Automatic non‐linear solution with arc length and Newton‐Lanczos methods Available to Purchase

The application of the preconditioned Lanczos method is proposed for the solution of the linearized equations resulting from a non‐linear solution routine based on Newton methods. A path‐following solution algorithm with an arc length method is employed for tracing all types of post‐critical branches of a load‐displacement curve. The proposed methodology retains all characteristics of an iterative method by avoiding the complete factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.