A New Parameter to Arc-Length Method in Nolinear Structural Analysis

Abstract

Path following methods have been widely used in nonlinear analysis due to their greater efficiency in tracing the equilibrium trajectories of a structure with nonlinear behavior. The arc-length method is the most powerful path following method in the solution of equilibrium paths, bifurcation points and limit points by introducing a constraint condition which establishes the nonlinear equations in which the unknown load parameter is determined. Unfortunately, this method presents some difficulties and imperfections in the control of load increment to reach convergence at specific locations along the trajectories of load-deflection. Therefore, this paper proposes to present a modification in the arc-length method introduced by Crisfield (M.A.Crisfield, Compt. Struct., 13:55-62 (1981)) with the objective of improving the performance analysis of equilibrium paths. The mentioned change was firstly proposed by Teng and Luo (J.G.Teng, Y.F.Luo, Comm Num Meth Eng, 14 (1):51-58 (1998)) . It introduces a new parameter with the function to add all previous arc lengths of Crisfield’s method up to now and then includes a new current load step, which can achieve convergence to levels of pre-defined values for loads or other parameter (i.e., displacements, strains). With this, the difficulties found in the arc-length method are efficiently overcome.