一类周期结构的部分组集有限元法及静动力分析

PERIODIC STRUCTURES: FINITE ELEMENT METHOD WITH PARTIAL ASSEMBLAGE, STATIC AND DYNAMIC ANALYSES

本文分析了周期结构经有限元离散所形成系数矩阵的元素分布，提出部分组集的有限元法；随后将块ＳＯＲ、块共轭梯度等方法用于求解相应的线性代数方程组，并以此改造求解大型特征值问题的Ｌａｎｃｚｏｓ算法。这些工作使得在一类周期结构静动力分析中能够避免对大规模代数方程组的直接计算。

After analyzing the coefficient matrices of periodic structures resulted from the finite element method(FEM), a FEM with partial assemblage was put forward. Some block iteration processes, such as BSOR and BCG/BPCG, were employed to solve the linear algebraic equation. The Lanczos algorithm for treating large eigenvalue problems was then modified by these iteration procedures. The endeavor makes it possible to avoid direct treatment with large scale matrices during the static and dynamic analyses of periodic structures. Examples show that the above work dramatically reduces the necessary incore and outcore space of computers.