Figure 2.19 shows an example of where displacement boundary elements may be used. When the foundation collapses, the bottom of the structure will move. However, the structure will not move the entire 0.5" because of the stiffness of the bolts. Therefore a stiffness must be applied to the displacement boundary element to properly model this situation.
Figure 2.19: Sample Displacement Boundary Element Application
Another example is any situation where you know the deformation or displacement to be imparted to a given design but do not know the force required to achieve it. For example, say you are shouldering a roller bearing against a dished or conic washer. The washer acts like a spring to keep the assembly tight and free of clearance. You know that you are to compress the washer axially by 0.05 inches. Enter this movement as a displacement boundary condition and the program will tell you the resultant forces and stresses.
Using Local Coordinate Systems
To illustrate the use of a local coordinate system, we will use a simple model of a cube with a hole running through it. A meshed archive of this model (Cube.ach) is located in the
"Chapter 2 Example Models\Input File" folder in the class directory or in the copy of the solutions folders on your computer. We want to apply nodal forces to the interior of the hole so that they are normal to the surface. We could calculate the normal vector at every location along the circumference and apply the nodal forces individually. A better way would be to create a cylindrical coordinate system with the origin at the center of the hole. We can then apply the forces in the radial, R, direction.
"Start: All Programs:
Autodesk: Autodesk Algor Simulation 2012: Autodesk Simulation 2012"
Press the Windows "Start" button and access the "All Programs" pull-out menu. Select the "Autodesk" folder and then the "Autodesk Algor Simulation 2012" pull-out menu. Choose the "Autodesk Simulation 2012 software"
command.
"Getting Started: Launch:
Open"
Click on the "Open" button in the Launch panel.
Alternatively you select “Open” from the quick access toolbar or Application Menu.
"Autodesk Simulation Archive (*.ach)"
Select the "Autodesk Simulation Archive (*.ach)" option in the Autodesk Simulation Files section of the "Files of type:" drop-down box.
"Cube.ach" Select the file "Cube.ach" in the "Chapter 2 Example Models\Input File" directory.
"Open" Press the "Open" button.
"OK" Select the location where you want the model to be extracted and press the "OK" button.
"View: Navigate: TopView"
Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel.
Select "TopView" from the pull-out menu. The model should now look like Figure 1.10. The View Cube can also be used to access the views. The model will appear as shown in Figure 2.20.
Figure 2.20: Model in FEA Editor Environment
We must first determine the location of the center of the hole.
"Selection: Shape: Point" Select the "Selection" tab. Make sure the "Point" button is selected in the "Shape" panel.
"Selection: Select: Vertices" Also make sure the "Vertices" button is selected in the
"Select" panel.
Mouse Click on the bottom left corner of the cube in the XY view.
Mouse Right-click in the display area.
"Inquire" Select the "Inquire" command. A tool tip will appear with the coordinates of the selected vertex. It is (0, 0, 2).
Mouse Click on the upper right corner of the cube in the XY view.
Mouse Right-click in the display area.
"Inquire" Select the "Inquire" command. A tool tip will appear with the coordinates of the selected vertex. It is (2, 2, 2).
Since the hole is at the center of the cube, we can determine that the centerline of the hole is at X=1 and Y=1.
Mouse Double-click on the "Coordinate Systems" heading in the tree view.
"Cylindrical" Select the "Cylindrical" option in the "Coordinate System Type" drop-down box.
Referring to the image in the dialog, Points A and B can be any two points along the centerline of the hole. We will use (1, 1, 0) for point A and (1, 1, 1) for point B. Point C must be in the plane perpendicular to the vector from point A to point B. We will use (2, 2, 0).
1 <Tab> 1 <Tab> 0 Type "1" in the first field for "Point A", press <Tab>, type
"1", press <Tab> and type"0".
1 <Tab> 1 <Tab> 1 Type "1" in the first field for "Point B", press <Tab>, type
"1", press <Tab> and type"1".
2 <Tab> 2 <Tab> 0 Type "2" in the first field for "Point C", press <Tab>, type
"2", press <Tab> and type"0".
Center of Hole Type "Center of Hole" in the "Description" field.
"OK" Press the "OK" button.
Next, we are going to select the two edges that will use the cylindrical coordinate system and assign this coordinate system to them.
"Selection: Select: Edges" Select the "Edges" button in the "Select" panel.
Mouse Select one of the edges of the hole
<Ctrl> Keeping the <Ctrl> key pressed select the other 3 circular edges
Mouse Right-click in the display area.
"Coordinate Systems: Id 1:
Center of Hole"
Select the "Coordinate Systems" pull-out menu and select the "Id 1: Center of Hole" command.
"View: Appearance: Nodal Coordinate System "
If small miniaxes are not already visible at the selected nodes; Select the "View" tab. Make sure the "Nodal Coordinate System" button is selected in the
"Appearance" panel options.
Small miniaxes will be visible on each selected vertex. The red axis (indicating the local x–direction) should point away from the center of the circle, as shown by the radial miniaxis lines in Figure 2.21. Next, we can add an edge load.
