Closed Form Solutions for The Stability and Free Vibration Analysis of Laminated Composite Plates

Abstract

Analytical formulations and solutions to fundamental frequency and buckling loads analysis of simply supported isotropic and layered anisotropic cross-ply composite plates are presented. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes piece-wise linear variation of in-plane displacement components and constant transverse displacement through thickness of the plate. It also includes the quadratic variation of transverse shear stresses within each layer of the plate. The large deflection theory (in Von Karman sense) is incorporated into the buckling analysis. The equations of motion are obtained using Hamilton’s principle. Closed form solution is derived following the Navier’s technique and by solving the eigenvalue problem. The effects of side-to-thickness ratio, aspect ratio, coupling between bending and stretching and number of layers on the fundamental frequencies and critical buckling loads are investigated. The results of the presented theory (GLPT) are compared with the exact 3D elasticity theory, Higher-order Shear Deformation Theory (HSDT) and Classical Laminated Plate Theory (CLPT) solutions. The study concludes that the present model accurately predicts fundamental frequencies and buckling loads of composite plates, while the CLPT is inadequate for the analysis of non-homogeneous laminated plates.