Spectral stochastic finite element analysis for laminated composite plates

A spectral stochastic finite element formulation with consideration of multi-layer effect and spatial variability of material properties is developed for probabilistic analysis of laminated composite plates. The material properties of each lamina are modeled as a set of random fields and represented by the Karhunen–Loève expansion. The expansion is incorporated into a spatial discretization in accordance with a standard finite element procedure based on the first-order shear deformation theory. A spectral expansion with use of polynomial chaos is employed to represent the stochastic nodal displacements in terms of standard normal random variables. A preconditioning matrix is then proposed for the solution of spectral stochastic finite element equations with use of a preconditioning conjugate gradient technique. The various statistics of interest of the system responses are finally obtained by means of the coefficients of the spectral expansion. The numerical accuracy and the computational efficiency of the method are demonstrated by comparison with Monte-Carlo simulation.