Abstract
The problem of optimal design for quasi-brittle elastic bodies with cracks is considered in cases of static and cyclic loading. Optimization problems considered consist of rinding the boundary of a body such that the optimized functional (volume of the body) attains an extremal value, while satisfying prescribed bounds on stress intensity factors and minimum number of cycles (structural durability). Such problems are characterized by incomplete information concerning crack size, location, and orientation. In this context, the paper presents some possible formulations of optimal structural design problems based on minimax (guaranteed) approaches. Using these approaches, optimal designs are obtained for beams and plates with surface and internal cracks.
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