A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics
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This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems. 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 five numerical examples involving truss and beam models.
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