Geometrically nonlinear analysis of laminated composite plates using a layerwise displacement model

In this paper the geometrically nonlinear laminated finite element model is developed using the principle of virtual displacements (PVD). The 3D elasticity equations are reduced to 2D problem using kinematical assumptions based on assumed layerwise displacement field of Reddy. With the assumed displacement field, nonlinear Green-Lagrange small strain large displacements relations and linear orthotropic material properties for each lamina, the PVD is used to obtain the weak form of the problem. The weak form or nonlinear integral equilibrium equations are discretized using isoparametric finite element approximation. The nonlinear incremental algebric equilibrium equations are solved using the direct iteration procedure. The original MATLAB computer program is coded for finite element solution and is used to investigate the geometrical nonlinear effects on displacement and stress field of thin and thick, isotropic, orthotropic and anisotropic laminated composite plates with various boundary conditions and the sign of the loading (loading/unloading). The accuracy of the numerical model is verified by comparison with results from the literature and the linear solutions from the previous paper. Appropriate conclusions are derived.