基于成对曲线组合的柔顺机构形状与拓扑优化设计研究

This project will conduct systematic research on compliant mechanism design by structural topology optimization using pairs of curves. In this work, a novel representation scheme is presented. The representation scheme is characterized by pairs of curves, that are used to connect Input/Ouput(I/O) regions of the structure. The areas bounded by a pair of curves defined the material distribution between them. While it is still unknown how the rest of the design space will be occupied by the structure, the I/O regions must exist somewhere because any mechanism must have parts which interact with its surroundings. All I/O regions are connected to one another (either directly or indirectly) by pairs of curves in order to form one single connected load-bearing structure. The presented scheme offers several benefits: capability of simultaneously implementing shape and topological changes while retaining a smooth boundary. The representation scheme also eliminates topological anomalies such as checkerboard patterns, point connection and de facto hinges. No post-processing is needed for topology uncertainty. Based on the view that muscles of arthropods connect to the exoskeleton and enable the animal to control movement, a multi-material compliant mechanism or structure is represented. This can improve productivity and performance of multimaterial compliant mechanisms. The synthesis of such compliant mechanisms is accomplished by formulating the problem as a structural topology and shape optimization problem with multiple objectives and constraints to achieve the desired behavior. A multi-objective genetic algorithm is then applied coupled with the representation scheme for defining and encoding the structural geometry as a chromosome in the form of a graph. Prototypes of compliant mechanisms will be fabricated and tested to demonstrate that the presented representation scheme is appropriate and to find where it can be further optimized.

本项目深入系统研究基于成对曲线组合的柔顺机构形状拓扑优化设计理论和方法。提出了一种基于成对曲线组合以输入输出区域为核心的柔顺机构几何表述方式。虽然在初始阶段不知道机构在设计域的分布，但是载荷加载需要借助机构输入输出点，因此必须有至少一个加载区域，一个支撑区域和一个输出区域。将这些输入输出区域利用成对参数曲线直接或间接连接起来形成一种可以承载负荷的柔顺机构。机构边界为参数曲线函数之组合，可以同时进行形状和拓扑优化并且保持结构边界的光滑，解决了柔顺机构拓扑优化中的的单元铰接、棋盘格现象、锯齿和模糊边界等数值不稳定问题；采用仿生学的观点，参照节肢动物的外骨骼能与内壁所附着的肌肉共同完成各种运动，表征多材料柔顺结构，提升柔顺机构的整体性能和可加工性；建立多目标拓扑优化设计模型，采用图的形式对机构进行编码，利用遗传算法的全局寻优能力寻找全局最优解；建立实验平台，对理论研究的正确性进行验证。

本项目深入系统研究了基于成对曲线组合的柔顺机构形状拓扑优化设计理论和方法，设计了柔顺假手，柔顺定位平台等复杂柔顺机构，并进行了相应的实验研究。提出了一种基于成对曲线组合以输入输出区域为核心的柔顺机构几何表述方式。虽然在初始阶段不知道机构在设计域的分布，但是载荷加载需要借助机构输入输出点，因此必须有至少一个加载区域，一个支撑区域和一个输出区域。将这些输入输出区域利用成对参数曲线直接或间接连接起来形成一种可以承载负荷的柔顺机构。机构边界为参数曲线函数之组合，可以同时进行形状和拓扑优化并且保持结构边界的光滑，解决了柔顺机构拓扑优化中的单元铰接、棋盘格现象、锯齿和模糊边界等数值不稳定问题。采用仿生学的观点，参照节肢动物的外骨骼能与内壁所附着的肌肉共同完成各种运动，表征多材料柔顺结构，提升柔顺机构的整体性能和可加工性。认真研究了诸如变密度法、基础桁架结构法、水平集法等现有的主流拓扑优化方法的相关理论，并对这些方法的优缺点、适用性等进行了分析与总结。基于对单材料拓扑优化的研究，本项目创新地提出了一种简单而又具有普遍适用性的多材料并行优化策略用以解决多材料的拓扑优化问题。主要通过结合刚度插值-惩罚模型、杆单元模型、水平集模型这三个常见的模型进行了具体的理论设计，并通过大量的算例对这种新方法进行了评估。某种意义上说，拓扑是“定性”的，几何结构中的拓扑变化是不连续的变化；因此，利用本质上是离散优化算法的遗传算法有效地解决了拓扑优化问题。建立了多目标拓扑优化设计模型，采用图的形式对机构进行编码，利用遗传算法的全局寻优能力寻找全局最优解；对于可靠性问题，采取反优化方法。设计了柔顺假手，假手手指是基于拓扑优化设计的柔顺机构的手指，并开发了表面肌电信号(sEMG)采集与识别系统，对之进行了控制研究。设计了精密定位平台等复杂柔顺机构，为获得柔顺机构柔度，提出了波纹状结构的悬臂梁。该悬臂梁由于相对长度大，具有很大的柔性，因此可以应用到大柔度柔性机构的设计中。建立了实验平台，对理论研究的正确性进行验证。