Geometrically Nonlinear Analysis of Laminated Composite Plates

Abstract

Abstract. The low mass density and the high tensile strength, usually expressed through the specific modulus of elasticity and the specific strength, have made composite materials lighter and stronger compared with most traditional materials (such as steel, concrete, wood, etc.) and have increased their application not only for secondary, but during the last two decades also for primarily structural members in aerospace and automotive industry, ship building industry and bridge design. Although weight saving has eliminated constrain of slenderness and thickness and has made possible use of very thin plate elements, they have become susceptible to large deflections. In such cases, the geometry of structures is continually changing during the deformation and geometrically nonlinear analysis should be adopted. In this paper the geometrically nonlinear laminated plate finite element model is obtained using the principle of virtual displacement. With the layerwise displacement field of Reddy [1], nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. The obtained displacement dependent secant stiffness matrix is utilized in Direct interation procedure for the numerical solution of nonlinear finite element equilibrium equations. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the previous paper [2].