We consider the probability of failure for components made of brittle mate-rials under one time application of a load as introduced by Weibull and Batdorf- Crosse and more recently studied by NASA and the STAU cooperation as anobjective functional in shape optimization and prove the existence of optimalshapes in the class of shapes with a uniform cone property. The correspondingintegrand of the objective functional has convexity properties that allow toderive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). Theseproperties require less restrictive regularity assumptions for the boundariesand state functions compared to [arXiv:1210.4954]. Thereby, the weakformulation of linear elasticity can be kept for the abstract setting for shapeoptimization as presented in the book by Haslinger and Maekinen.
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