Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

6 Issues per year


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Open Access
Online
ISSN
2300-1917
See all formats and pricing
More options …
Volume 61, Issue 1 (Mar 2013)

Issues

Application of grid convergence index in FE computation

L. Kwaśniewski
  • Corresponding author
  • Faculty of Civil Engineering, Warsaw University of Technology, 16 Armii Ludowej Ave., 00-637 Warszawa, Poland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-05-01 | DOI: https://doi.org/10.2478/bpasts-2013-0010

Abstract

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

Keywords : discretization error; grid convergence index; finite element; mesh refinement; verification

  • [1] J.T. Oden, T. Belytschko, J. Fish, T.J. Hughes, C. Johnson, D. Keyes, A. Laub, L. Petzold, D. Srolovitz, and S. Yip, “Revolutionizing engineering science through simulation”, in NationalScience Foundation Blue Ribbon Panel Report 65, National Science Foundation, Arlington, 2006.Google Scholar

  • [2] L.F. Konikow and J.D. Bredehoeft, “Ground-water models cannot be validated”, Advances in Water Resources 15 (1), 75-83 (1992).Google Scholar

  • [3] L. Kwaśniewski, “On practical problems with verification and validation of computational models”, Archives of Civil Eng. LV (3), 323-346 (2009).Google Scholar

  • [4] I. Babuska and J.T. Oden, “Verification and validation in computational engineering and science: basic concepts”, ComputerMethods in Applied Mechanics and Eng. 193 (36-38), 4057-4066 (2004).Google Scholar

  • [5] U.S. Department of Defense, Verification, Validation, andAccreditation (VV&A) Recommended Practices Guide, Defense Modeling and Simulation Office, Office of the Director of Defense Research and Engineering, Virginia, 1996, www.dmso.mil/docslib.Google Scholar

  • [6] AIAA, Guide for the Verification and Validation of ComputationalFluid Dynamics Simulations, American Institute of Aeronautics and Astronautics, AIAA-G-077-1998, Reston, 1998.Google Scholar

  • [7] ASME, Guide for Verification and Validation in ComputationalSolid Mechanics, American Society of Mechanical Engineers, Virginia, 2006.Google Scholar

  • [8] J. Zhu and O. Zienkiewicz, “A posteriori error estimation and three-dimensional automatic mesh generation”, in Finite Elementsin Analysis and Design, vol. 25, no. 1-2, pp. 167-184, Elsevier, London, 1997.Google Scholar

  • [9] L.E. Schwer, “Is your mesh refined enough? Estimating discretization error using GCI”, 7th LS-DYNA Anwenderforum I-I-45-54, CD-ROM (2008).Google Scholar

  • [10] P.J. Roache, “Verification and validation in computational science and engineering”, Computing in Science Eng. 1, 8-9 (1998).Google Scholar

  • [11] L.F. Richardson, “The approximate arithmetical solution by finite differences of physical problems including differential equations. with an application to the stresses in a masonry dam”, Philosophical Trans. Royal Society of London A 210 (459-470), 307-357 (1911).Google Scholar

  • [12] NASA NPARC Alliance Verification and Validation, ExaminingSpatial (Grid) Convergence, http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html.Google Scholar

  • [13] J.O. Hallquist, LS-DYNA Keyword User’s Manual-Version971, Livermore Software Technology Corporation, Livermore, 2007.Google Scholar

  • [14] ABAQUS Users Manual V. 6.10-1, Dassault Systemes Simulia Corp., Providence, 2010.Google Scholar

  • [15] J. Gere and S. Timoshenko, Mechanics of Materials, Brooks, Cole Publishing, New York, 2000.Google Scholar

About the article

Published Online: 2013-05-01

Published in Print: 2013-03-01


Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/bpasts-2013-0010.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Changchao Guo, Zhijun Wei, Kan Xie, and Ningfei Wang
Journal of Propulsion and Power, 2017, Volume 33, Number 4, Page 815

Comments (0)

Please log in or register to comment.
Log in