Approximate solution and optimum design of compression-loaded, postbuckled laminated composite plates

The approximate solution for the postbuckling of infinitely long and symmetrically laminated composite plates is obtained by using a simple functional representation for the buckling mode in conjunction with the Galerkin method. The results given by this solution are compared for axial compression in the longitudinal direction with the results given by the nonlinear finite element method for finite length rectangular long plates. Good agreements between the two solutions are obtained for the balanced laminate configurations, and the approximate solution appears useful for design purposes. To determine the optimum design for postbuckling, an optimization is carried out on the approximate solution using lamination parameters as design variables. The objective functions to be minimized are the maximum normal displacement and the strain given by the end shortening in the longitudinal direction. Optimum laminate configurations are determined for layer angles fixed to the common values of 0, 90, 45, and -45 deg. For high postbuckling loads the optimum laminate configurations are cross-ply laminates. When the loads decrease, the optimum laminate configurations become combinations of cross-ply and angle-ply laminates. The optimum laminate configurations for postbuckling problem are different than the optimum laminate configurations for buckling.