Timoshenko has derived for the large deflection in the case of beam fixed at one end and free at the other end (image attached). Where in the length of the buckled beam is found by integrating tangent of the deflected profile to the vertical from 0 (fixed end) to alpha (free end). He also shows how we can find the final profile of the buckled beam.
When we try to apply the same method for the case of beam where both the ends are fixed, the angle made by the tangent at both the fixed ends and at the center of the beam is zero.
Is there a method to find the shape of the buckled beam, where in both the ends are fixed?
Rotate deformed beam in the figure by 180º around point O. Both these beams (AOA') form 1/2 symmetrical part of a beam with fixed ends and the length 4l which is deformed under action of force P applied at upper end.
I think if you can consider the model as Non linear analysis with large deflection switched on. The deflection can be extracted for both end fixed condition in ANSYS WORKBENCH or any other software.
- Badges
- Science topic