Composite structures optimization using sequential convex programming

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described. Several modifications of these approximations are presented. They are now based on gradient information at two successive iterations, avoiding the use of the expensive second-order derivatives. A two-point fitting scheme is also described, where the function value at the preceding design point is used to improve the approximation. Numerical examples compare these new purely non-monotonous schemes to the existing ones for the selection of optimal fibers orientations in laminates. It is shown how these two-point based approximations are well adapted to the problem and can improve the optimization task, leading to reasonable computational efforts. A procedure is also derived for considering simultaneously monotonous and nonmonotonous structural behaviors. The resulting generalized approximation scheme is well suited for the optimization of composite structures when both plies thickness and fibers orientations are considered as design variables. It is concluded that the newly developed approximation schemes of the MMA family are reliable for composite structures optimization. All the studied approximations are convex and separable: the optimization problem can then be solved using a dual approach.

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