Implementation of a direct procedure for critical point computations using preconditioned iterative solvers

摘要: Computation of critical points on an equilibrium path requires the solution a non-linear eigenvalue problem. These could be either bifurcation or limit points. When external load is parametrized by single parameter, stability problem consists solving equations along criticality condition. Several techniques exist for such system. Their algorithmic treatment usually focused direct linear solvers and thus use block elimination strategy. In this paper special emphasis given strategy which can used also with iterative solvers. Comparison to given. Due non-uniqueness eigenmode normalizing condition required. addition, points, Jacobian matrix augmented system singular at point additional stabilization required in order maintain quadratic convergence Newton's method. Depending condition, negative parameter value happen. The form equation critically discussed. slenderness buckling sensitive structures resulting matrices are ill-conditioned good preconditioner mandatory efficient solution.