Shape Optimization of Electrostatically Actuated Micro Cantilever Beam with Extended Travel Range Using Simulated Annealing

The pull-in instability places substantial restrictions on the performance of electrostatically driven MEMS devices by limiting their range of travel. Our objective is to present a systematic method of carrying out optimal design of novel types of electrostatic beams that have enhanced travel ranges. In this paper, we implement a shape optimization methodology using simulated annealing to maximize the static pull-in ranges of electrostatically actuated micro-cantilever beams. We use the Rayleigh-Ritz potential energy minimization technique to compute the pull-in displacement and voltage of each micro cantilever beam. A versatile parametric width function is used to characterize non-prismatic micro-cantilever geometries and the pull-in displacement of the cantilever is maximized with respect to the parameters of the proposed width function. Geometric constraints encountered in typical MEMS applications are incorporated into the optimization scheme using a penalty method. The simulated annealing algorithm uses different cooling schedules with the same number of objective function computations. We consider a matrix of several test cases in order to successfully demonstrate the utility of the proposed methodology. Our results indicate that an increase in the pull-in displacement of as much as 20% can be obtained by using our optimization approach. We have also compared our results with those obtained using traditional optimization approaches. We find the results are fairly independent of the cooling schedule used which demonstrates the usefulness and flexibility of this method to carry out optimal design of structural elements under electrostatic loading.