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

这项合作研究致力于开发一种基于严格有限元方法的方法来研究微电子机械系统(MEMS)的稳健性和可靠性。利用有限元公式将高阶矩引入到概率分析中，而不会产生过高的成本。利用选择泛函的有限元形式，消除了引入高阶矩带来的计算负担。将探索新的MEMS建模方法，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，该方法将在精度和效率之间取得良好的平衡。如果研究成功，这项研究将有助于改善MEMS社区的质量评估，并更好地理解稳健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对于需要这种导数信息的其他应用也是有益的。对各种概率分析方法进行比较研究，可以为选择最合适的技术提供更好的指导。基于可靠性分析的概率分析方法可望适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