Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects

Abstract

An accurate three dimensional elasticity solution for rectangular laminated plates subjected to Levy-type boundary conditions is presented using the recently developed mixed-field multi-term extended Kantorovich method (EKM) in conjunction with Fourier series. Such a solution accurately characterizes the edge effects in finite laminated plates under general bending, which can be used as a benchmark for assessing two-dimensional (2D) laminate theories for predicting of edge effects. The variables are expanded in Fourier series along the direction intersecting the simply-supported edges, and the 3D EKM is applied for the inplane and thickness directions. Using the Reissner-type variational principle, the governing partial differential equations are converted into two sets of 9n algebraic-ordinary differential equations for each Fourier term. The boundary conditions are satisfied exactly at all points on the boundaries. It is shown that similar to the case of cylindrical bending of infinite panels, the present solution for the general bending of finite plate also converges within two or three terms in the trial function. The numerical results are presented for composite and sandwich plates with four different boundary conditions. The effect of aspect ratio and width to length ratio on the boundary layer effect in the in-plane and interlaminar stresses are investigated.