初期応力下の構造体の固有振動数コントロールを目的とする形状最適化手法

抄録

In this study, a solution to the shape design optimization problem of a 3D structure vibrating with initial stress is proposed, where a set of specified vibration eigenvalues with weighting coefficients is introduced as the objective functional. The eigen-equation with geometric stiffness term and the volume are considered as the constraint functionals. The problem is formulated as a distributed-parameter shape optimization problem, and the sensitivity function with respect to the shape variation is theoretically derived using the Lagrange multiplier method, the material derivative method and the adjoint variable method. The optimal shape variation is determined by the H¹ gradient method, where the shape sensitivity function is applied as a distributed force to vary the shape. The repeated eigenvalue problem is also considered by switching the original objective functional to the repeated one. With the proposed method, the vibration eigenvalue can be controlled to the target without parameterization of the design variables, while maintaining the smoothness of the boundary shape.