Topology Optimization of Electrostatic MEMS

Since the manufacturing of the first polysilicon surface micromachined devices by Howe and Muller1 in the early 1980s, the advantageous interaction between electrostatic fields and ideal conducting materials, such as silicon, has been exploited in many different areas of engineering. This category of devices is generally referred to as MEMS (Micro-Electro-Mechanical Systems) and are used as sensors and actuators in medical devices, automobiles, locking systems, communications and many other areas. One reason that MEMS applications have experienced such growth is that the manufacturing cost of a surface micromachined device is independent of its in-plane complexity. This allows the design of arbitrary planar devices without regard to cost feasibility. The use of complex geometries can alleviate certain issues in performance and reliability that affect MEMS. Often, MEMS do not perform as intended, this can be due to several factors, such as design by experimental and analytical methods, poor tolerances in manufacturing2 and inexact knowledge of material properties.3 The two latter issues can be addressed through reliability based4 and robust design methods, which are not discussed herein. The issue of low-fidelity design methods is addressed by applying numerical optimization methods, with high-fidelity numerical models, to the design of MEMS. Here, the synergism of combining MEMS and optimization is realized, as the performance gains obtained through numerical optimization can be realized in the production of actual devices. A common difficulty in design optimization is that the designs are often too complex to manufacture in a cost-effective manner, but this issue is resolved by the manufacturing techniques used for MEMS. Since MEMS are often used in new contexts and applications, there are not generally “standard” designs that can be simply inserted into a design problem, or even modified slightly through shape optimization techniques in order to perform a desired task. Conceptually new designs are often demanded by the changing scope of MEMS applications. Therefore, this study applies topology optimization to the design of MEMS such that conceptually new designs can be generated in an automatic fashion. For the developments in this study, the topology optimization of MEMS is extended to a class that are electrostatically actuated, which is a significant portion of realistic devices. The electrostatic actuation leads to a coupled electro-mechanical problem in which the electrostatic and structural fields occupy distinct regions of space. A major challenge in the development of a topology optimization methodology is the generation of the interface between the structural and electrostatic domains in an automatic way. This paper is arranged in the following manner. The computational methodology used for the high-fidelity, electro-mechanical optimization problem is presented in section II. In section III, the developments necessary for topology optimization without restriction on the electro-mechanical interface are discussed. Relevant optimization results are presented in section IV followed by a summary in section V.