STATIC RELIAILITYB ANALYSIS OF STRUCTURES WITH RANDOM PARAMETERS BASED ON NON-ORTHOGONAL POLYNOMIAL EXPANSION

摘要

In this paper,non-orthogonal polynomial expansion whose basis comes from a complete Hilbert space is adopted to describe the response of random structures.Meanwhile,structural system parameters such as material parameters and geometrical parameters (e.g.the thickness of plate),and static loads subjected to are regarded as random quantities.In the solution process of random equations,the first step is that the assumed coefficients of the non-orthogonal polynomial terms are determined through perturbation technique.As the following step,a set of new non-orthogonal polynomial basis is built up based on the initially obtained coefficients.Then the Galerkin projection scheme is employed to find out the coefficients of the redefined non-orthogonal polynomial basis.After the final non-orthogonal polynomial expression of structural response is explicitly obtained,according to the definition of reliability,the failure probability of performance function can be calculated by FORM/SORM as well as Monte-Carlo simulation.In the end,one example is investigated to demonstrate the effectiveness of the proposed approach.