Frame eigenvalue problem
Objective
To verify the truss element when used with skew coordinate systems.
Problem description
The truss structure is shown in figure below.
Numerical values for this problem are: E=2e11, L=5.0, A=0.0001, b=h=0.5, P=1000 (units: N, m).
Finite element model
The truss structure is modeled with 2-node truss elements.
The structure is inclined in the global coordinate system so it is effective to employ skew coordinate systems.
Solution
The displacement of the point of load application in the direction of the cantilever is:
This displacement is calculated and compared to that calculated by FEEA:
The displacement of the point of load application in the direction of the cantilever
| Displacement |
FEEA |
Theory |
| Node 22 | 1.125E-3 | 1.125E-3 |
The internal forces of some elements also are shown below:
The internal forces of some elements
| Internal Force |
Nodes |
FEEA |
Theory |
| Element 1 | 1,2 | -10000.00 | -10000.00 |
| Element 2 | 2,3 | -9000.00 | -9000.00 |
| Element 11 | 12,13 | 9000.00 | 9000.00 |
| Element 21 | 12,2 | 1414.21 | 1414.21 |
Conclusion
The results obtained with FEEA SDK show that it handles efficiently multiple coordinate systems,
and nodes assigned skew coordinate systems.