Geometrically Nonlinear Analysis of Laminated Composite Plates subjected to Uniform Distributed Load Using a New Hypothesis: FEM Approach

Document Type: Research Paper


Department of Mechanical Engineering, Sanjivani College of Engineering, Koprgaon,423 603, Savitribai Phule Pune University, Pune, India



This paper presents a finite element method (FEM) for linear and geometrically nonlinear behaviors of cross ply square laminated composite plates subjected to uniform distributed load (UDL) with simply supported boundary conditions (SS-BCs). The original MATLAB codes are written to achieve finite element (FE) solution for bending of the plate. In geometrically nonlinear analysis, changes in geometry takes place when large deflection exist consequently provide nonlinear changes in the material stiffness and this effect on constitutive and equilibrium equations. The Von Karman form nonlinear strain displacement relations and a new inverse trigonometric shear deformation hypothesis are used for deriving the FE model. Here in-plane displacements make a use of an inverse trigonometric shape function to account the effect of transverse shear deformation. This hypothesis fulfills the traction free BCs and disrupts the necessity of shear correction factor (SCF). Overall plate is discretized using eight-noded isoparametric serendipity element. The equilibrium governing equations associated boundary conditions are obtained by using the principle of virtual work (PVW). The numerical results are obtained for central deflections, in-plane stresses and transverse shear stresses for different stacking sequences of cross ply laminates. The results are also computed by FE software ABAQUS for few cases. The obtained results show worthy agreement with previously published results. The results recommend the potential use of new FE model for linear and nonlinear deformations of composite plates.