连接组合结构协同动力学拓扑优化设计

工程实际结构通常是由多个部件组合而成, 且各部件通过连接构件传递彼此间的载荷和振动能量. 连接构件的布局设计与约束状况对整个结构的拓扑构型、动态性能以及承载能力等均有较大的影响. 本文研究连接组合结构构型与部件间连接构件布局的协同动力学优化问题, 使整体结构在简谐激励作用下动柔顺度达到最小. 以弹簧连接单元模拟连接构件的约束及承载状况, 将承力构件材料的相对密度与弹簧连接单元的相对刚度同时作为设计变量. 在材料体积约束以及连接构件数量约束的条件下, 采用基于梯度的优化算法开展组合结构的拓扑构型与连接构件的布局协同优化设计. 通过与无连接约束构件的单体式结构拓扑优化结果进行对比, 展示了组合结构拓扑构型的变化, 以及连接约束的布局设计对整体材料分布和结构动力性能的影响. 数值结果表明, 虽然组合结构协同优化设计的动柔顺度总是大于单体式结构的结果, 但结构固有频率的变化却具有一定的偶然性, 即可提供更加优越的结构构型与连接布局设计. 

COLLABORATIVE DYNAMICS TOPOLOGY OPTIMIZATION OF COMBINED STRUCTURE

An engineering structure is usually composed of multiple components for carrying loads. Between them, the loads or vibration energies are transferred through the linkage members. Then, the layout and properties of the linkage members have a great influence on the topological configuration, mechanical performance and load-bearing capacity of the entire structure. In this paper, the collaborative dynamic topology optimization of the configuration of the combined structure and the layout of the linkage members between components is studied. A spring connection element is employed to represent the linkage member for its restraint behaviors. With the constraints of the material usage and the linkage member number, the dynamic compliance of the entire structure is pursued for minimization under the external harmonic excitation. By taking the relative material densities of the load-bearing members and the relative stiffness of the spring connecting elements as the design variables, the topological configuration of the combined structure and the layout of the linkage members are optimized collaboratively with use of the gradient-based optimization algorithm. By comparison with the optimal topology designs of the integral structures without linkage members, the topological configuration changes of the combined structure and the influences of the layout of the linkage members are illustrated on both the overall material distribution and dynamic properties. In addition, the dynamic topology optimization of the combined structure is implemented with the linkage members subjectively arranged. Numerical results show that the dynamic compliance of the collaborative optimization results for the combined structures are always greater than the equivalent integral structures. However, the variations of the structural natural frequencies of the combined structures are usually unpredicted mainly due to the changes of the corresponding mode shapes, which can provide a more superior structural configuration and connection layout in the process of the conceptual design stage of a practical structure.