Extensions of the shape functions with penalization parameterization for composite-ply optimization

The extensions of the shape functions with penalization parameterization for composite-ply optimization, was examined. The shape functions of a hexahedral element were used to define the weighting factors, with an exponent p to avoid the mixtures of candidate materials at the solution. Three design variables were enough to select the optimal ply in a set of eight candidates, what significantly decreases the size of the optimization problem compared with discrete material optimization (DMO), which would require eight design variables. The parameterization for the eight candidate orientations could be altered in order to propose solutions for less than eight candidate materials. The optimization problems consisted to maximize the global in-plane structural stiffness of a nonhomogeneous composite membrane, in a linear static analysis. The sensitivities were computed by finite differences.