2.092/2.093
FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I
FALL 2009
Homework 6
Instructor:
TA:
Prof. K. J. Bathe
Seounghyun Ham
Assigned: Session 14
Due: Session 16
In all analyses, use ADINA.
Problem 1 (20 points):
The figure below shows a cantilever beam subjected to distributed pressure. Use ADINA to analyze the
problem and undertake a convergence study using 9-node elements. Compare the stress fields obtained
with meshes of 1×4, 2×8, 4×8, and 4×16 elements. Also evaluate your results comparing with a beam
theory result.
z
y
p0 =1×108 N
10mm
m2
· Plane strain, thickness 1.0
· Linear analysis
· E=1×1011 N
40mm
m2
, ν=0.3
Problem 2 (20 points):
Consider the same cantilever beam but this time subjected to the prescribed surface temperature shown
below. Compare the temperature distributions obtained with meshes of 1×4, 2×8, 4×8, and 4×16 4-node
elements, and comment briefly on your results.
z
y
θ 0 =20°C
θp=0°C
10mm
40mm
· 2-D linear analysis
· k=71.8 W
1
mK
Problem 3 (20 points):
Consider the problem shown below of a fluid flowing around a cantilever beam. Assume that the
cantilever beam is a rigid body. Study the velocity and pressure distributions in the fluid domain by
increasing the number of elements, and choose appropriate meshes. Comment briefly on your results. Use
4-node elements.
Vinlet =0.0025 m
s
· 2-D planar analysis
· ρ=1000
z
Slip wall
y
120mm
No slip walls
10mm
40mm
35mm
80mm
Out-flow boundary
2
kg
m3
µ=1×10-3Pa·s
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2.092 / 2.093 Finite Element Analysis of Solids and Fluids I
Fall 2009
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