How to perform post-buckling analysis using ABAQUS correctly?

Hello Wanbot,

I have very good experience with utilization of the  standard static analysis with stabilization - *STATIC, STABILIZE (see Abaqus help for details).

Concerning the final shape of the structure, it is possible that the primary buckled shape may have changed into the secondary buckled shape as the load increased. This happens when the load corresponding to the secondary load path intersects the primary buckling load path.

V. Obdrzalek

Hello Wanbot,

You can make a sequence of incremental load steps and buckle steps in order to detect a potential mode change during the loading history (accompanying eigenvalue analysis). This way, you can probably find a more appropriate imperfection.

Please note that the ABAQUS buckling eigenvalue prediction does not consider material nonlinearity (yielding)! This can lead to dramatically wrong results.

Unfortunately, predicting complicated post-buckling responses is something that is not trivial to do with ABAQUS (or most other FE codes). Watch out for negative eigenvalue warnings that may indicate that you missed a bifurcation point! 

 Thomas Daxner 

Using a linearized eigenvalue buckling analysis as a means for
arriving at a rational seed imperfection for use in asymptotically
tracing the transition from primary to secondary equilibrium paths in
an incremental nonlinear finite element analysis can be somewhat
non-trivial.

It is helpful to realize from the start that good candidates for
such an approach are typically problems exhibiting bifurcation
instabilities, where pre-buckling deformations are small (i.e. actual
column buckling problems) In such cases, it is not terribly hard to
get reasonable results using a wide variety of initial imperfection
magnitudes (i. e. the scaling factor for the eigenmode imperfection
used to seed the nonlinear incremental analysis).

However, if the problem under consideration is something like
lateral-torsional buckling of a beam (where pre-buckling deformations
can be large) then there are many things to consider; not the least
of which is the appropriate scaling factor magnitude for use with the
mode shape employed as the seed imperfection. A seemingly rational
approach in this regard might be to obtain such scaling factors by
using fabrication tolerances that govern the structure considered.

Also important in this context, is the actual formulation employed
in the finite element code that you are using. There a so-called
“classical”, “secant”, “combined linear / non-linear
eigenvalue” buckling approaches for formulating the problem
associated with generating the seed imperfection. Depending on the
approach adopted in your code, different “mode 1s”, etc., can
obtained, depending on which method the commercial codes adopts.
Commercial codes such as ABAQUS, ANSYS, and ADINA state in their
theory manuals (with varying degrees of detail) what is going on “up
under the hood” of the code within such an analysis. However, this
description cannot always be relied on; as numerical experimentation
on commercial codes can uncover inconsistencies in stated
formulations employed for linearized eigenvalue buckling.

The bottom line here is that unless you are dealing with a strict
column buckling problem, you should proceed very cautiously in using
mode shapes obtained from linearized buckling analyses as seed
imperfections when performing incremental nonlinear finite element
stability analyses.