Nonlinear stability of unsymmetrically laminated angle-ply shear-deformable plates in biaxial compression

The generalized Karman–Reissner equations governing large deflection of unsymmetrically laminated angle-ply shear-deformable rectangular plates are presented in this paper, based upon Karman and Reissner plate theories. Much effort has been concentrated on derivation of the Karman–Reissner equations for the laminates taking account of transverse shear effects so that only two unknown functions for nonlinear analysis need to be treated to gain a precise insight into the complexities; otherwise high-order refined plate theories must be applied. An asymptotic series solution is constructed according to the Karman-type refined theory for postbuckling behavior of the plates with the boundary condition of four edges simply supported. Typical numerical examples are presented for comparison with other nonlinear analytical and experimental results. The effects of shear deformation, lamination angle and geometrical imperfection on buckling and postbuckling behaviors of the laminates subjected to a combination of biaxial compressive loadings are examined for industrial application.