Linear buckling analysis can estimate the maximum load that can be supported prior to structural instability, i.e load factors based on classic elastic buckling. Imperfections and non-linearities tend to prevent most ‘real’ structures from achieving their theoretical elastic (or "Euler") buckling strength, so the Eigen-value buckling load factors are therefore somewhat overestimated. To get a more accurate answer non-linear analysis can be undertaken.
For a detailed structural buckling assessment a geometrically non-linear analyses should be carried out. With this, material and boundary non-linearity can also be investigated if found to be required. With a geometrically non-linear analysis the stiffness matrix of the structure is automatically updated between loading increments to incorporate deformations which affect the structural behaviour, i.e. P-delta effects. A structure may also experience some material non-linearity during a buckling event (yielding for example) and/or some boundary non-linearity (lift-off supports). Generally it is recommended that modelling of non-linear effects is done progressively in order to evaluate the results of each stage. This helps in developing an understanding of the structural behaviour and helps to identify the cause of any potential failed analyses.