Composite Materials Research Progress

Optimization of Laminated Composite Structures… 95
first buckling load λ1 over the iterations are plotted, as well as some characteristic buckling
modes.
Figure 8.20. Convergence history for the buckling optimisation with Conlin (left) and SAM (right)
Bruyneel et al. (2007)
It is seen that when Conlin is used (Figure 8.20, left) a solution can not be reached. With
SAM (Figure 8.20, right), the solution is obtained after an erratic convergence history. Those
oscillations come from the fact that local buckling modes appear during the optimisation
process, and some parts of the structures are no longer sensitive to this criterion. A small
thickness is therefore assigned to those parts to decrease the weight, what makes them very
sensitive to buckling at the next iteration, leading to oscillations of the design variables and
functions values. It was observed in Bruyneel et al. (2007) that when a large number of
buckling loads are used in the optimization problem (say 100 for the problem of Figure 8.20),