RudiBR
Structural
- Dec 7, 2020
- 2
Hi,
I am new to FEM theory, and I have a small issue with a very simple example.
It's a square in x/y as shown below. "Bottom" nodes, (0) and (3), are fixed.
There is a 10000 kN down force at node (1) and a horizontal force of 11000 kN at node (1).
Simple 2D mesh.
Nodes (0) and (3) are fixed.
All sides equal length and k values.
length = 1000 mm
k = 10000 kN/mm^2
Here are the stiffness matrices for each beam one at the time, and finally the sum.
As the last step, the rows/columns representing the fixed nodes are removed.
However, I end up with an unsolvable matrix.
What am I doing wrong?
I am new to FEM theory, and I have a small issue with a very simple example.
It's a square in x/y as shown below. "Bottom" nodes, (0) and (3), are fixed.
There is a 10000 kN down force at node (1) and a horizontal force of 11000 kN at node (1).
Code:
y
^
|
| Fy
| |
|
beam 1 |
(2) v (1)
+----------+--->Fx
| |
| |
beam 2 | | beam 0
| |
| |
+----------+ ------> x
(3)^ beam 3 ^(0)Nodes (0) and (3) are fixed.
All sides equal length and k values.
length = 1000 mm
k = 10000 kN/mm^2
Here are the stiffness matrices for each beam one at the time, and finally the sum.
As the last step, the rows/columns representing the fixed nodes are removed.
However, I end up with an unsolvable matrix.
What am I doing wrong?
Code:
beam 0 stiffness matrix
0 1 2 3
0 1 2 3 0 1 2 3 F [N]
0 0 0 0 0 0 0 x
1 0 10000 0 -10000 0 y
1 2 0 0 0 0 -11000 x
3 0 -10000 0 10000 -10000 y
2 4 x
5 y
3 6 x
7 y
beam 1 stiffness matrix
0 1 2 3
0 1 2 3 0 1 2 3 F [N]
0 0 x
1 y
1 2 10000 0 -10000 0 -11000 x
3 0 0 0 0 0 y
2 4 -10000 0 10000 0 0 x
5 0 0 0 0 0 y
3 6 x
7 y
beam 2 stiffness matrix
0 1 2 3
0 1 2 3 0 1 2 3 F [N]
0 0 x
1 y
1 2 x
3 y
2 4 0 0 0 0 0 x
5 0 10000 0 -10000 0 y
3 6 0 0 0 0 0 x
7 0 -10000 0 10000 0 y
beam 3 stiffness matrix
0 1 2 3
0 1 2 3 0 1 2 3 F [N]
0 0 10000 0 -10000 0 0 x
1 0 0 0 0 0 y
1 2 x
3 y
2 4 x
5 y
3 6 -10000 0 10000 0 0 x
7 0 0 0 0 0 y
Main (summed) stiffness matrix
0 1 2 3
0 1 2 3 0 1 2 3 F [N]
0 0 10000 0 0 0 0 0 -10000 0 0 x
1 0 10000 0 -10000 0 0 0 0 0 y
1 2 0 0 10000 0 -10000 0 0 0 -22000 x
3 0 -10000 0 10000 0 0 0 0 -10000 y
2 4 0 0 -10000 0 10000 0 0 0 0 x
5 0 0 0 0 0 10000 0 -10000 0 y
3 6 -10000 0 0 0 0 0 10000 0 0 x
7 0 0 0 0 0 -10000 0 10000 0 y
Constrained (fixed) nodes removed stiffness matrix
1 2
2 3 0 1 F [N]
1 2 10000 0 -10000 0 -22000
3 0 10000 0 0 -10000
2 4 -10000 0 10000 0 0
5 0 0 0 10000 0