A plate bending element based on a generalized laminate plate theory

Abstract

.( SUMMARY A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions ofthe generalized plate theory and the 3D-elasticity theory. The element accounts for transverse shear deformation and layer­ wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented. 1. BACKGROUND Laminated composite plates are often modelled using the classical laminate plate theory (CLPT) or the first-order shear deformation plate theory (FSDT). In both cases the laminate is treated as a single-layer plate with equivalent stiffnesses, and the displacements are assumed to vary through the thickness according to a single expression (see Reddy 1 ), not allowing for possible discontinuities in strains at an interface of dissimilar material layers. Recently, Reddy2 presented a general laminate plate theory that allows layer-wise representation of inplane displacements, and an improved response of inplane and transverse shear deformations is predicted. Similar but different theories have appeared in the literature. 3-6 In the generalized laminate plate theory (0LPT) the equations of three-dimensional elasticity are reduced to differential equations in terms of unknown functions in two dimensions by assuming layer-wise approximation of the displacements through the thickness. Consequently, the strains are different in different layers. Exact analytical solutions of the theory were developed by the authors 7 ,8 to evaluate the accuracy ofthe theory compared to the 3D-elasticity theory. The results indicated that the generalized laminate plate theory allows accurate determination ofinterlaminar stresses. The present study deals with the finite-element formulation of the theory and its application to laminated composite plates. In the interest of brevity only the main equations of the theory are reviewed and the major steps of the formulation are presented. The accuracy of the numerical