所望変形を実現するマルチスケール構造の同時形状最適化

抄録

We propose a novel shape optimization for designing a multiscale structure with desired static deformation. The square error norm between actual and target displacements of the macrostructure is minimized as an objective function. The design variables are the shape variation field of the outer shape of the macrostructure, the interface shape of the macrostructure and the shapes of pores of the microstructures. In this study, the macrostructure is divided into some arbitrary domains, which have independent periodic microstructures. The homogenized elastic tensors are calculated using the asymptotic homogenization method, and apply to the correspondent domains of the macrostructure. The shape gradient functions with the state and the adjoint variables are derived for the shape variation of the macrostructure and the microstructures are introduced, and apply to the H1 gradient method to determine the optimum shapes. The proposed method is applied to a both ends fixed beam and it is confirmed that the objective function decrease to zero, or the desired static deformation can be achieved as expected while obtaining the clear and smooth boundaries.