Aerospace Structural Composites I
Homework 2
Anirban Chaudhuri
1.
Material A has Young's modulus of 10 million psi, and a shear modulus of 3.7 million psi.
Material B has a Young's modulus of 20 million psi, and a Poisson's ratio of 0.5. Design a
laminate made of the two materials, with total thickness of 0.5 inches, with maximum Young
modulus, so that its Poisson's ratio is not larger than 0.4.
Solution:
E
A
= 10e6 psi, G
A
= 3.7e6 psi; E
B
= 20e6 psi,
B
= 0.5; h = 0.5 in.
Poisson’s ratio for the material A,
A
= E
A
/(2G
A
) – 1 = 0.3514
[considering isotropic material]
Let the thickness of material A be t
A
. So, the thickness of material B is t
B
= h – t
A
.
The terms in Amatrix for the composite are shown in equation (1).
11
22
2
2
12
2
2
1
1
1
1
A
B
A
B
A
B
A
A
B
B
A
B
A
B
E
E
A
A
t
t
E
E
A
t
t
…(1)
Now, the effective Young’s modulus of the laminate has to be maximized, so that the effective
Poisson’s ratio is not greater than 0.4. The optimization problem that needs to be solved is given
in equation (2) with the design variable as t
A
.
,
0.4
A
eff
t
eff
E
Subject to
Max
…(2)
where,
2
11
22
12
22
12
22
1
eff
eff
A A
A
E
h
A
A
A
The above optimization problem is then solved in MATLAB using the
fmincon
command. The
code used to solve the problem is given in the Appendix I. After solving the optimization
problem, the thickness of
material A
is found to be
0.4139 in.
Thus the thickness of
material B
is
0.0861 in
.
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 Spring '08
 PETERIFJU
 TA, inplane strains

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