Composite Materials Research Progress

Optimization of Laminated Composite Structures… 83
180
160
140
120
100
θ2
80
60
40
20
Strain energy density
(N/mm)
θ init
θ opt
θopt unconstrained
0
0 20 40 60 80 100 120 140 160 180
θ1 Figure 8.2. Illustration of the design space. Staring point, unconstrained and constrained optimum.
The iteration histories for the 3 approximation schemes are illustrated in the Figure 8.3.
The convergence of the optimization process is controlled by the relative variation of the
design variables at 2 successive iterations. The MMA approximation converges in 41
iterations. 29 iterations are enough for GCMMA. When the SAM approximation is used the
solution is reached in a very small number of iterations.
25
20
15
10
5
150
100
Objective function (N/mm)
0
0 20 40 60
50
Evolution of angles (deg.)
0
0 20 40 60
20
15
10
5
150
100
Objective function (N/mm)
0
0 10 20 30
50
Evolution of angles (deg.)
0
0 10 20 30
20
15
10
5
150
100
Objective function (N/mm)
0
0 5 10 15
50
Evolution of angles (deg.)
0
0 5 10 15
MMA GCMMA SAM
Figure 8.3. Iteration history for the 3 approximation methods.