薄板有限元广义混合法及克服病态问题研究

Generalized Mixed Finite Elements for Thin Plate Bending and Its Application to the Research on Ⅲ-Conditional Problems

以薄板理论的广义混合变分原理为基础 ,建立了一种适用于薄板弯曲分析的有限元广义混合模式 ,给出了较实用的选择分裂因子的方法 ,算例表明有限元广义混合法比常规位移模式的精度高 ,同时还能克服常规有限元中的某些病态问题。本文还讨论了该法克服常规有限元中某些病态问题的机理。

Using the generalized mixed variational principle (GMVP) of thin plate, the generalized mixed finite elements method (GMFEM) is established, a practical method to choose the splitting factor is given too. The numerical example shows that the method to choose the splitting factor is correct, and shows that some ill conditioned problems in traditional finite elements of thin plate can be conquered by GMFEM. The cause why GMFEM can conquer ill conditioned problems is discussed.