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Bulletin of the Polish Academy of Sciences Technical Sciences
The Journal of Polish Academy of Sciences
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Application of grid convergence index in FE computation
1Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej Ave., 00-637 Warszawa, Poland
This content is open access.
Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences. Volume 61, Issue 1, Pages 123–128, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/bpasts-2013-0010, May 2013
- Published Online:
This paper presents an application of the grid convergence index (GCI) concept based on the Richardson extrapolation to a selected simple problem of a cantilever beam loaded with vertical forces at the tip end. The GCI method, popular in computational fluid dynamics, has been recently recommended for finite element (FE) applications in solid and structural mechanics. Based on the results obtained usually for three meshes, the GCI method enables one to determine, in an objective manner, the order of convergence to estimate the asymptotic solution and the bounds for discretization error. The example shows that the characteristics of the convergence depend on the selection of the quantity of interest, which can be local or a global functional such as the deflection considered here. The results differ for different FE formulations, and the difference is bigger when the nonlinearities (e.g., due to plastic response) are taken into account