Ply optimization of carbon fiber-reinforced plastics laminates based on a gradient-based optimization method with manufacturing constraints

We optimized the number of plies and the stacking sequence of carbon fiber-reinforced plastics laminates using a gradient-based optimization method.To attain industrial relevance and reduce the risk of failure and the cost, certain manufacturing constraints were considered in the optimization.Manufacturing constraints were:1) candidate fiber orientations were limited to a finite set, 2) the bottom layer must be solid;3) an intermediate void was not allowed, and 4) two or three identical contiguous layers were allowed at most.In the optimization, the mass was minimized with stiffness and manufacturing constraints.In order to avoid introducing linear constraints to the optimization model, a material property interpolation scheme called a bi-value coding parameterization scheme was modified and the manufacturing constraints concerning fiber orientation were expressed as nonlinear constraints.Meanwhile, a dispersion constraint and penalty index were introduced to eliminate intermediate variables.The optimization problem was solved by a convex programming dual algorithm.Numerical examples validate the optimization method.