About Buckle Steps

General Eigenvalue Buckling

Eigenvalue buckling is generally used to estimate the critical buckling loads of stiff structures (classical eigenvalue buckling). Stiff structures carry their design loads primarily by axial or membrane action, rather than by bending action. Their response usually involves very little deformation prior to buckling. A simple example of a stiff structure is the Euler column, which responds very stiffly to a compressive axial load until a critical load is reached, when it bends suddenly and exhibits a much lower stiffness. However, even when the response of a structure is nonlinear before collapse, a general eigenvalue buckling analysis can provide useful estimates of collapse mode shapes.

Base State

The buckling loads are calculated relative to the base state of the structure. You can specify the initial values of quantities such as stress, temperature, field variables, and solution-dependent variables. If the eigenvalue buckling procedure is the first step in an analysis, the initial conditions form the base state; otherwise, the base state is the current state of the model at the end of the last general analysis step. Therefore, the base state can include preloads. The preloads are often zero in classical eigenvalue buckling problems.

If geometric nonlinearity was included in the general analysis steps prior to the eigenvalue buckling analysis, the base state geometry is the deformed geometry at the end of the last general analysis step. If geometric nonlinearity was omitted, the base state geometry is the original configuration of the body.

Eigenvalue Extraction Methods

Abaqus/Standard offers the Lanczos and the subspace iteration eigenvalue extraction methods. The Lanczos method is generally faster when a large number of eigenmodes is required for a system with many degrees of freedom. The subspace iteration method might be faster when only a few (less than 20) eigenmodes are needed.

By default, the subspace iteration eigensolver is employed. You can use subspace iteration and the Lanczos solver for different steps in the same analysis.

For both eigensolvers you specify the desired number of eigenvalues; Abaqus/Standard chooses a suitable number of vectors for the subspace iteration procedure or a suitable block size for the Lanczos method (although you can override this choice, if needed). Significant overestimation of the actual number of eigenvalues can create very large files. If the actual number of eigenvalues is underestimated, Abaqus/Standard issues a corresponding warning message.

If you use subspace iteration, you can also specify the maximum eigenvalue of interest; Abaqus/Standard extracts eigenvalues until either the requested number of eigenvalues has been extracted or the last eigenvalue extracted exceeds the maximum eigenvalue of interest.

If you use the Lanczos eigensolver, you can also specify the minimum and/or maximum eigenvalues of interest; Abaqus/Standard extracts eigenvalues until either the requested number of eigenvalues has been extracted in the given range or all the eigenvalues in the given range have been extracted.