This study deals with the topology optimization (TO) of linear elastic composite structures considering fundamental natural frequency maximization. The concept of functionally graded structures (FGS) is used for anisotropic composite material structure design to improve the structural dynamic performance. The rational approximation of material properties (RAMP) method was employed as an alternative to the solid isotropic material with penalization (SIMP) method to improve the convergence stability for eigen-frequency problem. In the SIMP method, the occurrence of local eigen-modes at low frequencies in the void region causes ill-convergence, whereas the RAMP method prevents local eigen-modes from occurring. The method of moving asymptotes is used as an optimizer. Numerical verification was performed for three structural types: cantilever beam, double-clamped beam, and four-pinned beam structure. In addition, for cantilever beam design, bi-objective optimization for maximizing fundamental natural frequency as well as minimizing structural compliance was performed using the adaptive weighting method that quantitatively reflects the designer's preference by adjusting the weight for each objective function at each iteration.

中文翻译：

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最大化基本固有频率的复合材料结构的多尺度设计

本研究涉及考虑基本固有频率最大化的线弹性复合材料结构的拓扑优化（TO）。功能梯度结构（FGS）的概念用于各向异性复合材料结构设计，以提高结构的动态性能。采用材料特性有理逼近（RAMP）方法作为固体各向同性材料惩罚（SIMP）方法的替代方法，以提高特征频率问题的收敛稳定性。在 SIMP 方法中，空区域中低频局部本征模的出现会导致收敛不良，而 RAMP 方法则可以防止局部本征模的出现。使用移动渐近线的方法作为优化器。对悬臂梁、双夹梁、四销梁结构三种结构类型进行了数值验证。此外，对于悬臂梁设计，使用自适应加权方法进行双目标优化，以最大化基本固有频率并最小化结构柔量，该方法通过在每次迭代时调整每个目标函数的权重来定量反映设计者的偏好。