结构矩阵分析中高斯消元法的物理意义  

The Physical Meaning of Gaussian Elimination of the Structure Matrix Analysis

作　　者：陈静[1] 许薇[1] 

机构地区：[1]南通大学建筑工程学院,江苏南通226007

出　　处：《淮阴工学院学报》2007年第1期4-8,共5页Journal of Huaiyin Institute of Technology

摘　　要：结构矩阵分析中,经常利用高斯消元法来求解未知位移,一般认为高斯消元仅为一种数学过程,而实际其包含着深刻的物理意义。高斯消元法求解方程包括消元和回代两个过程,消元的物理意义为原结构的未知自由度逐步转化为子结构内部自由度,而得到新结构的过程;回代的物理意义为子结构内部自由度逐步释放回到总体结构,最终还原为原结构的过程。Gaussian elimination is always used to solve the unknown displacement in structure matrix analysis. It is not only the process of mathematics, but also contains deep physical meanings. Solving the equation by Gaussian elimination involves the process of elimination and back substitution. The physical meaning of elimination is the process of obtaining new structure by which the original structure unknown degree of freedom is gradually transformed into the inner structure degree of freedom. The physical meaning of back substitution is the process of reverting to the original structure, by which the inner degree of freedom is gradually released into the gross structure.

关 键 词：高斯消元 物理意义 结构刚度矩阵 子结构 自由度 

分 类 号：TB11[理学—数学]