First Order Reliability Analysis Using Stochastic Finite Element Methods

Abstract

Stochastic finite element methods are suitable for the reliability analysis of components with stochastic material, loading and geometry parameters, which are described by correlated and non-gaussian random variables and random fields. The first order reliablility method (FORM) can be considered for calculating the failure probability. The design point is usually evaluated within FORM by means of an optimization scheme, which requires the gradient of the structural response with respect to the random problem parameters. The large number of random variables of the probabilistic model requires the usage of the adjoint method to obtain this gradient information. The complexity of the mechanical model necessitates the use of commercial finite element codes. In the present contribution the finite element equations of the real and the adjoint problem are derived. Then, these equations are solved with the commercial finite element code ABAQUS. For this purpose, “adjoint elements” are defined for linear-elastic isotropic and anisotropic material behaviour. As an illustration, the proposed method is applied to a model turbine blade.