均質化手法による形状,レイアウト最適設計(<特集>最適化の数理)

抄録

The algorithm of shape and layout optimization method using homogenization method is described. The optimal shape and layout design is considered as the optimal distribution of the microstructure with rectangular and rectangular body holes. The continuous distribution of the sizes and rotation angles of the holes are taken as the design variables, which is discretized using the same mesh as finite element mesh used in the structural analysis. The homogenization method are used to compute the equivalent stiffness. As the optimization method the optimality criteria method is used for the computational efficiency, and the formulation in modified to make it possible to use the optimality criteria method. Several examples are shown for the demonstration of the method.