A Polynomial Chaos Expansion Based Reliability Method for Linear Random Structures

Abstract

Within the framework of mechanical engineering, reliability assessment is usually involved in the procedure of finite element analysis (FEA) combined with Monte Carlo simulation (MCS). Unfortunately, such approaches require high computational effort. To improve efficiency, we propose a polynomial chaos expansion (PCE) based MCS method for linear random structures, in which the time consuming repeated FEA is avoided in manner of approximating the random response by PCE. However, applications of PCE are always restricted for the first passage problem due to the curse of high dimensionality. To overcome this, we use the convolution form to compute the dynamic response, in which PCE is raised to approximate the modal properties so that the dimension of uncertainties is reduced since only structural random parameters are considered. Four examples are studied to show the effectiveness and relevancy of the proposed method.