Failure Probability Evaluation of an Anisotropic Brittle Structure Derived from a Thermal Stress Solution

Abstract

A method is presented which will allow the failure probability of a brittle structure to be evaluated from a thermal stress solution. It is based on a statistical approach, a generalisation of the simple Weibull distribution, and takes into account material variability, component size and anistropic strength. The principal stress values at the nodes of a finite element mesh are assumed to be known for the structure. The stress distribution within each element is then expressed in terms of these nodal values through suitably derived shape functions. Certain stress volume integrals are evaluated and the failure probability of each element, and hence that of the whole structure, is calculated. The accuracy of the method is assessed for various types of finite elements by analysing a simple structure.