AE 322
Homework #4
Due Monday, February 22, 2010
NOTE:
If you use MATLAB
®
, show your command sequence and output.
1. The components of a displacement field are (in meters):
( ) ( )
2
4
32
3
20
10 ,
2
10 ,
10 ,
x
yz
u
x
u
yz
u
z
xy
−−
−
= +×
=
×
=−×
(a) Consider two points (2, 5, 7) and (3, 8, 9) in the undeformed configuration. Find the change
in distance between these points.
(b) Compute the components of the infinitesimal strain tensor.
(c) Compute the components of the rotation tensor.
(d) Does this displacement field satisfy compatibility?
2.
For steel
E
= 207 GPa and
ν
= 0.3. Assume that the strain in a
( )
123
,,
xxx
frame at a given
point is
0.004 0.001
0
0.006
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 Spring '08
 Voulgaris,P
 Finite strain theory, infinitesimal strain tensor

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