Stochastic bending and buckling analysis of laminated composite plates using Latin hypercube sampling

Deterministic and stochastic bending and buckling characteristics of antisymmetric cross-ply and angle-ply laminated composite plates are thoroughly examined. Partial differential equations for cross-ply and angle-ply laminates are derived using the three variable refined shear deformation theory based on the Hamilton principle. Deterministic Navier’s solutions are obtained for specific boundary conditions and numerical results are validated with the first-order and third-order shear deformation theories. Two stochastic sampling methods, namely Monte Carlo simulation and Latin hypercube sampling, are presented and analyzed to determine the optimal one based on convergence studies and criteria of sampling errors. Comprehensive probability characteristics of stochastic bending deflections and stochastic critical buckling loads of antisymmetric cross-ply and angle-ply laminated composite plates are investigated using the optimal sampling technique. Probability distribution functions of various stochastic cases provide good assessments for the effects of each inevitable source uncertainty on the bending and buckling behaviors of the laminated composites. This study presents a good alternative for the classical and expensive Monte Carlo simulations and provides a fundamental understanding of bending and buckling statistics of laminated composites.