A Mixed Finite Element for the Nonlinear Bending Analysis of Laminated Composite Plates Based on FSDT

Abstract

A mixed finite element model for the nonlinear bending analysis of laminated composite plates is presented. The finite element model is obtained using a mixed variational formulation of the first-order shear deformation theory of plates in which displacements and bending moments are treated as independent fields. A p-type Lagrangian basis is used to approximate the nodal degrees of freedom that consist of three displacements, two rotations, and three moment resultants. The geometric nonlinearity in the sense of the von Kàrman is included in the plate theory. The mixed plate element developed herein is employed in the linear and nonlinear bending analysis of a variety of layered composite rectangular plates. The effects of transverse shear deformation, material anisotropy, and bending-stretching coupling on deflections and stresses are investigated. The predictive capability of the present model is demonstrated by comparison with analytical, experimental, and numerical solutions available in the literature. The model provides an accurate prediction of the global bending response of thin and moderately thick plates subjected to moderate and moderately large rotations. The inclusion of the bending moments at the nodes results in increased accuracy in the computation of stresses over those determined by conventional displacement-based finite element models.