DETERMINATION OF TRAVEL DIRECTIONS IN PATH-FOLLOWING METHODS

Many variants of continuation methods have been put forward in the las t decade to trace solution paths in nonlinear static structural proble ms. Since 'forward' or 'backward' directions at a point along the solu tion path could not be identified without further reference to the who le solution procedure, solution paths may be incorrectly followed. To this end, determination of the correct travel directions in every aspe ct of continuation methods is discussed in this paper. In addition, a new criterion used to determine the sign of the loading parameter incr ement in the predictor phase of the nonconsistent are-length method ha s been proposed, which may avoid a misleading travel direction of the continuation method due to inappropriate initial guesses. The new crit erion can be incorporated into both direct and iterative solvers, and has proved to be very successful for the test problems considered.