Topology optimization of MEMS considering etching uncertainties using the level‐set method

Abstract

SUMMARYBecause of the specific fabrication process of microsystems, the geometric uncertainties are relatively large compared with the size of the structures. However, the performance of microstructures is very sensitive to these uncertainties especially when slender structural members are included in the design. This paper presents a level‐set‐based topology optimization method for robust microelectromechanical systems. The presented method focuses on the effects of geometric uncertainties on the performance of microelectromechanical systems in the topology optimization. The geometric uncertainties arising from the etching process are treated as bounded‐but‐unknown uncertainties. This approach can be used to obtain designs with optimal performance for the worst‐case. The etching uncertainties can be conveniently included in topology optimization using the level‐set method. The signed distance property of the level‐set function allows easy construction of under‐etched and over‐etched structures. Therefore, models with variable etching‐induced uncertainties can be easily constructed. The effectiveness of the proposed approach is demonstrated using benchmark problems including compliance minimization and compliant‐mechanism design problems. Although the reinitialization scheme used to maintain the signed‐distance property can cause problems in the optimization process, this effect is limited using an approximate Heaviside function with a relatively large bandwidth. Copyright © 2012 John Wiley & Sons, Ltd.