ME 360 Homework Assignment #5
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ME 360
Homework Assignment #5
Problem 1.
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Problem 2.
A cylindrical rod changes diameter at the fillet shown in Fig. 1. Generous fillets are beneficial in reducing stress concentration at changes of cross section. This is particularly important because the bar in question is made from a relatively brittle material, gray cast iron, and the fillet radius is not very large.
As such, the rod may be subject to significant effects of stress concentration at the geometric
discontinuity. Consider the rod supported (Immovable/Fixed) at its left-end and subject total of 1,200 lb tensile force applied to its opposite end.
Details
• Material: Gray Cast Iron (Use IPS units)
• Mesh: In the Mesh property manager, select a Standard mesh and use three different meshes as specified below.
• Fixture: Fixed/Immovable applied to left end of shaft.
• External Load: 1,200 lb applied normal to the right-end causing tension in the bar.
Fig. 1. Gray Cast Iron cylindrical rod subject to an axial tensile load of 1,200 lb. (Dimensions shown in inches.) The right photo shows failure at a shoulder in a similar stepped shaft.
Problem 2, continued.
a) Develop a finite element model using a default size, high quality mesh. For this mesh, perform the following:
• Create a stress contour plot of the most appropriate stress to permit comparison of maximum stress magnitude in the vicinity of the fillet with that predicted by classical stress equations computed at the same location. Include a mesh on this plot. See part(d) for classical stress calculations.
• Use the Probe feature to produce a graph of the most appropriate stress commencing approximately 3/4-in to the right of the fillet and progressing along the surface of the model, in as near a straight-line as possible, through the fillet area up to the outside diameter (large diameter) of the left segment of the shaft. Choose both corner and mid-side nodes.
b) Repeat part (a) after resetting the mesh size to fine. Use the duplicate feature to save time creating this study.
c) Repeat part (a) a third time beginning with the default size mesh. Use the duplicate feature to save time creating this study. Then, alter the mesh by applying mesh control on the fillet. Use a mesh control ratio setting of Ratio a/b = 1.15. Zoom in on the mesh when using the Probe feature to select nodes.
d) Use classical equations and available stress concentration factor charts to compute maximum stress at the fillet.
e) Compare results predicted using the three different meshes with that predicted by classical stress equations; clearly label each calculation. Compute the percent difference for each comparison.
f) Determine the Factor of Safety, or lack thereof, at the change of cross-section (i.e., at the fillet). Create a plot showing regions (if any) of the model with a Factor of Safety less than two. NOTE: Cast iron, being a brittle material, has an ultimate strength rather than a yield strength. Account for this fact when selecting safety factor failure criteria. Name the failure criteria that was used.
g) Comment upon which FEA results are in best agreement with predictions of the classical equations. Based on your comparison, which method of mesh refinement is preferred and why?
2023-08-05