考虑可制造性约束的声子晶体多目标拓扑优化

对声子晶体进行拓扑优化可得到具有目标带隙特性的声子晶体结构, 在减振、隔声等领域具有潜在应用价值. 然而, 优化结果常会出现孤立材料单元而导致的制造困难问题. 针对该问题, 本文提出协同考虑带隙性能和可制造性约束的二维多相声子晶体多目标拓扑优化方法. 以在特定频率段带隙最宽和结构质量最小为优化目标, 在对微结构进行连通性分析的基础上, 引入考虑可制造性因素的附加约束, 并利用有限元法和具有精英选择策略的非支配排序遗传算法对该优化模型进行数值求解. 通过数值算例验证了本文模型及方法的合理性和有效性. 结果表明, 附加可制造性约束的拓扑优化模型可有效避免二维声子晶体构型中出现孤立材料单元的情况, 优化结果在满足带隙性能预期指标的同时也可兼顾到实际可制造性要求. 与仅仅考虑带隙性能的单目标优化结果相比, 本文提出的同时兼顾带隙性能和可制造因素的多目标优化模型可以针对实际应用和制造条件, 实现不同目标间的平衡, 具有显著优势和良好的应用前景. 

MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION OF PHONONIC CRYSTALS CONSIDERING MANUFACTURING CONSTRAINT1)

Topology optimization of phononic crystals can achieve the structures with the targeted band-gap characteristics, which provides potential applications in the vibration reduction and sound insulation. However, the topology optimization results of phononic crystals often have isolated material elements, which are rather difficult to be manufactured. In this paper, a manufacturing-constrained topology optimization model considering both the band-gap performance and the manufacturability for the multi-objective topology optimization of two-dimensional (2D) multi-phase phononic crystals is proposed. The objective functions for maximizing the band-gap width in a specified frequency range and minimizing the structural weight are established. The manufacturing constraint is additionally introduced based on the connectivity analysis of the micro-structures of the constituent materials. The optimization problem is solved by the finite element method (FEM) and the non-dominated sorting genetic algorithm II (NSGA-II). The rationality and effectiveness of the proposed model and strategy are demonstrated by representative numerical examples. The results show that the isolated material elements can be avoided effectively by introducing an additional manufacturing constraint. Moreover, the optimized results can ensure both the band-gap performance and the manufacturability requirement. Compared with the results of the single-objective optimization (SOOP), the multi-objective optimization (MOOP) shows great advantages, since it can obtain non-dominated solution sets and achieve a balance between different optimization objectives.