A consistent refined theory for flexure of a symmetric laminate

Abstract

Any two-dimensional plate theory is an approximation of the real three-dimensional elasticity problem. The classical laminated plate theory is based on the Kirchhoff hypothesis and ignores the effects of transverse shear deformation, normal stress, normal strain and nonlinear in-plane normal strain distribution through the plate thickness [ 1,2]. Two types of composite plates are generally identified in practice: (i) 'fibre reinforced laminates' in which layers of composite materials with high ratios of Young's-to-shear modulii are bonded together and (2) 'sandwiches' in which layers of isotropic materials with some layers having significantly lower elastic modulii than others, are bonded together. The effects of shear deformation are significant in these situations and thus the classical theory is inadequate. Exact elasticity solutions for flexure of some standard composite and sandwich plate problems have been obtained by Pagano [ 3] and Pagano and Hatfield [4]. Whitney [5] and Mau [6] have presented first-order laminate theories in which transverse shear strain is assumed constant through the thickness. This required, however, use of a transverse shear correction factor which generally varied with the lamination scheme.