Approximate closed-form postbuckling analysis of shear deformable laminated plates with rotationally restrained edges

Abstract

This paper presents a novel closed-form analytical approach for the buckling and postbuckling behaviour of shear-deformable composite laminated plates under uniaxial compression. The laminates under consideration are assumed to be symmetric, balanced and orthotropic, so that laminate-specific coupling effects do not play a role in the structural response. The laminates are assumed to be simply supported at all edges, while the longitudinal edges are subject to elastic rotational edge restraints. The analysis approach is developed in the framework of three different laminate theories and is based on the formulation of appropriate shape functions for the out-of-plane deflections and the bending angles. The requirement for compatibility of the inplane strains and the balance of forces in the thickness direction govern the given problem in the form of the von Kármán equations, and the first equation is solved in an exact manner for the Airy stress function, while the second equation cannot be solved exactly. Instead, the principle of the minimum of the total elastic potential is used, which eventually leads to a nonlinear equation for the postbuckling amplitude that can be solved in an exact analytical way. The analysis approach is tested on examples of laminated plates and verified with geometrically nonlinear finite element analyses. It is shown that the presented analysis method provides results with excellent accuracy and is able to convincingly reproduce the postbuckling behaviour of laminated plates under compressive load. Since the present approach consists of explicit expressions for all state variables of the plate, the computational effort is negligible.