Homework #2
1. This problem utilized the equations for Hertz stresses and obtained a
dimensionless stress plot and is solved using Maple. File for this problem is
Homework 2 #1. The formula were input into the file but was unable to
produce the plot of the stresses.
2. This problem evaluated a semi-infinite body linear elastic body loaded by a
rigid flat punch, first completed using pure Aluminum and then pure Copper.
a. For all of these “punch problems”, with the exception of problem #9, the
punch was modeled using rigid connector with an applied force so that
this force could also be used within the calculation for comparison. The
displacement was determined by evaluating the “y” displacement of the
punch edge. This distance was then also utilized in the calculation for
comparison.
b. Some screen shots of the aluminum and copper results are provided
below. The COMSOL files for these problems are
Homework2_2_Aluminum.mph and Homework2_2_Copper.mph. The
MAPLE file for this problem is Homework 2#2.mw.
c. The results of the analysis are as follows:
Aluminum
COMSOL
1.38E-8
MAPLE
1.49E-8
Copper
COMSOL
9.1E-9
MAPLE
8.67E-9
Aluminum
Copper
3. Repeat problem #2 but with Elastic-Plastic. I performed this problem by
repeating the analysis from above, but used the force that initiated yield.
After further review in class this problem will have to be revisited. Files for
this problem are Homework 2_3 Aluminum.mph and Homework 2_3
Copper.mph for COMSOL and Homework 2#3.mw for MAPLE. The results were
as follows.
Aluminum
COMSOL
2.9E-8
MAPLE
2.77E-8
Copper
COMSOL
1.2E-8
MAPLE
1.12E-7
4. This problem evaluated a 3D model with a load at a point (at the origin). The
COMSOL files are Homework 2_4 Aluminum.mph and Homework 2_4
Copper.mph and Homework 2#4.mw for MAPLE. This problem did not match
the values from COMSOL and MAPLE very well. Additional work will need to
be accomplished on this problem as more is learned in class.
COMSOL
MAPLE
COMSOL
MAPLE
Aluminum
U
V
W
U
V
W
Copper
U
V
W
U
V
W
-0.001
0
-0.004
-1e-6
-5.5E-8
3.7E-6
-4.9e-4
0
-2.1e-3
-5.99e-7
-4.2e-8
2.3e-6
Aluminum:
5. Repeat problem #4 but with Elastic-Plastic. I performed this problem by
repeating the analysis from above, but used the force that initiated yield.
After further review in class this problem will have to be revisited. Files for
this problem are Homework 2_5 Aluminum.mph and Homework 2_5
Copper.mph for COMSOL and Homework 2#5.mw for MAPLE. The results were
as follows.
COMSOL
MAPLE
COMSOL
MAPLE
Aluminum
U
V
W
U
V
W
Copper
U
V
W
U
V
W
-1e-6
0
-4.1e-6
-3.15e-9
-1.65e-10
1.12e-8
-4.9e-4
0
-2.1e-3
-8.9e-9
-6.3e-10
3.53e-8
6. Abaqus model of Hertz stresses. Eluded to an example of this problem will be
coming, will update homework when example is given in class.
7. See Homework 2#7.mw for MAPLE worksheet and solution.
8. See Homework 2#8.mw for MAPLE worksheet and solution.
9. See Homework 2_9 Al Both.mph and Homework 2_9 Al Hertz.mph for COMSOL
programs for the flat punch and Hertz pressure and Hertz pressure alone,
respectively. The combination loading had more of a flat displacement
profile, while the Hertzian pressure alone had much more of a parabolic
displacement distribution. See below.
Combination Loading:
.
Hertzian Pressure Distribution Alone:
10. See Homework 2#10.mw for MAPLE worksheet and solution.