Figure 2.21: Model with Local Coordinate System Defined
"Setup: Loads: Force"
With the edges of the hole's still still selected, Select the
"Setup" tab. Select the "Force" button in the "Loads"
panel
10 Type "10" in the "Magnitude" field.
"Y" Select the "Y" radio button in the "Direction" section.
This corresponds to the tangential direction.
"OK" Press the "OK" button.
The forces will appear tangential to the surface as shown in Figure 2.22.
Figure 2.22: Model with Forces Applied
A completed archive of this model (Local coord.ach) is available in the "Chapter 2 Example Models\Results Archives" folder in the class directory or in the copy of the solutions folders on your computer.
An alternate method of defining cylindrical coordinate systems is to draw construction lines across the center of the hole or similar round feature, one at each end of the feature, and to divide these two lines into two increments each. The line command can be accessed from the
"Draw" panel with the "Draw" tab. Be sure that the "Use as Construction" option is enabled so that you're not adding actual FEA entities but merely reference geometry. To divide the lines, you must be in "Select Construction Objects" mode, select the lines, right-click, and choose the "Divide..." command. Next, place construction vertices at the midpoints of the construction lines using the "Construction Vertex" command. This method provides two vertices along the centerline of the hole that can easily be selected when defining the coordinate system.
When using this method it is best to specify an existing part number for the construction lines.
This will prevent the addition to the model tree of a part with no actual FEA entities. Such an
"empty" part would need to be deactivated prior to performing the analysis.
Using Surface Variable Loads
Surface variable loads can be used when a load follows a known function across a surface. A classic example would be a bearing load where the force profile is parabolic. This will be practiced in a future exercise. For now we will attempt to apply a load to a side of the cube model that we used previously to demonstrate the creation of local coordinate systems. We want this load to have a magnitude of 55 psi at the top of the block (Z=2) and decrease linearly along the Z axis to 8 psi at the bottom (Z=0). A diagram of this load is shown in Figure 2.23.
Figure 2.23: Diagram of the Surface Variable Force
We will continue using the "Cube" model from the prior example. If this model is not still open, reopen it.
"View: Navigate: Right View"
Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel.
Select "Right View" from the pull-out menu.
"Selection: Shape: Point" Select the "Selection" tab. Make sure the "Point" button is selected in the "Shape" panel.
"Selection: Select: Surfaces" Also make sure the "Surfaces" button is selected in the
"Select" panel.
Mouse Click on the surface facing the screen.
"Setup: Loads: Variable Pressure"
Select the "Setup" tab. Click on the "Variable Pressure"
button in the "Shape" panel options. The dialog shown in Figure 2.24 will appear.
Figure 2.24: Surface Variable Load Dialog
From the given minimum and maximum loads and positions we can derive the equation for the pressure as a function of z. The equation is P=23.5z+8. When defining the equation, the x, y and z coordinates will be represented by the variables r, s and t, respectively. You can use basic operators such as +,-,*,/, () and ^. Pressing the "Available Primitives >>" button will allow you to access several common functions.
"Normal to Surface" Select the "Normal to Surface" radio button.
Linear Pressure Type "Linear Pressure" in the "Active function" field.
23.5*t+8 Type "23.5*t+8" in the "Expression (Use 'r', 's', and 't' as variables)" field.
"View" Press the "View" button.
"T Z"
Select the "T Z" radio button. A graph will appear as shown in Figure 2.25. This shows a force increasing from 8 to 55 from z=0 to z=2.
Figure 2.25: Variable Load Graph
"Close" Press the "Close" button.
"OK" Press the "OK" button.
Mouse Right-click on the "Material" heading in the tree view.
"Edit Material…" Select the "Edit Material…" command.
"Steel (ASTM-A36)" Highlight the "Steel (ASTM-A36)" item from the list of available materials.
"OK" Press the "OK" button.
"Analysis: Analysis: Check Model"
Select the "Analysis" tab. Click on the "Check Model"
button in the "Analysis" panel.
"View: Navigate: Front View"
Select the "View" tab. Click on the options button to the bottom of "Orientation" button in the "Navigate" panel.
Select "Front View" from the pull-out menu.
The model will now appear as shown in Figure 2.26. You can see the force vectors increasing in the positive Z direction.
Figure 2.26: Surface Variable Load in the Results Environment
You will notice that the arrow at the very top of the surface is shorter than the arrows immediately below it. This is because when two elements share a node, the nodal forces receive a partial contribution from each of the adjacent element faces. These are combined into one force at the shared node and displayed as such in the Results environment. Nodes along surface edges and at corners represent fewer element faces. For a uniform pressure on a perfectly uniform mesh, corner nodes will see half of the force that the other nodes along the edge will see and one-fourth of the force that the interior nodes will see. Similarly, non-corner edge nodes will see half the force that the interior nodes will see.
A completed archive of this model (Surf var load.ach) is available in the "Chapter 2 Example Models\Results Archives" directory in the class directory or in the copy of the solutions folders on your computer.