Nonlinear analysis of imperfect laminated thin plates under transverse and in-plane loads and resting on an elastic foundation by a semi-analytical approach

The large deflection and postbuckling behavior of imperfect composite laminated plates exposed to a combined action of transverse loads and in-plane edge compressions and resting on an elastic foundation are investigated in this paper by a semi-analytical approach. The formulations are based on the classical laminated plate theory (CLPT), and include the plate–foundation interaction effects via a two-parameter model (Pasternak-type) from which Winkler elastic foundation can be recovered as a limiting case. The present approach employs a perturbation technique, one-dimensional differential quadrature approximation and the Galerkin procedure to model the nonlinear performance of the plate with arbitrary combination of simply supported, clamped or elastic rotational edge constraints. Studies concerning its accuracy and convergence characteristics are carried out through some numerical illustrations. Effects of foundation stiffness, plate aspect ratio, total number of plies, fiber orientation, initial geometrical imperfection, the character of boundary conditions, and load patterns on the nonlinear behavior of the plate are studied. Typical numerical results are given in dimensionless graphical forms.