Eigenvalue buckling analysis: Modelling implications

In most cases a buckling analysis follows on from a linear static analysis, so a model set up for static analysis is the normal starting point. As buckling effects are three dimensional, it is inadvisable to define global restraints on the structure, as this can potentially provide an artificial degree of stiffness to the model.

Buckling analysis

In a p-delta analysis there is a geometric or differential stiffness in addition to the normal structure stiffness. The geometric stiffness is derived from the forces in the structure, so the solution requires two passes. The first pass establishes the forces in the structure allowing the geometric stiffness to be established for the second pass, which solves for the modes. The GSA solver handles both passes in a single solution procedure.

A buckling analysis is set up using the Analysis Wizard from the Analysis > New analysis task menu command. Select the option to create new analysis cases, then select the Modal buckling option. The next page allows the user to specify the task name (a name to associate with this modal analysis), the number of modes and start mode, and the maximum number of iterations. In most cases only the number of modes needs to be changed here. The number of modes that are required will depend on the structure and what is to be done with the modal results. For a simple structure or where all that is required is the frequency of the fundamental mode only a few modes are required, while a large, complex structure may require up to or in excess of 100 modes.

Limitations

Eigenvalue buckling only works for linear elements. Tie and strut elements are treated as bars for buckling analysis. In the GSA solver cable elements in general act like tie elements. For a buckling analysis cables are assumed to act in a similar way to bar elements. So for a buckling analysis the geometric stiffness of the tie, strut and cable elements are identical to those for a bar.

Generating an imperfect geometry

It is useful, particularly for non-linear buckling to be able to specify an imperfect geometry. The results of an eigenvalue buckling can be scaled to give an appropriate imperfection. Using the Model > Coordination tools > Create new model from deformed geometry menu command allows the user to select an analysis case and specify either a scale factor or maximum imperfection to apply to the displacements to be used to update the model geometry.