强非线性超弹折纸结构功能化需求的拓扑优化方法研究

Hyperelastic origami structures, having the advantages of flexibility, rigidity, and easy to undergo large geometric deformation, are suitable for flexible machine jaw structures. The design of the hyperelastic origami structure, normally involving a strong nonlinear problem, is usually achieved by empirical methods. Topology optimization method can theoretically produce the effective configuration of the hyperelastic origami structures but involving two major bottlenecks: constructing the optimization model considering the functionality requirement and the element numerical instability problem. The project will systematically develop topology optimization methods for hyperelastic origami structures with functionality requirement in presence of strong nonlinearity. The main work includes that: (1) to propose the constraints for generating and suppressing the multi-hinge and develop the rigid-flexible coupling algorithm for connecting the multi-hinge and the panel. Then the well-posed mathematical optimization formula with cooperative objective function and constraint function is constructed. Therefore, the mathematical modeling of the hyperelastic origami flexible machine claw is achieved; (2) to develop the local hybrid superelement coupling algorithm based on finite element method and meshless method when strong geometric nonlinearity is involved. The finite element iterative computational divergence problem during the continuum topology optimization is solved; (3) to put forward the structural mechanical response and sensitivity solution formats. And based on the established optimization formula, to develop a progressive and parallel robust optimization algorithm for solving the problems of high computational cost and numerical instability; (4) to carry out numerical simulations and experimental verification. The research will promote the development of the topology optimization theory. It can further provide a novel hyperelastic origami structure design method for the robot rigid-flexible coupling mechanism with high performance.

超弹折纸结构兼顾柔性、刚性和易于发生几何大变形等优点，适用于柔性机器爪结构。超弹折纸结构设计涉及强非线性问题，目前依赖于经验设计，而拓扑优化可以从理论上获得有效构型，但两者结合存在两大瓶颈问题：功能化优化建模问题和单元数值不稳定问题。本项目将系统地发展强非线性超弹折纸结构功能化需求的拓扑优化方法，包括：提出多铰链产生和抑制约束，发展多铰链和面板刚柔耦合算法，构建目标函数和约束函数协同的、适定的结构优化数学列式，实现超弹折纸柔性机器爪优化数学建模；基于有限单元和无网格法，发展局部混合超单元耦合算法，解决强几何非线性下连续体拓扑优化过程中结构有限元迭代计算发散问题；发展结构力学响应及灵敏度求解格式，构建并行计算的渐进稳健的优化求解算法，解决非线性拓扑优化计算量大和算法不稳定难题；开展数值模拟和试验验证。项目研究将丰富和发展拓扑优化理论，为高性能机器人刚柔耦合机构设计提供超弹折纸结构设计新方法。

超弹折纸结构兼顾柔性、刚性和易于发生几何大变形等优点，适用于柔性机械爪结构。超弹折纸结构设计涉及强非线性问题，目前依赖于经验设计，而拓扑优化可以从理论上获得有效构型，但两者结合存在两大瓶颈问题：功能化优化建模问题和单元数值不稳定问题。本项目从优化算法、数值模拟和物理试验等方面，考虑材料非线性、几何大变形、超大规模计算自由度等典型力学难题，系统地发展了强非线性超弹折纸结构功能化需求的拓扑优化方法。具体包括：提出了高效和保精度的多分辨率连续体拓扑优化方法，实现了超大规模自由度结构精细化设计；基于多分辨率分析策略和附加超弹技术，发展了新的非线性结构/柔性机构连续体拓扑优化方法，解决了计算成本高和收敛困难两大典型难题；基于三浦折纸的折痕重分配策略，发展了一类具有可剪裁多级刚度的堆叠式折纸机械超材料，并阐明了多级刚度产生的物理机制，即结构不对称刚度和自锁现象；开展了嚼折纸启发的折纸柔性机械爪非线性拓扑优化设计，获得了具有高夹持比、大夹持范围和强夹持适应能力的折纸柔性机械爪，并开展了针对性夹持实验验证研究。本项目研究成果为推动拓扑优化理论在柔性/刚柔耦合机器人领域的应用具有一定价值。