Composite Materials Research Progress

90
10 5
10 0
15
10
10 -5
5
10 -10
Objective functions (N/mm)
0
0 10 20 30 40 50
3
2.5
2
1.5
1
Variations of the objective functions
0 10 20 30 40 50
Michaël Bruyneel
2 Maximum constraints violations
10
10 0
10 -2
10 5
10 0
10 -5
0 10 20 30 40 50
Maximum variables variation
0 10 20 30 40 50
Figure 8.11. Convergence history for MMA. k is equal to 3.
Objective functions (N/mm)
0.5
0 2 4 6 8 10 12
10 0
10 -2
10 -4
10 -6
Variations of the objective functions
2 4 6 8 10 12
10 1
10 0
10 -1
10 5
10 0
10 -5
Maximum constraints violations
0 2 4 6 8 10 12
Maximum variables variation
Figure 8.12. Convergence history for SAM. k is equal to 3.
2 4 6 8 10 12
Figure 8.13 illustrates the optimum stacking sequence for the different values of the load
parameter k. The solution corresponds to a [0/90]S with a variable proportion of 90° plies
(depending on k).
Figure 8.14 describes the design space for k = 4. The iso-values of both objective
functions are drawn. The arrow indicates the direction for an increase of the stiffness. The
optimal solution is characterized here by identical values of both objective functions.