Shape optimization of ceramic components using a failure probability based on extended multiaxial Weibull theory

For the design of components made of ceramic materials, a failure probability based on extended multiaxial Weibull theory is used. In the present paper, this failure probability is used as objective function in the framework of shape optimization performed by derivative-free and gradient-based numerical optimization. The failure probability is computed with three levels of complexity of the underlying fracture mechanics crack model: for the assumption of a locally constant or inhomogeneous stress field along the crack in a semi-infinite plane and for a locally inhomogeneous stress field along the crack in a plate. The sensitivity analysis of the failure probability is presented in detail. Finally, a numerical example assesses the effectiveness of both types of optimization algorithm.