Path following techniques for geometrically nonlinear structures based on Multi-point methods

The Multi-point methods are efficient and accurate techniques for solving nonlinear equations. In this article, these methods are used to develop incremental/iterative techniques for nonlinear analysis of structures. The numerical results show that these methods only have the ability to converge to the equilibrium path before the first limit-point. To improve the performance of Multi-point methods, modified techniques which have the ability to fully trace the geometrically nonlinear response of structures are proposed in this paper. Four novel algorithms are presented which follow the defined constraint while solving the equilibrium equations using modified Multi-point methods. The Multi-point methods and the modified ones are comparatively investigated for the geometrically nonlinear analysis of structures in both continuum and discrete problems (dome and cylindrical shell). Selected examples represent a host of nonlinearities, including large fluctuations in stiffness, snap-back, and snap-through behaviors. The numerical results show that the modified methods have the ability to fully capture the geometrically nonlinear response of structures, including snap-back and snap-through behaviors.