# Buckling Analysis Types

Most finite element packages will offer you two types of eigenvalue buckling analysis.

• The linear eigenvalue buckling analysis (called “Buckling load” in LUSAS), where, if the applied load is $$P$$, each eigenvalue is a load factor $$\lambda$$, such that the associated buckling load is $$\lambda P$$.
• The non-linear eigenvalue buckling analysis (called “Eigenvalues of stiffness matrix” in LUSAS), where the eigenvalues indicate whether the model is stable or not at the applied load. All eigenvalues positive indicates stable, whereas a negative eigenvalue indicates unstable (buckled). An eigenvalue equals zero at the buckling load for its associated mode. Non-zero eigenvalues also have associated modes, but these are not buckling modes.

The linear analysis is much simpler, quicker to run, and adequate in most cases but does not correctly model any of the following situations:

• pre-stressing / post-tensioning or initial deformations
• assymmetric buckling modes
• geometric or material non-linearity
• axial loads that cause lateral displacements or vice-versa