# Nonlinear Buckling Analysis

Nonlinear analysis is performed by the dynamic relaxation (DR) solver. Note that for some structures buckling is not a sudden phenomenon and can be preceded by a gradual reduction in stiffness as forces increase. The DR solver recalculates element forces and overall model stiffness based on the deformed geometry, therefore *P-delta*effects and the reduction in stiffness associated with the onset of buckling is considered automatically for all DR analyses. In addition, the stiffness of individual beam elements is reduced when they are in compression.

There are a number of nonlinear analysis options that can be used to investigate the behaviour of a structure as it approaches its first mode of buckling. It can be helpful to run the model through the modal buckling analysis first to get an estimate of the buckling load factor, then create a new model with imperfection introduced based on the first mode shape.

The automatic load increment option in nonlinear static analysis should be used to search for the collapse / buckling load of a model, starting form a predefined first increment. Note that the loads are increased monotonically in this analysis.

Individual component buckling analysis can be used to estimate the maximum axial force capacity of an element or a chain of elements. This option should be used to estimate the effective restraint to the elements offered by the surrounding structure under a particular load combination.

## Modelling implications for nonlinear buckling analysis

Beam elements should be used if buckling within the element need to be considered, Bars and struts will not buckle no matter how large of the compressive forces.

## Results for nonlinear buckling analysis

The results for nonlinear buckling analysis will include the real deflections and element forces from the applied loads. This differs from the modal buckling analysis, which gives displacements that represent a scaled mode shape rather than the actual magnitude of the deflection.

The individual component buckling analysis will give axial force - deflection/rotation results for the elements under consideration. These are reported in the ** Axial Force / Displacement Relationship** Output View option and the relationship can also be plotted using chart view.

The automatic increment analysis will give load factor deflection/rotation results per load increment for the node under consideration. These are reported in the ** Load Factor / Displacement Relationship** Output View option and the relationship can be plotted using chart view