Use of Lanczos Algorithm in Elastic Stability

The Lanczos algorithm is applied to the eigenvalue problems of elastic stability, wherein the geometric stiffness matrix is used to describe the effect of the stress resultants. This matrix need not be positive or positive definite for a general structural system. Despite this fact, it is found that a simple algorithm, without the use of sophisticated convergence criteria and its concomitant programming, can be employed in stability computations. Even though the procedure exhibits an unusual convergence pattern, it can solve for the important buckling loads without the use of any a priori assumptions concerning the eigenvalues or eigenvectors. The simple algorithm can also be applied to dynamic eigenvalue problems but, as the example considered herein demonstrates, it may not be efficient in computing all required eigenvalues for a given frequency range.