Optimal postbuckling design of variable angle tow composites using lamination parameters

An optimization study is presented for the postbuckling design of orthotropic variable angle tow (VAT) composite plates under axial compression. The postbuckling analysis of a VAT plate is done using a perturbation approach namely, an asymptotic numerical method (ANM) which transforms the nonlinear problem into a set of well-posed recursive linear problems. These linear problems are solved using a generalized differential-integral quadrature method and the postbuckling results are found to be reasonably accurate over a finite load step size around the critical buckling point. The generalized differential-integral quadrature method implementation of the ANM is found to be robust and computationally efficient for evaluating the initial postbuckling solution of VAT plates. Furthermore, the relatively high efficiency of the ANM approach can be used for optimal design of composite plates in the postbuckling region. The postbuckling design criteria of VAT composite plates are based on the minimization of the end shortening strain for a given compressive load. In this work, an efficient two-level optimization framework is used for design of VAT plates that maximizes the postbuckling performance. At the first level, a gradient based optimization algorithm namely, globally convergent method of moving asymptotes is adopted to determine the optimal lamination parameter distributions of the VAT plate. At the second level, a genetic algorithm is used to convert the lamination parameter distributions into realistic VAT layups. The optimization studies are carried out for VAT plates under different in-plane boundary conditions.