Probabilistic structural analysis using a general purpose finite element program

Abstract

This paper presents an accurate and efficient method to predict the probabilistic response for structural response quantities such as stress, displacement, natural frequencies, and buckling loads, by combining the capabilities of MSC/ NASTRAN, including design sensitivity analysis and fast probability integration. Two probabilistic structural analysis examples have been performed and ver ified by comparison with Monte Carlo simulation of the analytical solution. The first example consists of a cantilevered plate with several point loads. The random variables are the plate thickness and modulus of elasticity. The quantity of interest is the probabilistic distribution of the tip displacement. The second example is a probabilistic buckling analysis of a simply supported composite plate under in-plane loading. The random variables are the ply material properties, orientation angles, and thickness. The coupling of MSC/ NASTRAN and fast probability integration is shown to be orders of magnitude more efficient than Monte Carlo simulation with excellent accuracy.