The development of Micro-Electro-Mechanical devices is currently hampered by reliability problems. In this paper, these problems are addressed through the development of a computational framework for the reliability-based analysis and design optimization of electro-statically actuated Micro-Electro-Mechanical Systems (MEMS). A reliability-based analysis and design optimization framework is presented that accounts for stochastic variations in structural parameters and operating conditions. A First-Order Reliability Method (FORM) is embedded into a design optimization procedure by a modular nested loop approach. The steady-state electrostatic-mechanical response of the device is analyzed by a high-fidelity nonlinear finite element formulation, coupling a structural finite element model and a finite element discretization of the electrostatic field. The computational framework is verified by the analysis and optimization of a three-dimensional MEMS device. The appropriateness of the FORM approximation on the nonlinear problem is investigated by a comparison with Monte Carlo simulation results. While computationally significantly more expensive than deterministic electromechanical optimization, the example illustrates the importance of accounting for uncertainties and the need for reliability-based optimization methods in the design of MEMS.
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