不確定荷重に対する骨組構造のロバスト形状最適化

Abstract

This paper presents a robust shape optimization of frame structures with unknown loadings. The concept of minimizing the maximum compliance called principal compliance is applied to a shape optimization problem of a frame structure. The principal compliance minimization problem is transformed to the equivalent maximization problem of the fundamental eigenvalue of the stiffness tensor, and then formulated as a distributed parameter shape optimization problem. The derived shape gradient function is applied to the H^1 gradient method for frames to determine the optimal shape variation, or the optimal velocity field. With this method, the optimal free-form with smooth curvature distribution of a frame structure can be determined without any shape parameterization. The calculated results show the effectiveness of the proposed method for the robust shape optimization problem of a frame structure with unknown loadings.