AE 321
Homework 5
Due in class on October 4
1.
The components of a displacement field are (in meters):
u
x
=
x
2
+
20
()
×
10
−
4
,
u
y
=
2
yz
×
10
−
3
u
z
=
z
2
−
xy
(
)
×
10
−
3
(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 Lagrangian and the infinitesimal strain tensors.
(c) Compute the components of the rotation tensor.
(d) Compute and compare the Lagrangian strains and infinitesimal strains at location (2, 1, 3).
(e) Does this displacement field satisfy compatibility?
2
. The components of a strain tensor referred to the coordinate frame in the figure are
ε
ij
[]
=
0.02
−
0.003
0
0.01
sym
.0
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
.
0
1
and are constant in the region shown. The direction cosines of AC are (1/
√
2, 0, 1/
√
2) and of BD
are (1/
√
6,
√
2/
√
3, 1/
√
6).
A
B
C
D
O
x
x
x
1
2
3
1
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 Fall '07
 waller
 Finite strain theory, infinitesimal strain tensor, infinitesimal strain tensors

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