接触式柔顺机构非线性拓扑优化设计研究

Contact-aided compliant mechanisms can exhibit complicated non-smooth oupt paths characteristics similar to rigid-body mechanisms with a promising prospect in the field of precision positioning and precision manipulation. One of the key issues to be solved is topology optimization of large displacement contact-aided compliant mechanism which is a highly nonlinear optimization problem. In the project, the equivalent loads method will be employed to make the highly nonlinear response of large dsiplacement contact structure be equivalent to the linear structural response with multiple loads. Thus, the sensitivity of the large displacement contact structural response will be solved conveniently. We will explore the methodology of topology optimization of contact-aided compliant mechanisms with geometrical nonlinearites using the ground structure approach. In order to obtain better mechanical performance, topology optimization of large displacement contact-aided compliant mechanisms using multiple material will be presented. We will explore the internal relationship between the multiphase material factors and the mechanical performance.The influence law of the selection of multiple materials on the mechanical performance will be researched. The integrated topology, shape and size optimization method will be adopted to design contact-aided compliant mechanisms. Prototypes of contact aided compliant mechanisms will be fabricated and tested to demonstrate the presented design methodology and design theory.This research achievements will have important theoretical significance and practical application that compliant mechsisms can achieve non-soomth output paths precision manipulation.

接触式柔顺机构具有类似刚体机构复杂非光滑的输出轨迹特点，在精密定位及精密操作等领域具有广泛的应用前景。高度非线性的大变形接触式柔顺机构拓扑优化设计是目前亟待解决的关键问题之一。本项目采用等效载荷方法，将大变形接触结构复杂的高度非线性响应等效为多载荷作用的线性结构响应，使大变形接触结构响应的灵敏度容易求解，探索基于基础结构法的接触式柔顺机构非线性拓扑优化设计方法；为了获得具有更优整体性能的机构，建立基于多相材料的接触式柔顺机构非线性拓扑优化模型，探索多相材料因素与柔顺机构性能之间内在的关系，揭示多相材料的选取对机构性能的影响规律；采用拓扑、形状及尺寸集成综合优化方法进行大变形接触式柔顺机构优化设计研究；进行接触式柔顺机构性能测试，验证设计方法和理论的有效性。项目成果对柔顺机构实现复杂非光滑轨迹的精密操作具有重要的理论意义和应用价值。

柔顺机构在精密定位及精密操作等领域具有广泛的应用前景，本项目深入系统研究了接触式柔顺机构拓扑优化设计理论和方法。对于接触结构的高度非线性响应求解，采用Newton-Armijo方法求解接触边界的结构系统平衡方程，建立了接触边界条件拓扑优化的数学模型；进行了接触式柔顺机构拓扑优化设计研究；针对柔顺机构拓扑优化结果出现网格依赖性及单节点现象，提出了一种基于节点设计变量法的柔顺机构拓扑优化设计方法，在指定的子区域内，采用不依赖网格的映射函数表示节点设计变量与节点密度变量的关系，实现最小尺寸约束，有效避免了单节点等数值不稳定性现象；为了集成不同材料的优越特性提升机构性能，建立了多相材料插值数值模型，提出了一种改进的过滤技术进行修改灵敏度，进行多相材料柔顺机构拓扑优化设计研究，结果表明弹性模量大的材料主要分布在变形小的区域，弹性模量小的材料主要分布在变形大的区域，能够提升机构的机械性能，并且在一定条件下弹性模量比值的增加可以获得更好的性能的机构构型；研究了柔顺机构集成综合优化设计方法，对获得最优构型的机构拓扑图进行了光滑边界处理，并搭建了柔顺机构性能测试的实验平台，并进行了柔顺机构性能测试研究，对理论研究的正确性进行了验证。本项目研究成果为扩大柔顺机构在精密定位及精密操作等工程领域的应用具有重要的理论意义和应用价值。