基于并行策略的多材料柔顺机构多目标拓扑优化*

多材料柔顺机构能够让设计者充分利用各种材料的优良属性，在力，位移，以及能量转移等方面获得更大的设计自由度，因而受到重视。针对受到广泛研究的柔顺机构，结合多目标拓扑优化的方法，提出相应的基于并行策略的求解模型。该方法的核心是将一个复杂的多材料多目标问题离散成为单材料子问题，然后并行求解，再根据整体目标的需要，对所有子问题的解进行调整以得到原始问题的解。针对多目标情形，提出新的材料与输出目标关系，从而在将多材料问题离散成单材料子问题的同时，也将多目标问题离散成单目标子问题。对所有的单材料单目标子问题采用各向同性材料的刚度插值-惩罚法并行独立求解。以上方法有其独特优势：在理论和实践上都比较简单，可以处理任意多种材料，可以避免零碎的拓扑结构因而有利于制造。通过算例说明了此方法的有效性。研究结果表明，该方法在某些输出需要特定材料的设计场合更具优势。

Multi-objective Topology Optimization of Multiple Materials Compliant Mechanisms Based on Parallel Strategy

Compared to single-material mechanisms, multi-material mechanisms design enables designers to fully exploit the advantages of different materials and achieve more design freedom in force, motion, and energy transduction. A new multiple objective topology optimization for multiple materials compliant mechanisms is presented. Central to the method is a parallel penalization that works by decomposing an overall multi-material optimization into a series of single material optimization and coordinating the sub-optimization so that the joint solution is optimal for the overall system. A new material and objective corresponding relationship is proposed to ensure that each sub-problem contains only one objective. The single-material optimization sub-problems are accomplished by the solid Isotropic material with penalization (SIMP) method. The overall procedure has its unique benefits: it is simple in concept and practice; it is flexible to handle an arbitrary number of candidate materials; it can avoid fragile topologies and is therefore advantageous for manufacturing. Several numerical examples are given to illustrate the effectiveness of the proposed method. The results show that the proposed method is more effective in the design of specific materials.