Geometrically nonlinear and dynamic analysis of Euler-Bernoulli beams using isogeometric approach

Authors

  • Tran Vinh Loc
    Division of Computational Mechanics, Ton Duc Thang University HCM, VN
  • Thai Hoang Chien
    Division of Computational Mechanics, Ton Duc Thang University HCM, VN
  • Nguyen Xuan Hung
    Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science HCM, VN

Keywords:

Isogeometric analysis; Euler-Bernoulli beam; rotation-free; geometric nonlinear; dynamic

Abstract

This paper presents a numerical procedure for geometrically nonlinear and dynamic analysis of Euler-Bernoulli beams based on the framework of isogeometric approach. The method utilizes B-spline as the basis functions for both geometric representation and analysis. Only one deflection variable (without rotational degrees of freedom) is used for each control point. It allows us to use few degrees of freedom while retaining high accuracy of solution. Two numerical examples are provided to illustrate the effectiveness of present method.

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References

Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y. (2005), Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, Vol. 194 (39–41), pp. 4135–4195.

Piegl, L.A.,and Tiller, W. (1997), The NURBS book, Springer Verlag second edition.

Lguedj, T.E., Bazilevs, Y., Calo, V., Hughes, T. (2008), B and F projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order nurbs elements, Computer Methods in Applied Mechanics and Engineering, Vol. 197, pp. 2732-2762.

Beirão da Veiga, L., Buffa, A., Lovadina, C., Martinelli, M., Sangalli, G. (2012), An isogeometric method for the Reissner–Mindlin plate bending problem, Computer Methods in Applied Mechanics and Engineering, Vol. 209-212, pp. 45-53.

Benson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.R. (2010), Isogeometric shell analysis: The Reissner–Mindlin shell, Computer Methods in Applied Mechanics and Engineering, Vol. 199(5-8), pp. 276–289.

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Received: 04-06-2020
Accepted: 04-06-2020
Published: 31-08-2013

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How to Cite

Loc, T. V., Chien, T. H., & Hung, N. X. (2013). Geometrically nonlinear and dynamic analysis of Euler-Bernoulli beams using isogeometric approach. HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY, 3(1), 3–10. Retrieved from https://journalofscience.ou.edu.vn/index.php/tech-en/article/view/392

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Copyright (c) 2013 Tran Vinh Loc; Thai Hoang Chien; Nguyen Xuan Hung

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.