微机电系统中基于模态展开和边界元法的静电-结构耦合高效分析方法

为了提高微机电系统中静电-结构耦合数值计算速度,提出了一种新的针对微结构小变形的静电-结构耦合高效率数值计算方法。该方法将用于结构分析的微梁线性方程与用于静电场分析的边界积分方程相结合,微梁方程部分用标准的模态分析法处理,静电边界元方程则采用边界元法处理,并且将边界元方程用Taylor级数在微梁未变形的位置展开,以使静电计算能在微梁未变形的位置进行。同以往的常规算法相比,当微结构变形微小时,使用该方法,微结构变形后的面电荷密度可以在微结构未变形中计算,从而大大提高了静电-结构耦合数值计算效率。将该方法的计算结果与已有的文献计算结果和ANSYS的计算结果做了对比,验证了本方法的正确性,并且计算效率有显著提高。

EFFICIENT APPROACH FOR COUPLED ELECTROSTATIC AND STRUCTURAL ANALYSIS OF MEMS VIA BOUNDARY ELEMENT METHOD AND MODAL EXPANSION

In order to improve the efficiency for coupled electromechanical analysis of MEMS system, a new efficient numerical approach for electrostatic MEMS with small deformations is presented. The proposed method combines a linear beam theory for mechanical analysis and a boundary integral formulation for electrostatic analysis. The solution of beam equation is carried out by using the standard mode analysis technique. The boundary equation is carried out by using the boundary element method, and the boundary element equation is expanded in Taylor series to enable performing the analysis on the unde-formed geometry of the structures. Comparing with previous methods, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures using the new approach, so the computational efficiency for coupled electromechanical analysis is improved effectively. Finally, the approach is validated by comparing its results with those results available in literature and ANSYS software solutions, and is much faster than the previous methods.