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Simulation and analysis of micro-electro-mechanical systems (MEMS) with applications of sensitivity analysis and optimization.

机译：微机电系统（MEMS）的仿真和分析，以及灵敏度分析和优化的应用。

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Micro-electro-mechanical (MEM) devices consist of integrated movable micro-structures with electronics. Primary application areas of MEM structures are in the fields of micro-sensors and micro-actuators. Possible applications of such "micromachines" appear limitless. MEMS technology is still at a very early stage. Many nonlinear electromechanical behaviors have been observed in MEMS research, and much more need to be investigated. Accurate modelling and simulation and better understanding MEMS will be the basis for future research towards better devices and technologies.; The physical complexity in MEMS simulation arises from the multiple physical domains: electrical and mechanical, which are coupled by electrostatic forces giving rise to displacements. Additional complexities arise due to the infinite exterior domain for electrical field computation, large aspect ratio geometries for the structural members of MEMS, high natural frequencies, the iterative implicit dependence between electrostatic forces and deformation, nonlinearities and instabilities due to the electrostatic forces and the size of MEMS. There is no existing formulation which can be adopted directly for MEMS simulation. New theories and simulation techniques need to be developed. This is one major focus of this dissertation. Another aspect of this dissertation is to efficiently and accurately simulate, numerically predict and theoretically analyze MEMS structures, subjected to electric fields, and hence electrostatic forces. Static as well as dynamic problems are of interest in this work.; In this dissertation, a very important MEMS device--the comb drive, has been simulated. The performance of the driving force, the transverse load and the levitation of a comb drive have been analyzed. The instability and the non-linearity of a microtweezer, as well as its response to both DC and AC signals have been simulated and analyzed. Some inverse problems have been solved.; The general numerical technique adopted in this thesis is to couple an exterior boundary element method (BEM) problem for electrostatics with a finite element method (FEM) for elasticity, and obtain the solution of the coupled problem in an iterative manner. Other numerical techniques and simulation strategies, such as sensitivity analysis and optimization need to be employed sometimes. Simple physical analogs of MEMS provide understanding of their behaviors and help validate numerical results. Understanding the physics of MEMS is always important for both simulation and analysis of MEMS devices.; In addition to MEMS research, a novel method for error estimation and h-version adaptive mesh refinement for potential problems solved by the BEM is presented in this dissertation. In MEMS analysis, this approach can be used to increase the efficiency of electrostatic simulation.
机译：微机电（MEM）装置由集成的可移动微结构和电子设备组成。 MEM结构的主要应用领域是微传感器和微执行器领域。这种“微型机器”的可能应用似乎是无限的。 MEMS技术仍处于早期阶段。在MEMS研究中已经观察到许多非线性机电行为，还需要进一步研究。准确的建模和仿真以及对MEMS的更好理解将成为未来对更好的器件和技术进行研究的基础。 MEMS仿真的物理复杂性来自多个物理领域：电气和机械领域，它们通过静电力耦合而产生位移。由于电场计算的无限外部域，MEMS结构部件的宽高比几何形状，高固有频率，静电力与变形之间的迭代隐式依赖关系，由于静电力和尺寸导致的非线性和不稳定性，还会带来其他复杂性MEMS。没有现有的公式可以直接用于MEMS仿真。需要开发新的理论和仿真技术。这是本论文的重点之一。本论文的另一个方面是有效和准确地模拟，数值预测和理论上分析MEMS结构，受到电场以及因此受到静电力的作用。静态和动态问题都是这项工作的兴趣所在。本文对一种非常重要的MEMS器件-梳齿驱动器进行了仿真。分析了驱动力，梳齿驱动器的横向载荷和悬浮力的性能。已经对微镊子的不稳定性和非线性以及对DC和AC信号的响应进行了仿真和分析。一些反问题已经解决。本文采用的通用数值技术是将静电的外部边界元方法（BEM）问题与弹性的有限元方法（FEM）耦合，并以迭代方式获得耦合问题的解。有时需要采用其他数值技术和仿真策略，例如灵敏度分析和优化。 MEMS的简单物理类似物有助于理解其行为，并有助于验证数值结果。了解MEMS的物理特性对于MEMS器件的仿真和分析始终非常重要。除了对MEMS的研究外，本文还提出了一种新的方法，用于误差估计和h-version自适应网格细化，以解决边界元法所解决的潜在问题。在MEMS分析中，该方法可用于提高静电仿真的效率。

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