Topology Optimization Of Electromegnetic Structure Based On Finite Element Method

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.