• 论文 • 上一篇    下一篇

不存贮总刚度矩阵的迭代解法

何春发   

  1. 石油勘探开发科学研究院
  • 出版日期:1981-01-20 发布日期:1981-01-20

何春发. 不存贮总刚度矩阵的迭代解法[J]. 数值计算与计算机应用, 1981, 2(1): 17-28.

THE SOLUTION OF THE ITERATION WITHOUT STORAGE OF THE GLOBAL STIFFNESS MATRICE

  1. He Chun-fa Research Institute of Petroleum Exploration and Development
  • Online:1981-01-20 Published:1981-01-20
应用有限元方法解椭圆型边值问题的一类数值解法,最后都归结为解一个n阶线性方程组.这个方程组的系数按矩阵的形式排列,称为总刚度矩阵(例如位移法).尽管总刚度矩阵是稀疏和对称的,但用半带宽或变带宽来存贮它仍需占用计算机大量的存贮单元,使得中小型计算机难以求解这类大型结构的问题.本文将介绍不存贮总刚度矩阵的迭代
Linear equations of equilibrium established by finite element method have many solu-tions. Generally, it is necessary to form the global stiffness matriee. The larger struc-tural analysis requires a larger core storage of computer, which causes the middle orsmall size computers particularly difficult in making program. This paper presents asolution of the iteration without storage of the global stiffness matrice. It is very ef-ficient for the solution of larger structural problems on middle or small size computers.This iterative techniques can be used either to steepest descent method or to conjugategradient method, and only requires the product of the global stiffness matrice and theglobal nodal displacement in each process of the iteration. In fact, the result of suchanalysis is only a simple addition with the product of element stiffness matrice and ele-ment nodal displacement but does not refer to the formation of the global stiffness matrice.Thus, the storage requirements may be the least so that it can be used on middle or smallsize computers. However, each process of the iteration requires element nodal forcereformed and makes the running time increased. Thus, the paper uses three numericaltechniques so that the increament of running time is either zero or a little. In fact, this process may be one of the more powerful methods in solving linearequations of equilibrium on middle or small size computers.
()

[1] 何春发,林玉振,组合结构有限元法通用程序,中国科学院计算所,有限元法及其应用,1975.
[2] 何春发,板壳结构自动剖分网格的一种方法,武汉水利电力学院学报,1979.
No related articles found!
阅读次数
全文


摘要