When setting up a similar nonlinear buckling and post-buckling analysis, consider the following hints and recommendations:
When performing the nonlinear buckling analysis, consider the following hints and recommendations:
Understand that a nonlinear buckling analysis can be complex.
A nonlinear buckling or post-buckling analysis is not a single-run analysis but a set of analyses. Some advanced nonlinear techniques such as stabilization are necessary in the static analysis which may require trial-and-error experimentation.
Perform a linear buckling analysis first.
It is best to start with a linear buckling analysis to verify the correctness and completeness of the model, and to get a general idea of how large the buckling load may be. In the linear analysis, the mode shapes can be expanded to predict the buckled mode shapes (used for introducing geometric imperfections later).
Geometric imperfections or perturbation loads should be introduced.
Geometric imperfections introduced with modes from the linear buckling analysis are recommended. The magnitude of imperfection should be within the range of manufacturing tolerances.
Examine the monitor file.
When nonlinear analysis stops due to convergence difficulty, the monitor file should be inspected carefully. Many bisections in the substeps indicate instability, and a significant change in the displacement values could mean that buckling is starting to occur.
Restart the analysis using nonlinear stabilization.
To verify the nonlinear buckling load and to perform post-buckling analysis, the analysis should be restarted using some advanced nonlinear technique to examine the load-displacement behavior for a larger range of loads. In a static analysis, nonlinear stabilization is preferred and is the only option if local buckling or time-dependent materials exist.
Determine the optimal displacement to find the buckling load on the load-displacement curve.
The buckling load is the load at which the slope of the load-displacement curve reduces significantly. For which node and for which direction the displacement should be chosen depends upon the problem being solved, and a few trials may be necessary to find the optimal displacement. Some displacements show the start of buckling more clearly than others.
To apply nonlinear stabilization to achieve convergence in the post-buckling analysis, consider the following guidelines:
Establish what type of buckling (local or global) is present.
The buckling type helps to determine which stabilization method to use (damping or energy). For local buckling, the energy method is the only option. For global buckling, either the energy or damping method can be used.
Always try the energy method first using a small value.
Obtain the damping factor value and use it as a reference value if damping is the desired method to control the stabilization.
Energy is the preferred method in the post-buckling analysis. Because the energy ratio ranges only from 0 to 1, however, damping can be used to obtain very fine control of stabilization forces if necessary. The damping factor can be any positive number, but should not stray too far from the reference value.
When different energy ratios are tried, do not change the number of substeps or time, as this will affect your comparison and therefore your decision as to which stabilization method you should use.
Use the smallest damping factor or energy ratio possible.
The specified energy ratio or damping factor should be large enough to circumvent divergence and small enough to avoid excessive stiffness. The best solution should be the one converged using the smallest energy ratio or damping factor.
Activate stabilization via a multiframe restart.
Although you can activate nonlinear stabilization at the beginning of the solution, in most cases it is more efficient and accurate to activate stabilization in a multiframe restart.
If you do so, save the restart files and restart from the substep before the last converged substep. If the substep has many bisections or a large number of iterations, try one substep before, or the substep at which monitored displacement shows significant change (as it is likely the point where buckling starts).
Check results after applying stabilization.
Accuracy can be affected if the stabilization damping or energy values are excessive. The stabilization energy should be much less than the strain energy. Results checking can be done in either the POST1 (/POST1) or POST26 (/POST26) postprocessor.