Improved Shepard's Method for the Optimization of Composite Structures.

Stacking-sequence optimization of laminated composite structures is a combinatorial problem involving discrete variables when ply angles are used as design variables. Such an optimization problem can be solved using genetic algorithms coupled with response surface methods to reduce the computational cost. Alternatively, the optimization problem can be formulated using lamination parameters as design variables, allowing efficient gradient-based optimization methods to be used. Nevertheless, practical stacking sequences have to be reconstructed in a second step, which can be problematic. A synthesis of the two-step approach and the response surface approach to composite design is proposed in this paper. The synthesis is effected by constructing a new multipoint structural approximation scheme based on an innovative use of the classical Shepard's method applied in the space of laminate stiffness. A distance measure in the stiffness space is proposed to adapt the method to composite design. The response surface genetic algorithm optimization is performed starting from a continuous optimum defined by prior continuous optimization. The method is first applied to single-laminate design example problems to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using two patch design examples. [ABSTRACT FROM AUTHOR]