Nonpolynomial Zigzag Theories for Random Static Analysis of Laminated-Composite and Sandwich Plates

Abstract

The present paper aims to study the random static behavior of laminated composite and sandwich plates using nonpolynomial zigzag theories. The nonpolynomial zigzag theories are proposed earlier by the authors, which satisfy the transverse shear-stress continuity conditions at the layer interfaces including the traction-free boundary conditions on the top and bottom surfaces of the plate. These theories incorporate the realistic nonlinear distribution of transverse shear stresses across the thickness of the plate. A probabilistic procedure is developed using a stochastic finite element method that is in the conjunction of finite element method with a mean-centered first-order perturbation technique, to obtain the second-order statistics of deflections of the laminate. The problem is analyzed considering the material properties of laminated composite and sandwich structures to be random in nature while the other system properties are assumed to be deterministic. The stochastic results in terms of mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, stacking sequences, span–thickness ratios, and boundary conditions and compared with those existing in the literature and Monte Carlo simulation approach.