Composite Materials Research Progress

100
Michaël Bruyneel
The solution is provided in Figure 8.27. The optimal value for the angle θ is zero. The
convergence is achieved in 5 iterations with the SAM approximation and in 15 for MMA
(Figure 8.28). Although the solution of this problem is trivial, the procedure could be used for
more realistic structures subjected to several complex load cases.
Figure 8.27. DCB beam and variation of GI along the crack front for the optimal design. On the left the
displacements of the lips are multiplied by 50
Figure 8.28. Convergence history for the optimization with respect to damage tolerance. SAM
converges in 5 iterations while MMA needs 15 iterations to reach the solution
9. Conclusion
In this chapter the optimal design of laminated composite structures was considered. After a
review of the literature an optimization method specially devoted to composite structures was
presented. This review helped us in selecting a formulation of the optimization problem that
satisfies the industrial needs. In this context the fibers orientations and the ply thicknesses
were selected as design variables. It was shown on the proposed applications that the
developed solution procedure is general and reliable. It can be used for solving laminated
composite problems including membrane, shells, solids, single and multiple load cases, in