Collaborative Research: Exploitation of Finite Element Method in Robustness and Reliability Assessments for Micro-Electro-Mechanical Systems

这项合作研究涉及一种严格的基于有限元方法的方法来研究微机电系统（MEMS）的鲁棒性和可靠性的发展。提出了利用有限元公式将高阶矩纳入概率分析而不产生过多成本的方法。引入高阶矩的计算负担将通过利用选择性泛函的有限元公式来消除。将探索新的MEMS建模方法，并研究各种MEMS器件。为了克服现有方法传播不确定性影响的局限性，提出了一种基于可靠性分析的概率分析方法，该方法在准确性和效率之间取得了很好的平衡。如果成功，该研究将有利于MEMS社区提高质量评估和更好地理解鲁棒性和可靠性之间的内在关系。在有限元方法中有效地计算高阶导数的能力也有利于需要这些导数信息的其他应用。对各种概率分析方法进行比较研究，可以为选择最合适的方法提供更好的指导。基于可靠性分析的概率分析方法有望应用于具有非线性行为和大不确定性变化的设计问题

This collaborative research deals with the development of a rigorous finite element method-based approach to studying robustness and reliability of Micro-Electro-Mechanical Systems (MEMS). Exploitation of the finite element formulation is proposed to incorporate higher order moments into the probability analysis without incurring excessive cost. The computational burden from introducing higher order moments will be eliminated by taking advantage of the finite element formulation of selective functionals. New modeling methods for MEMS will be explored and a variety of MEMS devices will be studied. To overcome the limitations of existing methods for propagating the effect of uncertainty, a reliability analysis-based procedure for probability analysis is proposed, which will achieve a good balance between accuracy and efficiency.If successful, the research will benefit the MEMS community with improved quality assessment and a better understanding of the intrinsic relationship between robustness and reliability. The ability to efficiently evaluate higher order derivatives in the finite element method is also beneficial to other applications where this derivative information is needed. Comparative study on various methods for probability analysis can provide better guidelines for choosing the most appropriate technique. The reliability analysis-based procedure for probability analysis is expected to be applicable to design problems with nonlinear behavior and large uncertainty variations