# 借助 COMSOL® 仿真 App 执行弱形式

2015年 4月 16日

### 简单示例

(1)

\left(\begin{array}{cccccc}
1 & -1 & 0 & 0 & 0 & 0 \\
-1 & 2 & -1 & 0 & 0 & 0 \\
0 & -1 & 2 & -1 & 0 & 0 \\
0 & 0 & -1 & 2 & -1 & 0 \\
0 & 0 & 0 & -1 & 1 & 1 \\
0 & 0 & 0 & 0 & 1 & 0
\end{array}
\right)
\left(
\begin{array}{c} a_1 \\ a_2 \\ a_3 \\ a_4 \\ a_5 \\ \lambda_2 \end{array}
\right)
= \left(
\begin{array}{c} -2 \\ 0 \\ 0 \\ 0 \\ 0 \\ 9 \end{array}
\right)

### 另一种求解矩阵方程的方法

(2)

\left(\begin{array}{cc}
K & N_F \\
N & 0 \end{array}\right)
\left(\begin{array}{c}
U \\
\Lambda \end{array}\right)
=
\left(\begin{array}{c}
L \\
M \end{array}\right)

(3)

K \, U+ N_F \, \Lambda = L

(4)

N \, U = M

(5)

U=U_d+Null \, U_n

N \, Null \equiv 0

(6)

K_c \, U_n = L_c

\begin{align}
K_c& = Nullf^T \, K \, Null \\
L_c& = Nullf^T \, (L-K \, U_d)
\end{align}

Nullf^T \, N_F \equiv 0

### 在 COMSOL® App 中查看所有矩阵

COMSOL Multiphysics 支持我们计算及查看上面提到的所有矩阵和矢量。这里只需重复查看刚度矩阵和载荷矢量节的操作步骤。但我们很快发现，需要花费大量时间来点击模型开发器中的每个系统矩阵节点和每个设定窗口中的”计算”按钮。同样，我们一次只能查看一个矩阵或矢量，因此如果要检查所有的矩阵及矢量，将相当耗时。

### 结束语

#### 评论 (6)

##### wang shuo
2016-03-13

(-2,0,0,0,0,lamda_2)^T

##### Chien Liu
2016-03-15

Dear shuo,
lambda_2 belongs to the vector formed by U and Lambda. Please see Eq. (2) and the graph below it.
Sincerely,
Chien

2016-04-07

KU=L

##### Chien Liu
2016-04-08

Dear 峰 程,

I am not sure how you got KU=L which seems inconsistent with Eq. (3). The references I mentioned in my previous reply may be helpful.

Sincerely,
Chien

2016-11-25

##### Yuansheng Zheng
2016-11-29

Yi, 您好！

Email: support@comsol.com

Yuansheng