ME 341 FEM/FEA Homework
P1: Truss Problem
d) Model the truss in Abaqus
First create a wire feature and sketch the structure.
Then assign a section and material to the elements of the model.
Add the load and boundary conditions to the model
Apply nodes and a mesh to the model
e) Find the displacements at each node
Run a job to get results
Probe values at each of the nodes to get the results.
The displacement is given under the U column.
f) Find the stress in each member
Similar to the displacement, probe the elements for the stress data
Note that the stress is given in the S column in KSI.
P2 Stepped Bar with Radius (stress concentration)
Only a quarter of the original shape needs to be modeled to save node availability.
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Apply a shell section.
Fix the left side and add a pressure to the other.
Use a partition edge and the seed edge tool to layout the nodes.
Run the Job to find the maximum stress of 2.5 MPa
3) Circular Stepped shaft (treat as beam elements)
Sketch the wire for the beam
Create and apply beam sections with a circular profile
After assigning the sections and beam alignment you can choose to render the beam profile
Use and encastre boundary condition and a concentration load in the load module
Use the Seed edges tool to control the number of nodes placed along the beam.
Find the maximum stress caused by this load and compare to the hand
calculations.
Run the job to see the results, the following results are with 17 nodes. With 17 nodes the
maximum stress was 23.1 MPa
After reducing the node count to 9, the maximum stress was only 21.5 MPa. Remember that the
hand calculation value was 23.9. Now it’s time to increase the node count. With a node count of
41 the max value is 24 MPa, that is close enough to the hand calculation value for the purpose
of this assignment.
Find the maximum displacement caused by this load
Use this menu and change the middle window to U to find displacement.
The maximum displacement was found to be 0.411 mm at the right most side of the beam.
4) Pneumatic Cylinder Deflection
Create this rod as a single truss element in Abaqus. Explain why we can treat it as
such?
We can treat the cylinder as a single truss element because it is a 2 force member. This makes
the required calculations very simple.
Sketch for the single truss element:
Find the area and create the section properties for the truss.
Seed the mesh along the edge of the beam. 40 elements were created for this problem.
Solve for the maximum displacement:
Run a job and review the results. The Abaqus calculations state that the maximum displacement
is 2.6363E-04 inches while the hand calculations show 2.64E-4 as well. These are very similar to
each other.
5) Practical Application (cantilever beam)
Analyze within Abaqus and compare the maximum stress to your hand
calculation. Reflect on the results.
Set up a beam:
Use the Pipe profile:
Add the concentrated load and fixed boundary condition.
Add the elements and run the job
Re-run your model with 3,5,20, and 50 elements, and plot the number of
elements (x-axis) vs. the maximum stress (y-axis). How many elements do you
need to get an accurate result?
Number of Elements
3
5
20
50
Maximum Stress (psi)
6652
7184
7783
7903
Element count vs Stress value
8000
7800
Stress value (psi)
7600
7400
7200
7000
6800
6600
6400
0
10
20
30
40
50
60
Number of Elements
With a hand calculated result being 7152psi, 5 elements and up have been fairly accurate. This
plot also shows the diminishing returns of adding more nodes. I would play it safe and use 20
elements.