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

Kadapa, Chennakesava

Authors



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.

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