Mechanical APDL Structural Analysis Guide

Because the post-buckling stage is unstable, special techniques must be used.Nonlinear stabilization
can help with local and global buckling, and the arc-length method is useful for global buckling. For
more information, see Unstable Structures (p. 258).

Nonlinear stabilization analysis is more straightforward for a post-buckling analysis. Because the buckling
load is unknown at the beginning of an analysis, you can do perform a nonlinear analysis as usual using
automatic time stepping. When the buckling load is reached or a convergence problem occurs, you
can activate stabilization during a multiframe restart and continue the analysis. If the deformation be-
comes stable later, you can deactivate stabilization until the next buckling occurs.

If only local buckling exists, the total load could still increase when buckling occurs because the total
loading is distributed differently. For these cases, nonlinear stabilization is the only applicable technique.

Because nonlinear stabilization cannot detect the negative slope of a load-vs.-displacement curve, it
may yield less accurat e results for history-dependent materials, and the maximum loads (buckling loads)
may not be obvious. For such cases, use the arc-length method.

7.5. Procedure for Eigenvalue Buckling Analysis

Again, remember that eigenvalue buckling analysis generally yields unconservative results, and should
usually not be used for design of actual structures. If you decide that eigenvalue buckling analysis is
appropriate for your application, follow this procedure:

1. Build the model.


2. Obtain the static solution.


3. Obtain the eigenvalue buckling solution.


4. Review the results.

7.5.1. Build the Model

See Building the Model in the Basic Analysis Guide. For further details, see the Modeling and Meshing
Guide.

7.5.1.1. Points to Remember

• Only linear behavior is valid. Nonlinear elements, if any, are treated as linear. If you include contact elements,
  for example, their stiffnesses are calculated based on their initial status and are never changed. The program
  assumes that the initial status of the contact elements is the status at the completion of the static prestress
  analysis.


• Young's modulus (EX) (or stiffness in some form) must be defined. Material properties may be linear, iso-
  tropic or orthotropic, and constant or temperature-dependent. Nonlinear properties, if any, are ignored.

7.5.2. Obtain the Static Solution

The procedure to obtain a static solution is the same as described in Structural Static Analysis (p. 9),
with the following exceptions:

• Prestress effects (PSTRES) must be activated. Eigenvalue buckling analysis requires the stress stiffness
  matrix to be calculated.

Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

Buckling Analysis