A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics. (1st May 2021)

• Record Type: Journal Article
• Authors: Kadapa, Chennakesava
• Is Part Of: Engineering structures. Volume 234(2021)
• Publication Date: 2021-05-01
• Subjects: Finite element analysis -- Arc-length method -- Structural stability -- Limit points -- Buckling; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2020.111755
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: A simple extrapolated predictor for the arc-length method based on two previous solutions. Successfully overcomes the well-known starting and tracking issues in the arc-length method. Negligible computational cost, and no ad hoc parameters. Successful computation of complex equilibrium paths of nonlinear truss and beam models. Abstract: 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.