On The Determination Of The Path Direction For Arc-Length Methods In The Presence Of Bifurcations And 'Snap-Backs'

This paper discusses the choice of the sign of the incremental load factor in the predictor solution phase of are-length methods. It is shown that the criterion recently proposed by Y.T. Feng, D. Perie, 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 are-length methods, Comput. Struct. 58 (1996) 479-485] produces a reliable path direction prediction even in the presence of bifurcations and/or 'snap-backs', 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-back' phenomena. (C) 1999 Elsevier Science S.A. All rights reserved.