Modern fracture mechanics for structural optimization with incomplete information

Abstract

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