The reliability of the arc-length method in the analysis of mode-jumping problems

The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial finite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Are-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence difficulty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example. © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.