Levy-type finite element analyses of vibration and stability of thin and thick laminated composite rectangular plates

Abstract

Abstract Levy-type (semi-analytical) finite element analyses of free vibration and stability of laminated composite rectangular plates based on both classical and first-order shear deformation theories are presented. In this finite element version, discretization occurs in one coordinate direction (say the y-axis), leaving the behavior in the x-direction and in time undetermined at the outset. In this formulation, arbitrary boundary conditions may be imposed on the two opposite ends of the plate in the y-direction. Hamilton's principle is used to derive the stiffness, mass and initial stress matrices that enter into the equations of motion. Periodic solution forms are taken in the x-direction, whereupon the analyses take the form of algebraic eigenproblems from which the frequencies and critical buckling loads may be extracted. To illustrate the method as well as the effect of transverse shear deformation on the frequencies and the buckling loads, a series of two- and three-layer regular cross-ply and angle-ply laminated composite square plates were analyzed. The influence of shear deformation for the material considered was shown to be quite considerable at plate thickness/length ( H a ) ratios of 0.05 and higher.