This analysis type is for bifurcation buckling using a linearized model of elastic stability. Bifurcation buckling refers to the unbounded growth of a new deformation pattern. A linear structure with a force-deflection curve similar to Figure 15.6: Types of Buckling Problems (a) is well modeled by a linear buckling (ANTYPE,BUCKLE) analysis, whereas a structure with a curve like Figure 15.6: Types of Buckling Problems (b) is not (a large deflection analysis ( NLGEOM,ON) is appropriate, see Large Rotation). The buckling problem is formulated as an eigenvalue problem:

(15–113)

where:

= stiffness matrix

= stress stiffness matrix

= ith eigenvalue (used to multiply the loads which generated [S])

= ith eigenvector of displacements

The eigenproblem is solved as discussed in Eigenvalue and Eigenvector Extraction. The eigenvectors are normalized so that the largest component is 1.0. Thus, the stresses (when output) may only be interpreted as a relative distribution of stresses.

By default, the Block Lanczos and Subspace Iteration methods find buckling modes in the range of negative infinity to positive infinity. If the first eigenvalue closest to the shift point is negative (indicating that the loads applied in a reverse direction will cause buckling), the program should find this eigenvalue.

In the case of an eigenvalue with a very large multiplicity due to symmetries or geometric patterns in the model, the algorithm may miss some occurrences of repeated eigenvalues. The default block size is equal to 4 for buckling analysis, and the algorithm may have difficulties finding a higher number of repeated eigenvalues. Requesting more eigenvalues can solve the problem.