### Saturday, December 23, 2006

## Buckling Analysis with ABAQUS

In searching for helps with ABAQUS, I found this documentation page informational, although I am not sure if we are using Version 6.5.

The particular question I have at the moment is about a static buckling analysis. I found in Section 6.2 a good introduction to linear eigenvalue buckling predcition (6.2.3) and nonlinear post-buckling analysis (6.2.4).

The first step in buckling analysis is to find the critical load, which should be related to the lowest eigenvalue. However, to relate the output eigenvalues to the critical load, one must clarify the following:

(1) What is the base state? The buckling loads are calculated relative to the base state. This could be the initial condition or the current state of the model at the end of the last analysis step. Geometric nonlinearity may be included in the general analysis steps prior to the eigenvalue buckling analysis (a linear perturbation to the current state).

(2) Does the base state have a preload? It is not clear to me what this preload means and how it is specified in ABAQUS.

(3) What is the perturbation load pattern? This must be specified as applied load, which could be nodal forces, distributed pressure, or thermal load. The amplitude of the applied load is not important, becasue it will be scaled by the eigenvalues.

For example, to analyse buckling due to thermal stress, the critical temperature can be obtained by multiplying the lowest eigenvalue with the applied temperature, assuming a base state with zero preload.

The particular question I have at the moment is about a static buckling analysis. I found in Section 6.2 a good introduction to linear eigenvalue buckling predcition (6.2.3) and nonlinear post-buckling analysis (6.2.4).

The first step in buckling analysis is to find the critical load, which should be related to the lowest eigenvalue. However, to relate the output eigenvalues to the critical load, one must clarify the following:

(1) What is the base state? The buckling loads are calculated relative to the base state. This could be the initial condition or the current state of the model at the end of the last analysis step. Geometric nonlinearity may be included in the general analysis steps prior to the eigenvalue buckling analysis (a linear perturbation to the current state).

(2) Does the base state have a preload? It is not clear to me what this preload means and how it is specified in ABAQUS.

(3) What is the perturbation load pattern? This must be specified as applied load, which could be nodal forces, distributed pressure, or thermal load. The amplitude of the applied load is not important, becasue it will be scaled by the eigenvalues.

For example, to analyse buckling due to thermal stress, the critical temperature can be obtained by multiplying the lowest eigenvalue with the applied temperature, assuming a base state with zero preload.

## ABAQUS Tutorial from Brown Univ.

This link could be a good place to start learning ABAQUS.