Large Deflection of Unsymmetric Cross-Ply and Angle-Ply Plates

Abstract

An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total number of layers. The present third approximation is in good agreement with the existing solutions for large deflections of isotropic and unsymmetric angle-ply plates having the ratio of central deflection to thickness up to the value of 2.