Passing of instability points by applying a stabilized Newton-Raphson scheme to a finite element formulation: Comparison to arc-length method

摘要

In the vicinity of limit and bifurcation points the global stiffness matrix of a finite element formulation becomes ill-conditioned and at the critical point singular. This disturbs the convergence behavior of the standard Newton-Raphson scheme as well as the arc-length method. The stabilization procedure suggested solves the numerical defects and is thus able to pass critical points. Bifurcation points are passed on the primary path. Branch switching to the secondary path is done automatically. The stabilization procedure and the imperfection force are derived based on the eigenvalues and -vectors of the structure.