  This paper presents a simplified implementation of the arc-length method for
computing the equilibrium paths of nonlinear structural mechanics problems
using the finite element method. In the proposed technique, the predictor is
computed by extrapolating the solutions from two previously converged load
steps. The extrapolation is a linear combination of the previous solutions;
therefore, it is simple and inexpensive. Additionally, the proposed
extrapolated predictor also serves as a means for identifying the forward
movement along the equilibrium path without the need for any sophisticated
techniques commonly employed for explicit tracking. The ability of the proposed
technique to successfully compute complex equilibrium paths in static
structural mechanics problems is demonstrated using seven numerical examples
involving truss, beam-column and shell models. The computed numerical results
are in excellent agreement with the reference solutions. The present approach
does not require prohibitively small increments for its success.
