Geometrically Nonlinear Analysis of Laminated Composite Plates subjected to Uniform Distributed Load Using a New Hypothesis: the finite element method (FEM) Approach

This paper presents a finite element method (FEM) for linear and geometrically nonlinear behaviours of cross ply square laminated composite plates (LCPs) subjected to a uniform distributed load (UDL) with simply supported boundary conditions (SS-BCs). The original MATLAB codes were written to achieve a finite element (FE) solution for bending of the plate. In geometrically nonlinear analysis, changes in geometry take place when large deflection exists to consequently provide nonlinear changes in the material stiffness and affect the constitutive and equilibrium equations. The Von Karman form nonlinear strain displacement relations and a new inverse trigonometric shear deformation hypothesis were used for deriving the FE model. Here, in-plane displacements made  use of an inverse trigonometric shape function to account for the effect of transverse shear deformation. This hypothesis fulfilled the traction free BCs and disrupted the necessity of the shear correction factor (SCF). Overall the plate was discretized using the eight-node isoparametric serendipity element. The equilibriums governing equations associated boundary conditions were obtained by using the principle of virtual work (PVW). The numerical results were obtained for central deflections, in-plane stresses and transverse shear stresses for different stacking sequences of cross ply laminates. The results were also computed by the FE software ANSYS for limited cases. The results obtained showed an acceptable agreement with the results previously published. The findings suggested the future use of a new FE model for linear and nonlinear laminated composite plate deformation.