Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility

Abstract

A global numerical technique, the differential quadrature (DQ) method, is examined here for its suitability to solve the boundary-value problem of symmetric cross-ply laminates using the first-order shear deformation plate theory by Whitney and Pagano [J. Appl. Mech.37, 1031–1036 (1970)]. The bending behaviours of symmetric cross-ply laminates, subject to different boundary constraints, are investigated. In this study, the method is used to transform the sets of governing differential equations and boundary conditions of the laminated plates into sets of linear algebraic equations. Boundary conditions along the edges are implemented through the discrete grid points by constraining the displacements, bending moments and rotations. The theoretical formulations and solution procedures of the method are illustrated through solving several numerical examples. The accuracy and validity of the present formulation, if available, are examined by direct comparison with the known values.