Modern fracture mechanics for structural optimization with incomplete information

Abstract

Questions described in this paper are concerned with shape optimization of brittle or quasi-brittle (axisymmetric) elastic shells. These questions take into consideration possibilities of crack arising and damage accumulation in process of application of cyclic load to shell structure. Initial structural defects, arising cracks and damage accumulation are characterized by incomplete information concerning initial crack sizes, crack position and its orientation. In this context we develop statements of optimization problems based on guaranteed approach for considered problems with incomplete information. For many realistic cases it is reasonable to use variants of mini-max optimization, named as optimization for the worst case scenario. Considered in this paper structural optimization problems consist in finding of shape and thickness distribution of axisymmetric quasi-brittle elastic shells with arising cracks in such a way that cost functional (volume or weight of shell material) reaches minimum, while satisfying some constraints on stress intensity factor and geometrical constraints. In case of cycling loadings, we consider number of loading cycles before fracture as main constraint.