Finite Element Model for the Static Analysis of Laminated Composite and Sandwich Plates

Abstract

Finite element model for the static analysis of laminated composite and sandwich plates, based on Generalized Laminate Plate Theory (GLPT) is presented in this paper. Within each layer, the theory assumes piece-wise variation of in-plane displacement components, constant transverse displacement component and parabolic distribution of shear stresses, thus accurately modeling the warping of cross section and including the effects of transverse shear deformation. Transverse shear stresses satisfy Hook’s low, 3D equilibrium equations and traction free boundary conditions. Using the assumed displacement field, linear strain-displacement relations and 3D constitutive equations of lamina, equilibrium equations are derived according to the principle of virtual displacements. In the finite element formulation, in-plane displacement components are through the thickness approximated using two-node linear 1D Lagrangian finite element, while the four and nine node 2D Lagrangian elements are used for approximation of displacements in plane. Numerical results for bending stresses, transverse shearing stresses and displacements are presented, showing the parametric effect of plate aspect ratio, side-to-thickness ratio, lamination angle schemes and degree of orthotropy. The accuracy of the results is verified with the 3D elasticity theory, Higher-order Shear Deformation Theory (HSDT), First-order Shear Deformation Theory (FSDT) and Classical Laminated Plate Theory (CLPT) available in the literature. It has been shown that GLPT finite element gives excellent agreement with 3D elasticity theory and may be used in the future linear and nonlinear analysis of laminated composites.