Finite element analysis of shells with multiple random material and geometric properties

Abstract

A stochastic formulation of the triangular composite facet (TRIC) shell element has been presented for the case of shell structures with multiple uncertain material and geometric (thickness) properties. These properties are described by statistically independent two-dimensional homogeneous stochastic fields. The majority of work done in the context of stochastic finite element analysis is based on the assumption that only one material property is described by a stochastic field, for example, the assumption is often made that the elastic modulus is varying over space in a random manner, while Poisson's ratio is a deterministic constant. The stochastic finite element analysis of the shell structures is performed using the spectral representation method for the description of the random fields in conjunction with Monte Carlo simulation (MCS) for the computation of the response variability. Useful conclusions regarding the influence of each one of the structural parameters on the displacement variability are derived from the numerical tests are also examined in the chapter.