The accumulated arc-length method in nonlinear and bifurcation analysis

The are-length method has been widely used in nonlinear analysis of structures. While the method can handle complex load deflection paths effectively by iterating on both loads and displacements for a constant are-length increment rather than a constant load or displacement increment, the analyst has no control over the are-length incrementation scheme to achieve convergence to specific locations along the load deflection path. There are a number of situations in which such control is necessary, for example when convergence to pre-defined load levels or to an anticipated bifurcation point is required. This paper describes the recently proposed method of accumulated are-length control (or simply the accumulated arc-length method) to overcome this deficiency of the are-length method.