基于应力约束的分布式柔顺机构几何非线性拓扑优化设计方法研究

Compliant mechanisms has a great potential application in micro-electro mechanical systems, precision positioning and precision operation. Topological design of compliant mechanisms may be prone to generate de facto hinges, which results in stress concentration and poor fatigue reliability. One of the key issues to be solved is topology optimization of hinge-free compliant mechanisms with large displacement. In the project, node design variables method and stress constraints will be employed to establish the topology optimization model of hinge-free compliant mechanisms with geometrical nonlinearities. Geometrically nonlinear structural response is obtained using meshless finite element method. The equivalent loads method will be adopted to avoid numerical instabilities during topological design of compliant mechanisms with geometrical nonlinearities. The law of inhibition one-node hinges with stress constraints is explored. In order to consider the impact of the distribution of piezoelectric driven component on mechanical performance of compliant mechanisms, a collaborative design method for layout of hinge-free compliant mechanisms and distribution of piezoelectric driven component is presented considering geometrical nonlinearities and multi-field coupling effects. It can make the micro-nano mechanism system more reasonable and perfect. Prototypes of hinge-free compliant mechanisms will be fabricated and tested to demonstrate the presented design methodology and design theory. The achievements of this project can promote engineering application of compliant mechanisms. It has important theoretical significance and practical application.

柔顺机构在微机电系统、精密定位及精密操作等领域具有广泛的应用前景。基于拓扑优化方法设计柔顺机构容易出现类（单节点）铰链问题，导致应力集中，疲劳可靠性差。大变形的无类铰链分布式柔顺机构拓扑优化设计是目前亟待解决的关键问题。本项目拟采用节点设计变量法进行应力约束的无类铰链分布式柔顺机构几何非线性拓扑优化设计研究，基于无网格有限元法进行结构的几何非线性求解，利用等效静载荷法避免几何非线性拓扑优化迭代过程中数值不稳定性，揭示应力约束抑制类铰链结构的机理；为了考虑压电驱动元件布局对柔顺机构机械性能的影响，考虑几何非线性和多场耦合效应进行无类铰链分布式柔顺机构与压电驱动元件布局协同优化设计，使整个微/纳机械系统的设计更趋合理完善；实际制作和测试优化设计获得的柔顺机构，验证设计方法和理论的有效性。本项目研究成果将为扩大柔顺机构的工程应用具有重要的理论和意义。

柔顺机构在微机电系统、精密定位及精密操作等领域具有广泛的应用前景。基于拓扑优化方法设计的柔顺机构容易出现单节点类铰链问题，导致应力集中现象，疲劳可靠性差。本项目研究了基于应力约束的分布式柔顺机构几何非线性拓扑优化设计方法。采用基于假设密度场的单元势能插值法避免几何非线性拓扑优化出现的数值不收敛问题，利用改进的P范数近似求解机构的最大应力，研究了全局应力约束的柔顺机构几何非线性拓扑优化设计方法，抑制了单节点铰链结构，使得柔度分布及应力更加均匀，分析了不同约束条件对机构构型及性能影响规律；提出了基于混合约束、多性能约束及最小尺寸控制的柔顺机构拓扑优化设计方法，能够获得无类铰链分布式柔顺机构；建立了柔顺机构与压电驱动元件布局协同优化设计模型，实现了同时优化柔顺机构拓扑构型压与电驱动元件布局，获得具有更优性能的机构。引入输入、输出耦合约束，提出了基于应力约束的多自由度柔顺机构拓扑优化设计方法，能够有效地抑制输入耦合和输出耦合效应，且保证机构具有足够的强度。项目研究成果将为扩大柔顺机构的工程应用具有重要的理论和实际意义。