A stochastic perturbation finite element-least square point interpolation method for the analysis of uncertain structural-acoustics problems with random variables

Abstract

In this paper, a novel stochastic perturbation finite element-least square point interpolation method (SP-FE-LSPIM) is introduced to improve the calculation accuracy for analyzing structural-acoustics problems. Inherited the element-compatibility of finite element method and the quadratic polynomial completeness of LSPIM, the present method obtains the global shape function for partition of unity (PU) and the least square point interpolation for local approximation. Besides, a first-order perturbation technique is also introduced into this theory for probabilistic analyzing. Thus, the response of the coupled systems can be expressed simply as a linear function of all pre-defined input variables by using the change-of-variable techniques. Due to the linear relationships between variables and the response, the probability density function and the cumulative probability density function of response can be obtained based on a simple mathematical transformation of probability theory. So the proposed approach not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also handles the randomness well in the systems. One numerical example for frequency response analysis of random structural-acoustics is presented and verified by Monte Carlo (MC) simulation and stochastic perturbation finite element method (SP-FEM) to demonstrate the effectiveness of the present method.