Static analysis of cross-ply laminated composite plate using finite element method

Abstract

Finite element Analysis is carried out to perform static analysis on a cross-ply laminated composite square plate based on the First order Shear Deformation Theory (FSDT). The theory accounts for constant variation of transverse shear stresses across the thickness of the laminate; and it uses a shear correction factor. The element formulated is an 8-noded iso-parametric quadratic (Serendipity) element. In this analysis, the square plate is analyzed for transverse loading viz., sinusoidal varying load and uniformly distributed load under simply supported boundary conditions. A program is written in MATLAB to obtain the finite element solutions for transverse displacements, normal stresses and transverse shear stresses. Solutions are obtained for 3, 4 and 5 layers of the laminate with cross-ply orientation for different values of side to thickness ratios. Reduced integration scheme is adopted to alleviate shear locking effects. Stresses are found at Gauss points from constitutive relations. The solutions are compared with closed form solutions of FSDT, 3D elasticity solutions and Classical Laminate Plate Theory (CLPT) solutions. It is observed that the results are in close agreement with the available solutions. The element being a C 0 continuous element, it ensures the continuity of generalized displacements only; not strains and thus stresses. The model is validated by its good convergence with the analytical results. Analysis can be done on thin as well as moderately thick plates satisfactorily by using this model.