Efficient approximate solutions for postbuckling of axially compressed orthotropic plates with rotationally restrained and free longitudinal edges

This paper presents approximate solutions for the postbuckling behavior of a plate consisting of laminated composites with symmetrical, balanced lay-up loaded in longitudinal compression. The transversal edges of the plate are simply supported, one longitudinal edge is free and the opposite one is rotationally restrained. Key to obtain an explicit and thus highly computational efficient solution is the use of a shape function with only few variables. First, the shape function is inserted into the compatibility condition of in-plane strains to derive a closed-form solution of Airy’s stress function. Then, the equilibrium condition is approximated with the Galerkin procedure yielding a load–deflection relationship. Subsequently, other state variables such as in-plane displacements and stresses can be obtained. Overall, results for displacements and strains show very good agreement with detailed nonlinear finite element analyses.