Shape optimization using weibull statistics of brittle failure

This paper is devoted to the problem of designing mechanical components of brittle materials such as ceramics using the Weibull probabilistic treatment of brittle strength combined with finite element based design optimization and mathematical programming. The analysis of probability of failure using Weibull statistics is introduced and expressions for design sensitivity analysis are derived. The numerical finite element based implementation is discussed, and a numerical example is used to verify the facilities for analysis and design sensitivity analysis. Finally, a shape optimization example of redesigning a cutting bit from a circular saw blade illustrates a design case where the objective is to reduce the probability of failure.