Hybrid perturbation-Galerkin methods for structural reliability analysis

A major challenge in the reliability analysis of complex structures is to determine the response function or surface from which the limit state function can be established and hence the failure probability of the structure can be predicted. The intention of this paper is to propose a new class of hybrid perturbation-Galerkin methods to determine the response function (surface) of the structure. The proposed methods, mainly including single-variable and double-variable approximations, are based on a combination of the perturbation technique and Bubnov-Galerkin projection, where various orders of summation terms of power polynomial expansions are used as the Galerkin trial functions or basis vectors. A series of examples is provided to demonstrate the accuracy and efficiency of the proposed method by comparison with various existing methods. It is found from the numerical examples that with a significantly lower computational effort with respect to the existing reliability methods, very accurate results can be obtained by the proposed methods.