".... how to predict "critical buckling loads" for hollow cylindrical shaft under torsion?"
To predict bucking, the *BUCKLE keyword can be used. In this procedure bucking is predicted using Eigenvalues. And therefore eigenvalues are extracted in this procedure.
A General Static Analysis can be used prior to the *BUCKLE procedure to prescribe the preloads . The *BUCKLE Analysis will take the end state of the previous analysis as the base state.
A *STATIC,RIKS analysis can be performed to ramp the load till the point of buckling and also to perform post buckling analysis. This RIKS analysis delivers the Load Proportionality Factor (LPF) as a solution. So it is enough to only give a reference load ( lets say Unit Load ) and the LPF at the time of bucking will then be buckling load.
For further information, please refer to :
Abaqus Analysis Users Manual
Section 6.2.3 Eigenvalue buckling prediction
Section 6.2.4 Unstable collapse and postbuckling analysis
Sunday, October 26, 2008