Reliability of composites in a random stress state

A general problem of reliability evaluation of an anisotropic material in a random 2-D or 3-D stress state is considered. Here, reliability is defined as a probability of the material non-failure. Strength characteristics of the material are also considered as random ones and determined by the respective mean values and all possible correlations. In contrast with the existing numerical or approximate methods, a simple analytical approach is offered for evaluating the main statistical characteristics of the reliability. A fundamental idea of the approach consists of analysis of the material's failure envelope in the form of a random linear function of certain non-linear combinations (products) of applied random stresses, instead of the traditional consideration of the envelope as a random non-linear function of the stresses. Thus, the approach allows one to take into consideration all possible kinds of failure envelopes in the simplest analytical form. Analytical expressions regarding calculation of necessary statistical characteristics are presented. Numerical examples of reliability evaluation are considered for unidirectional and laminated composites. (C) 1998 Elsevier Science Ltd. All rights reserved.