| 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. |
