On the determination of the path direction for arc-length methods in the presence of bifurcations and `snap-backsʹ Original Research Article

This paper discusses the choice of the sign of the incremental load factor in the predictor solution phase of arc-length methods. It is shown that the criterion recently proposed by Y.T. Feng, D. Perić, D.R.J. Owen, [Determination of travel directions in path-following methods, Mathl. and Comput. Modelling 21 (1995) 43–59; A new criterion for determination of initial loading parameter in arc-length methods, Comput. Struct. 58 (1996) 479–485] produces a reliable path direction prediction even in the presence of bifurcations and/or `snap-backsʹ, when some popular criteria may fail to predict the continuation direction. The robustness of the criterion is illustrated in a numerical example where finite element solutions are obtained to a structural stability problem characterised by the existence of several bifurcation paths and `snap-backʹ phenomena.