On the direct solution of critical equilibrium states

Summary. Determination of a critical point is the primary problem in structural stability analysis. Mathematically it means solution of a non-linear eigenvalue problem together with the equilibrium equa-tions. Several techniques exist to compute the critical equilibrium states and the corresponding modes. In this paper direct algorithms to solve the critical equilibrium state are discussed and a hybrid algorithm is proposed, which hopefully has enlarged domain of convergence. Key words: computational stability analysis, finite element method, critical points, eigenvalue problem, non-linear system