Shell Optimization under Constraint on Damage Accumulation

The optimization problems taken into consideration consist in finding the shape and thickness distribution of brittle or quasibrittle elastic shells with cracks, loaded by fixed statical forces in such a way that the cost functional (volume of the shell material or weight) reaches a minimum, while satisfying some fracture mechanics constraints. As constraints we use bounds on stress intensity factors or structural longevity. In the case of cycling loadings we consider the number of cycles before fracture as the constraint for optimization problem. Considered optimization problems are characterized by incomplete information concerning initial crack size, crack location and its orientation. In this context the paper presents some possible formulations of optimal structural design problems, based on guaranteed (minimax) and probabilistic approaches. Some examples of analytical and numerical solutions are presented.