Numerical methods for elastic structural stability analysis

The Gauss-Seidel, the successive overrelaxation, the conjugate gradient, the Cholesky's square root and the Cholesky's decomposition methods for solving systems of linear algebraic equations encountered in structural analysis are considered. Theorems for these methods establishing necessary and sufficient conditions for the matrix of the coefficients to be positive definite are converted into criteria for elastic structural stability. Numerical procedures, by using these methods in conjunction with their corresponding stability criteria, for checking the elastic stability and determining the elastic critical load of a structure are proposed. Application of these procedures to the stability analysis of plane frameworks leads to the conclusion that the proposed direct schemes are more efficient than the iterative ones.