A Model of Laminated Composite Plates Assuring the Continuity of Displacements and Transverse Shear Stresses

Abstract

In this paper, we describe a two dimensional model of plates which takes into account a parabolic variation of the transverse shear strains through thikness, so that there is no need to use shear correction coefficients in computing the shear stresses. These properties are very important for the modeling of moderately thick laminated structures. The contribution of the present work is to take into account exactly the contact between the layers of the structure. The present method uses a classic displacement approach for higher-order shear deformation. The form of the displacement, field is dictated by the satisfaction of the following conditions: i) continuity of displacements and stresses at the interfaces; ii) disappearance of the transverse shear stresses on the plate surfaces while non-zero elsewhere. This requires the use of a displacement field in which the inplane displacements are expanded as cubic functions of the thickness coordinate and the transverse deflection is constant throughout the plate thickness. Consequently, the normal transverse deformation is discarded, because we want to have a displacement field which contains the same dependent unknowns as in the first-order shear deformationtheory. So, it is possible to obtain numerical results by a C1 finite element approximation for the displacements. In the same way, a higher-order model with the five classic independent generalized displacements, and which takes the normal transverse deformation into account, involves a C2 finite element approximation for the displacement /1/.