Optimal postbuckling design of variable angle tow composite plates

Perturbation-based approximation methods are widely used in preliminary design studies of thin-walled structures. In this paper, postbuckling analysis of a variable-angle-tow composite plate is performed using the perturbation-based asymptotic numerical method, which transforms the nonlinear problem into a set of well-posed recursive linear problems. These linear problems are solved using a novel generalized differential-integral quadrature method, and the postbuckling solutions are sought over a finite load step size around the critical buckling point using asymptotic expansions. The accuracy of the asymptotic numerical method in evaluating the initial postbuckling of variable-angle-tow plates under compression is investigated. Subsequently, a novel postbuckling optimization approach based on asymptotic numerical method results is proposed for the design of variable-angle-tow laminates. The postbuckling features obtained from asymptotic numerical method are used in an efficient two-level optimization framework for the design of variable-angle-tow plates. At the first level, a globally convergent method of moving asymptotes is adopted to determine the optimal lamination parameter distributions that maximize the postbuckling performance of the variable-angle-tow plate. At the second level, a genetic algorithm is used to convert the optimal lamination parameter distributions into realistic variable-angle-tow layups. The optimization studies are performed for square variable-angle-tow plates for axial/biaxial compression under different in-plane boundary conditions.