
SPECIICATION OF THE PROJECT
The purpose of this lesson is to determine the modal frequencies of a wooden plate, 14 x 10.75 x .102 inches. The plate is free from any constraints.
Step 1: Geometry Modeling
1. Select the Geometry command in the PROCESS menu that is on the right and top corner of the screen
2. Select the Sketch command in the GEOMETRY menu
Note: Input a new project name if itís not available now.
3. Select the Rectangle command in the SKETCH menu
4. Move the cursor to the position (0, 0) then click the left button
Note: The cursor coordinates are shown at the bottom left corner of the graphics window.
5. Move the cursor to the position (14, 10.75), then click the left button (The rectangle is done.) If you can't get 10.75 exactly, 10.8 will be close enough.
6. Select the Done command in the SKETCH menu to finish sketch procedure and save the drawing to the database. The sketch grids will disappear and drawing is shown on the top view. Select the Return command in the GEOMETRY menu to return to the PROCESS menu
Step 2: Mesh Generation
Since this example has 3D geometry, we will mesh it as a shell element.
1. Select the Mesh command in the PROCESS menu
2. Select the Generate command in the MESH menu
3. Select the Shell command in the MESH Plate menu
4. Select the Accept commands in the Plate ELEM
Note: The commands Quad4 and Whole part are the default selections. If no highlighted on it, then click on it.
5. Input mesh length 1.0 in the dialog box
6. Click OK. The mesh creation procedure is finished and shown on the screen. Select the Return command in the MESH menu to return to the PROCESS menu.
Step 3: Assign Properties
The model must have a set of material properties. In this example we select the wood plate properties from the spreadsheet provided above.
1. Select the Property command in the PROCESS menu
2. Select the Material Property command in the PROPERTY menu
3. Select the Define command in the MATERIAL menu
4. Select Orthotropic from the M Type box, then fill in the properties from the spreadsheet using English units: Ex, Ey, Exy, nuxy, nuyz, Gxy and mass density.
5. Select the Whole part command in the M ASSIGN menu to assign the wood properties to the entire model. Click the Return command in the MATERIAL menu to return to the PROPERTY men.
The model must also have a third dimension. This step defines the plate thickness necessary for the plane stress element.
1. Select the Geometry Property command in the PROPERTY menu
2. Select the Thickness command in the GPROP menu
3. Select the Whole part command in the G SHELL menu
4. Input a value 0.102 in the dialog box for plate thickness, then click OK. Click the Return command in the GPROP menu, then click the Return in the PROPERTY menu to back to the PROCESS menu
Step 4: Define Boundary Conditions and Loads
1. Select the BC/Load command in the PROCESS menu
2. Select the Constraint command in the BC/Load menu
3. Select the Define command in the CONSTRAINT menu
4. Select the Edge and Pin Joint commands in the CNST DEFINE menu
Note: The commands Edge and Rigid joint are the default selections. If Edge and Pin Joint are not highlighted, then click on it.
5. Pick the "Y" edges of the plate
Note: Move the cursor to the "Y" edges of the plate, then click the left button. The symbol of the pin joint now appears along the "Y" edges of the plate.
6. In the CNST DEFINE menu choose X rotation and pick the same two "Y" edges as before. Now the X triangles on the edge will be partially filled with blue color.
7. Click the right button or click the left button on the empty place in the graphics window to finish the command. Click the Return command in the CONSTRAINT menu to back to the BC/Load menu. Click View in the toolbar and Elements to see the nodal grid.
8. Select the BC/Load command in the PROCESS menu
9. Select the Load command in the BC/Load menu
10. Select the Force command in the Load menu
11. Select Node, Z force and Accept in the Force Define menu.
12. I wanted to model the deflecting force of a steel rod weighing 1.5 lbs would have when placed along the center line of the plate parallel to the Y axis. To model uniform force across the plate I divided the force ( 1.5 lbs ) by the number of nodes ( 12 ) to get the vertical force to be applied to each node ( -0.125 lbs ). We now count the number of nodes along the X axis plate edge to the edge center (7), pick the first of 12 nodes and enter -0.125 as the force. Continue picking across the plate until you've reached the other edge. The finished figure should look like this:
It sounds quite tedious but since you just keep picking your way across and the same choice window appears with your force value filled in each time, it only takes a little while.
Now Return to the Process Menu
The modeling is completed.
Click Analysis on the top menu, then select Static to perform the static analysis.
In the Static menu, choose Calculate Stress, and check the box for Spring Value and enter the number 1e-7. These calculations take about 7 seconds on my computer.
By choosing List in the top menu, then Results, then Displacement, you can see a list of the displacements generated.
By going to the Process Menu and choosing Exam Results, then Displacement, then Plot, then Accept , you can then be treated to a view of the plate with deflection values.
If you have problems creating the file but want to see what the animations look like anyway, please download the following file and store it in the AutoFea folder:
Then open up the JL Analyzer and in the File menu choose Open Metafile. Choose PlateDeflect1.ses from the listing. Now you can go directly to the Process Exam Results section, choose Deflection, Animate, etc. and off you go.
Many other display options exist for the reader to explore on their own.
The next procedure will show a wooden disk with a fixed boundary (as time allows me to create the instructions).
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