一种微机械有限元仿真的多重网格预处理方法

Multi-grid precondition method in MEMS FEA simulation

在微机械结构设计中常用有限元方法进行仿真,然而,通用的三维有限元仿真算法在进行有限元分析时耗时较长,影响了仿真效率。针对常规MEMS工艺仅有二维成形能力的特征,提出了将二维多重网格方法融入条件共轭梯度法的预处理的方法。并以一种"三明治"式微加速度计的ANSYS模态分析为具体算例,提出了用多重网格思想对网点分布进行插值以求在不太提高条件数的情况下提高对这类低频非局部振型的模态分析问题的求解精度的二维预处理算法。所提出的多重网络的网络划分预处理算法将预处理前后的同精度分析计算时间由206 min减少到38 min,但相对精度从0.018%降低到了0.038%。这种算法可用于二维成形结构的静力分析和模态分析并提高设计效率。

The FEA method is commonly utilized in MEMS structure design.However,the common 3-dimension FEA（Finite Element Analysis） simulation algorithm costs much time in analysis,which lowers the efficiency.According to the 2-dimension shape ability of the routine MEMS fabrication process,the 2-dimention algorithm of preconditioning in PCG（Preconditioned Conjugate Gradient method） with multi-grid method is proposed.With a concrete example of ANSYS mode analysis for a MEMS sandwich accelerometer structure,a preconditioning arithmetic is put forward which does interpolation under multi-grid idea in order to improve the velocity of solving a mode-analyzing problem of low-frequency shaking modes without much loss to the precision.The proposed multi-grid mesh precondition method improves the calculation time from 206 min to 38 min,but decrease the precision from 0.018% to 0.038%.The method can be utilized for higher design efficiency in static analysis and mode analysis of 2-dimension shaped structures.