A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics

Kadapa, Chennakesava

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.

Citation

Kadapa, C. (2021). A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics. Engineering Structures, 234, Article 111755. https://doi.org/10.1016/j.engstruct.2020.111755

• Journal Article Type: Article
• Acceptance Date: Dec 17, 2020
• Online Publication Date: Feb 19, 2021
• Publication Date: 2021-05
• Deposit Date: Aug 29, 2022
• Journal: Engineering Structures
• Print ISSN: 0141-0296
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 234
• Article Number: 111755
• DOI: https://doi.org/10.1016/j.engstruct.2020.111755
• Keywords: Finite element analysis, Arc-length method, Structural stability, Limit points, Buckling
• Public URL: http://researchrepository.napier.ac.uk/Output/2893824