ME 422
FEM Homework #5
Distributed: January 10, 2013
Due: January 17, 2013
Recall the rod with a square cross-section from the previous homework. It
had internal heat generation g and conductivity k. Natural convection occured off of the long edges, with convection coefficient h and ambient temperature Ta . The ends of the rod were insulated.
convection coefficient h
2L
insulated
ends
2L
conductivity k
internal heat generation g
insulated
ends
ambient temperature Ta
Problem 1: We used ANSYS to model this in 3D, but we know that we
didn’t need a full three-dimensional model of the problem, we could have
used a two-dimensional model of the cross-section. There are several key
steps we need to accomplish to get Workbench to do a 2D analysis. Here is
the overview, and the details follow:
• Create a proper “surface body” geometry
– You need to create a “surface body” of the cross-section of your
solid body.
– That surface body must lie in the x-y plane at z=0.
– After you create the surface body you must suppress all the solid
bodies.
• You must select 2D before starting the Model phase.
• Now go into model and make a mesh and boundary conditions and
solve.
1
Create Surface Body
• Start in Geometry (DesignModeler), and generate your solid body as
usual.
• Then, on the top menu bar, select Concept → Surfaces from Faces.
• Select the cross-section face that is at z=0 and lies in the x-y plane,
and choose Apply. (If your cross-section face isn’t at z=0 in the x-y
plane you need to move the solid body or move the Surface Body there
after you create it.)
• Click Generate. You should have “2 Parts, 2 Bodies”. The new body
should be called “Surface Body”.
• Right-click on the original “Solid” and select “Suppress Body”. It
is EXCEEDINGLY important that you DO NOT PICK “Hide Body”!
Suppress Body makes the solid disappear from the analysis– Hide Body
only makes the solid disappear from the screen.
• Now left-click on the Surface Body and give it an (arbitrary) thickness
in the details menu (lower left).
• Close DesignModeler.
Choose a 2D Geometry Model Do NOT skip this step.
• In the main window (Project Schematic) right-click on Geometry and
pick “Properties”.
• Under “Advanced Geometry Options” → “Analysis Type” choose 2D.
• Close (X) the Properties menu.
Create your 2D Model
• Open Model (Mechanical).
• Generate a mesh.
• Apply boundary conditions. The “surface body” is considered a body,
not a face, so when you select internal heat generation it is ok if you
can’t select a face, just a body. You may not see the body highlight
when you click it because it may light up on the back side instead of
the front – spin it around to check. The edges are still edges so that
is what you choose for convection. (Note: If you skipped the “Choose
a 2D Geometry Model” step you will encounter trouble here because
you have the wrong KIND of surface model– it’s a 3D plate, and you
won’t be able to apply the boundary conditions. You will need to exit
Mechanical, then right-click on the Model (Mechanical) cell in the main
window (Project Schematic) and select “Reset”. Then go back to the
“Choose a 2D Geometry Model” step and start over.)
2
• Solve and create contour plots as usual.
So, try all of this and confirm that the picture looks exactly like what
you got for your 3D model last time. Print a picture of your temperature
contour plot.
Problem 2: Let us practice what we have learned about finite elements by
making a simple finite element model of the problem. By symmetry, we only
have to model one quarter of the cross-section:
symmetric L
(no heat flux)
L
symmetric
(no heat flux)
We can make this model with a single four-node isoparametric element,
and two two-node convection elements on the boundary.
T2
T1
symmetric
(no heat flux)
T4
T3
symmetric
(no heat flux)
a. Set up the 4×4 system of equations which arises from the finite element
discretization of this problem. Use the numbers for the physical parameters
that you used in problem 1. (Note: this is a long part.)
b. Solve the system of equations. Compare your answers to the answers you
had for problem 1. Make sure that your answers are reasonable. They won’t
be too close because your mesh is very coarse. Include a copy of the program
you used to get the answer, and the printout of the results.
c. Go back to ANSYS and redo the 2D analysis, but with a very coarse
mesh. (Right-click on mesh and Insert → Sizing. Pick the entire body.
Choose Element Size to be 1 m and Behavior as Hard. You won’t see the
mesh, because it lines up with the body walls. Click on mesh and check that
the Details → Statistics shows 1 element and 8 Nodes. Notice that this is a
3
bit different than what we have in (a).) Solve the coarse mesh and print the
contour plot of temperatures. The outer boundary temperatures should be
very close (but still not identical) to what you got in part b. The temperature
at the center will not be close.
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