Fast analytical method describing the postbuckling behavior of long, symmetric, balanced laminated composite plates under biaxial compression and shear

The present work deals with the postbuckling behavior of an infinitely long plate consisting of laminated composites with symmetrical, balanced lay-up. Along the longitudinal edges the plate is elastically clamped with torsional springs. As loading situation combinations of biaxial compression and shear are accounted for. Aiming at high computational efficiency the problem is solved by variational methods employing a shape function with only few variables. Inserting the shape function into the compatibility condition of in-plane strains, a closed-form solution for the Airy stress function can be obtained. The resulting equilibrium condition is then used to derive the load–deflection relationship by means of the Galerkin procedure. All other state variables such as displacements and stresses can then be calculated. Comparative finite element analyses reveal that apart from the cases involving transversal compression, where the application should be handled with care, the present solution procedure can serve to obtain good approximations of the stability behavior in the early postbuckling region with negligible computational effort.