Buckling Analysis

Buckling is a stability failure: a slender structure under compression suddenly deflects sideways at a load well below its material strength. Linear eigenvalue buckling analysis estimates the load at which this happens, and the shape the structure takes when it does.

What it computes

Buckling analysis works from two stiffnesses: the ordinary elastic stiffness, and a geometric stiffness that comes from the stress already in the structure (the prestress). As compression grows, the geometric stiffness erodes the effective stiffness until, at the critical load, it vanishes in some direction and the structure buckles.

The result is a set of critical load factors and their buckling mode shapes:

• A load factor scales the reference load. A factor of 4 means the structure buckles at four times the reference load; a factor below 1 means it buckles before reaching it.
• The mode shape shows the pattern it buckles into (a column bowing, a plate rippling). As with modal mode shapes, only the shape is meaningful, not the magnitude.

The prestress and its sign

Buckling needs a prestress: a reference stress field, computed by a static analysis on the same mesh, that the load factors scale. Because the factors scale that field, the reference state must actually contain compression (in the tension-positive convention). A purely tensile reference state has nothing to buckle, so the analysis returns no positive load factors.

Requirements and limits

• Solid (3D) elements only.
• A symmetric (half or quarter) model finds only symmetric buckling modes, and the critical mode is often antisymmetric. Run buckling on the full model unless you are sure the critical mode is symmetric (see Symmetry).
• Linear eigenvalue buckling is an estimate. It assumes the prestress scales linearly up to buckling and ignores imperfections and material nonlinearity, so it tends to overestimate the real buckling load. Treat it as an upper bound and apply a safety factor.