Response‐Surface Approach for Reliability Analysis

TLDR

The method targets structural and mechanical systems with spatially random geometrical and material properties. The paper introduces a stochastic finite element method. It employs a polynomial response‑surface expansion of the nonlinear structural operator, incorporating property‑specific error factors and requiring carefully designed experiments to identify model parameters. A numerical example on a light‑water reactor pressurized vessel demonstrates the method’s ability to compute stresses and strains via stochastic 3‑D finite‑element nonlinear analysis.

Abstract

The present paper introduces and discusses a stochastic finite element method. It can be used for the analysis of structural and mechanical systems whose geometrical and material properties have spatial random variability. The method utilizes a polynomial expansion of the numerical nonlinear structural operator (for which actual analytical form is unknown). The expansion is made according to a response‐surface approximation in terms of spatial averages bf the design variables. The polynomial form is then modified by suitable error factors, one for each geometrical or mechanical property. Each error factor is due to the deviations, of the single property, from its spatial average in the different finite elements. The method demands an accurate design of the experiments to be conducted in order to identify the model parameters. A numerical example has been worked out. In this numerical example, the stresses and the strains in a light‐water reactor pressurized vessel are computed by a stochastic three‐dimensional finite element nonlinear analysis.