Tracing Post-buckling Path of Structures by Interval Newton Method

Post buckling analysis was traditionally conducted by arc length method. In view of the feature of global convergence of the interval iteration method in solving nonlinear equation sets, an approach is proposed to apply this method in tracing post buckling path of structures. An incremental solution scheme is introduced. Smaller interval radius is suggested to avoid excessive number of iterations at low loading levels. When time stepping approaches the critical point, two equilibrium configurations of pre and post buckling can be detected automatically, which avoids iteration failure resulting from the singularity of stiffness matrix. The rest part of tracing is then conducted based on the later configuration. Validation of the new method is demonstrated by a typical numerical example. It also shows that the method can deal with the phenomenon so called Snap back problems without additional efforts.