Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties

Abstract

This paper presents two efficient modal approaches as an alternative to direct formulations for the time-harmonic dynamic analysis of structures with random material and shape parameters. In both approaches, the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters. The modal perturbation stochastic finite element method (SFEM) then condenses the response sensitivities to assess the response variability. The mixed perturbation/Monte-Carlo SFEM assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions (PDFs). Geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis. Two numerical applications examine both approaches in terms of accuracy, variability level and computational requirements. The applications involve a plate bending problem with random Young modulus or edge length and a plate with a random flatness default. Particular observations related to the influence of the parameter PDFs in simulation-based methods are also provided.