New non-intrusive stochastic finite element method for plate structures

Abstract

Currently, several intrusive stochastic finite element methods (SFEMs) such as perturbation method and spectral SFEM are widely applied for stochastic response analysis of continuous structures. However, the intrusive SFEMs need to modify conventional finite element formulations to establish the stochastic stiffness matrix, and cannot calculate the probability density function of structural response and the reliability straightforwardly. This paper proposes a new non-intrusive SFEM for efficiently computing stochastic responses and reliabilities of plates in a unified way. Firstly, the direct probability integral method (DPIM) is developed to obtain the probability density function of stochastic response by solving probability density integral equation (PDIE). Secondly, the non-intrusive SFEM based on DPIM decouples the deterministic finite element analysis and PDIE to calculate the stochastic responses and reliabilities of uncertain plate structures, and the discretization and quantification of random fields of elastic modulus and thickness are implemented through Karhunen-Loève expansion. Finally, several examples of uncertain Kirchhoff and Mindlin plates demonstrate the efficiency and versatility of the proposed non-intrusive method by comparing with the results from Monte Carlo simulation and literature. The effects of correlation length, mean and variability of random field on the probability distribution of responses and the reliabilities of plates are revealed. For Gaussian random thickness, the linearly elastic plate yields non-Gaussian distributed responses. Increasing the correlation length and variability of random field reduces the reliabilities of plates.