Stress and Displacement Analysis of Composite Laminated Plates

Abstract

Multilayered composite plates are of interest for a variety of structural applications in such industries as automotive and aerospace, where high strength-to-weight ratios are desirable. In this investigation a series of plate elements is developed for such structures. These plate elements are formulated based on a variational principle, namely modified complementary energy. Mindlin thin plate theory is selected to govern the general characteristics and behavior of these plates. Transverse shear deformation is included in the formulation. A series of in-plane strain functions is assumed from which the corresponding in-plane stresses for each lamina are determined. By satisfying the equilibrium equations, the transverse stresses are calculated. The strain parameters can be determined by satisfying the interlaminar transverse stress continuity and the traction-free condition at the bottom surface. The top traction-free condition is ignored in this formulation. It will be demonstrated that the impact of ignoring the top traction-free condition on the results is negligible.Eight-node isoparametric elements with five degrees of freedom per node are utilized to describe the displacement field. These elements are invariant, fast converging, and insensitive to the number of gauss points used in the numerical integrations. Moreover, it will be shown that these elements do not exhibit any shear locking in the thin plate limit. These elements are capable of handling the effects of transverse shear deformation, extensionbending, twisting-extension, and twisting-bending coupling that exist due to the different orthotropic material properties of each layer. It will also be demonstrated that these elements are capable of adequately predicting the displacements and the stresses for a variety of composite plate problems.