刚度矩阵

在有限元方法和弹簧系统分析中，刚度矩阵K是对称半正定矩阵，其将胡克定律中的刚度推广为矩阵形式，描述了所有自由度之间的刚度，从而得到

\mathbf{F}=-K\mathbf{x}

其中F是力，x是位移矢量，而

U=\frac{1}{2} \;\mathbf{x}^\top\! K \mathbf{x}

是系统的总势能。

对于简单的弹簧网络，刚度矩阵是拉普拉斯矩阵（为实施牛顿第三定律），描述了自由度之间的连通图。对于非对角线上的元素 $k_{ij}$ ，弹簧的负刚度将自由度i关联到j，例如

K=\left(\begin{array}{rrrrrr} 13 & -1 & 0 & 0 & -12 & 0\\ -1 & 3 & -1 & 0 & -1 & 0\\ 0 & -1 & 2 & -1 & 0 & 0\\ 0 & 0 & -1 & 3 & -1 & -1\\ -12 & -1 & 0 & -1 & 14 & 0\\ 0 & 0 & 0 & -1 & 0 & 1\\ \end{array}\right)

单词	Stiffness matrix
释义	Stiffness matrix 中文百科刚度矩阵在有限元方法和弹簧系统分析中，刚度矩阵K是对称半正定矩阵，其将胡克定律中的刚度推广为矩阵形式，描述了所有自由度之间的刚度，从而得到 $\mathbf{F}=-K\mathbf{x}$ 其中F是力，x是位移矢量，而 $U=\frac{1}{2} \;\mathbf{x}^\top\! K \mathbf{x}$ 是系统的总势能。对于简单的弹簧网络，刚度矩阵是拉普拉斯矩阵（为实施牛顿第三定律），描述了自由度之间的连通图。对于非对角线上的元素 $k_{ij}$ ，弹簧的负刚度将自由度i关联到j，例如 $K=\left(\begin{array}{rrrrrr} 13 & -1 & 0 & 0 & -12 & 0\\ -1 & 3 & -1 & 0 & -1 & 0\\ 0 & -1 & 2 & -1 & 0 & 0\\ 0 & 0 & -1 & 3 & -1 & -1\\ -12 & -1 & 0 & -1 & 14 & 0\\ 0 & 0 & 0 & -1 & 0 & 1\\ \end{array}\right)$ 英语百科 Stiffness matrix 刚度矩阵 For the stiffness tensor in solid mechanics, see Hooke's law#Matrix representation (stiffness tensor). In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation.
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Stiffness matrix

刚度矩阵

Stiffness matrix 刚度矩阵