Plate Theory and Assumptions
Figure 4.5: Plate Theory
Figure 4.5 shows the DOFs associated with plate elements. Please take note that the out-of-plane rotation (Rz) is not taken into account because of the plate theory. Thus, plate elements have 5 DOFs.
Limits of Plate Theory
• No warpage is accounted for in the undeformed element
• Stress through the thickness is not truly linear for thicker plates
• The theory is based on a square element with 90-degree corners
NOTE: Violation of these limitations does not mean you will get wrong results. It simply means that you should check your results.
Plate Formulations 1. Veubeke (Standard)
• This is the most accurate
• This is very sensitive to warpage of the elements 2. Reduced Shear
• This uses the reduced shear integration
• Hsieh, Clough and Tocher (HTC) plate bending theory is used (Constrained Linear Strain Triangle, CLST)
3. Linear Strain
• Without the reduced shear integration terms
• HTC plate bending theory is used (CLST) 4. Constant Strain
• HTC plate bending theory is used (CLST) Assumptions
• The thickness is small relative to the overall length and width of the model
• Small displacements and rotations
• Plane sections remain planar
• Linear stress distribution through the thickness
• The plate element is initially flat; that is, all points are in the same plane
• The out-of-plane rotations are negligible
Loading Options
The loading options for plate elements are almost identical to those for brick elements, as discussed in Chapter 2. The only addition is the control for the orientation of normal surface pressure, hydrostatic pressure, and surface force loads. For plate elements, this is controlled by an element normal point. This is an arbitrary point in space defined in the "X Coordinate", "Y Coordinate" and "Z Coordinate" fields in the "Element Normal"
section of the "Orientation" tab of the "Element Definition" dialog. A positive normal or hydrostatic surface load or surface force will be applied normal to the face of each element and will push against the side of the element that is facing the element normal point. A negative normal or hydrostatic surface load or surface force will act in the opposite direction.
See Figure 4.6 for a visual explanation.
Figure 4.6: Element Normal Point
Hydrostatic Pressure Loads: One additional option for plate elements is that hydrostatic pressure loads can be applied in any orientation. The model does not need to be oriented with gravity acting in the -Y direction. The plane representing the surface of the fluid will be defined by a point on the surface and a vector normal to the surface. The normal vector should point into the fluid, that is, in the direction of increasing depth and gravity.
Example of Defining the Element Normal Point
To illustrate the use of the element normal point, we will continue using the manifold assembly from the prior midplane meshing example. If this model is not currently loaded, reopen the file, Manifold Assembly.fem, saved at the end of the midplane meshing example.
By default, the element normal point will be set to the global coordinate origin (0, 0, 0). We will add a pressure load to all of Part 1 and see how the loads are oriented. We will then make necessary corrections to the element normal point definitions and recheck the model.
"View: Orientation: Isometric View"
Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel.
Select "Isometric View" from the pull-out menu.
"Selection: Select: Parts" Select the "Selection" tab and then click on the "Parts"
button in the Select" panel.
Mouse Select Part 1 in the display window. Then Right Click mouse.
"Selection: Subentities:
Surfaces"
Then click on the "Surfaces" button in the Subentities"
pull out panel.
"Setup: Loads: Pressure" Select the "Setup" tab. Click on the "Pressure" button in the "Loads" panel.
20 Enter "20" in the "Magnitude" field.
"OK" Press the "OK" button.
Before we can check the model, we will need to define the material for the plate and brick parts.
Mouse Double-click on the "Material" heading under Part 1 in the tree view.
"Steel (ASTM – A36)"
Expand the Steel folder and then expand the ASTM folder.
Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library.
"OK" Press the "OK" button.
Mouse Select the "Material" heading under Part 2 in the tree view.
<Ctrl> Mouse Holding the <Ctrl> key, also select the "Material" heading under Part 3 in the tree view.
Mouse Right-click on one of the selected headings.
"Edit Material…" Choose the "Edit Material…" command.
"Steel (ASTM – A36)"
Expand the Steel folder and then expand the ASTM folder.
Select "Steel (ASTM-A36)" within the Autodesk Simulation Material Library.
"OK" Press the "OK" button.
"Analysis: Analysis: Check Model"
Select the "Analysis" tab. Click on the "Check Model"
button in the "Analysis" panel.
It will initially be difficult to tell whether the orientations are correct or not because some of the load vectors will be rendered attached to the model at the arrow head end and some will be attached at the tail end. We will make the vector orientations consistent so that critiquing the model will be easier.
"Tools: Options: Application Options"
Select the "Tools" tab and then click on the "Application Options" button in the "Options" panel.
Mouse Go to the "Results" tab within the Options dialog.
"Global FEA Objects
Preferences…" Press the "Global FEA Objects Preferences…" button.
"All arrows point at point of attachment"
Under the "Arrow Pointing" heading, activate the "All arrows point at point of attachment" option for the
"Current" model (left radio button). You do not need to change the default setting.
"OK" Press the "OK" button to close the Global FEA Objects Preferences dialog.
"OK" Press the "OK" button to exit the Options dialog. The model should now appear as shown in Figure 4.7.
Figure 4.7: Pipe Model in FEA Editor Environment
Notice how the pressure is acting against the outside of half of each pipe leading out to the flanges.
Clearly, the origin is not a suitable location for the element normal point for these two surfaces. A more intuitive location for these normal points would be somewhere along the centerline of each pipe. This is already true for the middle pipe, since its axis passes through the coordinate origin.
There are two ways to correct the orientation:
1. Make each outlet pipe a unique part number by modifying the attributes of the lines comprising them. Then, each outlet pipe can have a unique, part-based element normal point.
2. Specify surface-based element properties for Part 1. In this way, the surfaces comprising the two outlet pipes may have unique element normal point definitions.
We will now demonstrate the latter approach. The centerlines of the two outlet pipes are at Z = +/- 7.5" and lie in the XZ plane. You may identify the surface numbers of the outlet pipes by selecting one surface at a time, right-clicking, and choosing the "Inquire" command. A pop-up tool tip will identify the part and surface numbers. The half-surfaces comprising the +Z pipe are 5 and 14. The half-surfaces of the -Z pipe are 4 and 15.
"Tools: Environments: FEA Editor"
Select the "Tools" tab. Press the "FEA Editor" button in the "Environments" panel.
"Element Definition…" Double-click the "Element Definition" heading under Part 1 in the tree view.
Note that the "Properties" setting defaults to "Part-based." Therefore, the data entered into the table will apply to the entire part. As an alternative, it is possible to change this setting to
"Surface-based," in which case each unique surface can have different properties.
Mouse
"Surface-based"
Access the pull-down menu in the "Properties" field and choose the "Surface-based" option.
-7.5 Enter "-7.5" in the "Normal Point (Z)" column for Surface 4 and for Surface 15.
7.5 Enter "7.5" in the "Normal Point (Z)" column for Surface 5 and for Surface 14.
"OK" Press the "OK" button.
"Analysis: Analysis: Check Model"
Select the "Analysis" tab. Click on the "Check Model"
button in the "Analysis" panel.
"View: Appearance: Visual Style"
Select the "View" tab. Select the options below "Visual Style" button in the "Appearance" panel. Select the
"Features" option. The model will now appear as shown in Figure 4.8.
Figure 4.8: Model in Results Environment
You can now see that the pressure is properly applied to all surfaces of the manifold.
A completed archive of this model (Manifold Assembly.ach) is available in the "Chapter 4 Example Model\Results Archive" folder in the class directory or in the copy of the solutions folders on your computer.