動的コンプライアンス最小化問題に対する3次元バイメタルの界面形状最適設計手法の開発

抄録

Shape design optimization of 3-dimensional solid structures must satisfy two key objectives: high mechanical performance and light weight. For machines in motion, time-response problems in design optimization are crucial for machine life and reliability, requiring optimal time-response characteristics depending on the given objective function. Time-response problems (e.g. the dynamic compliance minimization problem) arise not only in solid structures made of single materials but also in composite structures composed of heterogeneous materials. Heterogeneous composite structures can exhibit excellent mechanical behavior that is unattainable with single-material structures. For example, by using dissimilar materials with different thermal expansion coefficients, it is possible to control thermal displacement through interface shape design optimization between the two different materials. Shape design optimization is also beneficial for reducing the dynamic compliance of solid structures within a limited volume. Bimetals are a type of heterogeneous composite structure consisting of two different adhered metals. In recent years, metal additive manufacturing technology has rapidly advanced, allowing for precise fabrication of metal parts. This study aims to develop a gradient-based interface shape design optimization method for minimizing the dynamic compliance of 3D bimetal composites. First, we formulate the design problem, where the time-dependent dynamic compliance is set as the objective function to be minimized, with the time-response governing equation and the volume constraint serving as the constraint conditions. Then, we theoretically derive the shape gradient function (i.e., the sensitivity function) and perform the velocity analysis to obtain the optimal interface shape between the adhered metals. Furthermore, the effectiveness and feasibility of the proposed interface shape design optimization method are validated through design examples.