【作者】 江春冬；

【导师】 杜太行；

【作者基本信息】 河北工业大学 ， 电气工程， 2012， 博士

【摘要】 拓扑优化设计是现代结构优化设计的一个重要研究方向，该方法为工程师创新设计出低成本高品质的产品提供了保障。经过近二十年的发展，拓扑优化设计方法已由结构设计领域向其他领域发展，包括航空航天、微机电系统、电磁、流体等领域。耦合结构的拓扑优化亦是拓扑优化设计中的重要的研究课题之一及难点，电热固致动装置的优化设计属于这一类。使用拓扑优化设计方法对电磁相关结构进行设计可有效缩短产品开发周期，提高产品质量。“基于有限元方法的电磁结构拓扑优化”的研究工作是探索一种把现代拓扑优化设计理念应用于电磁结构设计的方法，重点是建立电磁致动机构拓扑优化设计数学模型，并编程实现该设计。主要研究工作包括：(1)为了更高效地进行电磁结构拓扑优化设计，推导了电磁结构的有限元方程，设计了适于拓扑优化的有限元实现流程，编写了相应的程序。通过计算不同边界条件、不同形式网格的电场问题和磁场问题的数值解对有限元方法的准确性进行评价。对实现拓扑优化设计而言，这些有限元计算程序使拓扑优化设计程序简化，接口工作减少，为基于有限元分析的电磁结构拓扑优化奠定了良好的基础。(2)编程实现了以三角形为基单元的微机电系统中柔性机构拓扑优化设计方法。分析了三角形单元的优越性。详细推导了三角形单元下的有限元法实现过程及其在拓扑优化时的敏度，给出了基于准则法的柔性机构拓扑优化数学模型。使用Michell结构、微夹钳机构二个典型算例验证了设计的拓扑优化方法的有效性和正确性。应用该算法设计了三角形微夹钳和微型扭矩产生器，得到了较好的拓扑形式。给出了不同参数情况下微型扭矩产生器的拓扑形式。(3)将拓扑优化设计方法用于存在耦合场作用的微致动器结构的设计。针对不同驱动方式的微致动器，考虑了其防热性能、承载能力以及功能，建立了拓扑优化数学模型，利用拓扑优化的思想，寻求电磁相关的多场耦合结构的最优拓扑分布。设计出特定状态下满足要求的电热致动器和压电致动器的拓扑形式，实现满足功能及约束条件下高效地使用材料、节约能源。更多还原

【Abstract】 Topology optimization is a hot research field for its ability to make engineer get low-costand high-quality products. Applications of topology optimization have also spread to otherphysics and multi-physics disciplines including electromagnetism, fluids, MEMS, optics andacoustics. Topology optimization is now a rather well-established field that after almost twodecades of emphasis on structural design is now being applied for optimal design in such diverseareas as electro-magnetism and fluids. Topology optimization of coupled structure has becomeone of the most important topics of engineering applications. Design optimization of structureand thermal actuated and electronically actuated mechanism have been an interesting area ofresearch in the field of engineering design for its ability to shorten the design cycle andenhancing product quality.This dissertation emphasizes the approaches and engineering computations required toeffectively design this kind of actuator. The research of this thesis focuses on an optimal designof actuator using topology optimization. Main works are included as follows.(1) This dissertation studies computational methods of finding numerical solutions toMaxwell’s equations and gives an introduction to the finite element method with applications inelectromagnetics and its numerical implementation. The accuracy of the finite element method isevaluated by computing the numerical solution based on different meshes under differentboundary conditions. Both triangular and quadrilateral elements are employed for diffrentanalysis. Several examples are illustrated to verify the accuracy and effectiveness of the code inthis work. Additionally, the solid model is simplified and the depicting parameters are eliminatedconsiderably compared with the whole structure, through which optimization can beimplemented easily.(2) This dissertation establishes the SIMP models of topology optimization for rotatingcompliant mechanisms. This work gives the mathematical formulation of rotating compliantmechanism, sensitivity analysis, and OC solving algorithm. The advantages of using triangleelement are presented. Numerical instabilities are eliminated in the implementation of progamming. Numrical examples of Michell structure and micro gripper show the rationality andefficiency of this algorithm. The micro triangle gripper and rotating actuator are designedthrough topology optimzation established in this study.(3) This dissertation establishes a computational algorithm for topology optimization ofcoupled solid-thermal-electronically structure and actuator. Based on the proposed algorithm, thepaper gives the numerical implementation of topology optimization and visualization. Itintegrates the thermal force and electrical force into the mahtematical model for the designing ofactuator through topology optimization. A thermal actuator and piezoelectric actuator aredesigned using the mathematical topology optimization formulation. The validity and robustnessof the new algorithm are verified by some widely used examples in topology optimization andthen can be used to design mechanism and/or actuator under coupled field.更多还原