2nd order buckling - Euler strut buckling
Problem definition
A 10 long simply supported beam is subjected to an axial tip load of P.
Assumptions
Shear deformations are excluded. The number of internal nodes varies from 0-5.
Key results
The theoretical value for the first buckling mode is calculated using the Euler strut buckling formula:
With P = -1.0 the following buckling factors are obtained
| No. internal nodes | Solver value | % error |
|---|---|---|
| 0 | 12.000 | 21.59 % |
| 1 | 9.944 | 0.75 % |
| 2 | 9.885 | 0.16 % |
| 3 | 9.875 | 0.05 % |
| 4 | 9.872 | 0.02 % |
| 5 | 9.871 | 0.01 % |
Conclusion
As the element is subdivided the result converges to the correct theoretical value.