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bifurcation buckling using ABAQUS


The following is taken from the book Concepts and applications of Finite element methods by Cook, Malkus and Plesha.

 For bifurcation buckling, we have the following eigenvalue problem:

(K+Lambda Ksigma)delta d= 0 

K =stiffness matrix corresponding to base state, Lambda is an eigenvalue, Kisgma is the stress stiffening matrix correspondng to base state.
My understanding is K and K sigma is determined at a base state under the application of any particular loading . If Geometric Non linearities are included K and K sigma will based on the deformed state under the action of the base state load.For a linear analysis K and K sigma is based on the undeformed structure.
Also, no additional load ( beyond the base state  load) is needed for the eigenvalue analysis.

Using the above concept. I tried to do an eigenvalue bifurcation analysis using ABAQUS. The requirement in ABAQUS is to apply the loads in two steps:  A base state load ( P) and an additional load Q. Isn't it different from the concept presented in the above mentioned book? That is why a second loading has to be applied when the change from one equilibrium state to the other is happening w/o any additional load.


Kindly advise.





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