骨組構造の形状設計のためのフリーフォルム最適化手法

概要

論文の詳細を見る
In this paper, a parameter-free shape optimization method is proposed for designing the smooth optimal free-form of a 3D framed structure. A stiffness design problem where the compliance is minimized under a volume constraint is solved as an example of a shape design problem. The optimum design problem is formulated as a distributed-parameter shape optimization problem under the assumptions that each member is varied in the out-of-plane direction to the centroidal axis and the cross section is prismatic. The shape gradient function and the optimality conditions for this problem are then theoretically derived. The optimal curvature distribution is determined by applying the derived shape gradient function to each member as a pseudo distributed force to vary the frame, while minimizing the objective functional. We call this method the free-form optimization method for frame, a gradient method in the Hilbert space. The validity and practical utility of this method were verified through several design examples. It was confirmed that axial-force-carrying structures was obtained by this method.