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2013 | Vol. 13, no. 1 | 72--81
Tytuł artykułu

A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper a new membrane finite element for linear and materially nonlinear analysis is developed. The displacements field of this element has been developed by the use of the strain based approach, and it is based on the assumed functions for the various components of strain which satisfy the compatibility equation. This rectangular finite element has the three degrees of freedom at each of the four corner nodes (the two translations and the in-plane rotation) and the displacement functions of the developed element satisfy the exact representation of the rigid body modes. For elastoplastic analysis, Von Mises, Tresca and Mohr–Coulomb yield criteria are adopted, and both initial stress and initial strain methods are employed. Numerical experiments in both linear and nonlinear analysis have been conducted to assess accuracy and reliability of the developed element compared to the theoretical results and other membrane finite elements.
Wydawca

Rocznik
Strony
72--81
Opis fizyczny
Bibliogr. 36 poz., rys., tab., wykr.
Twórcy
autor
  • Mechanical Engineering Department, University of Biskra, BP 145, Biskra 07000, Algeria, crebiai@yahoo.fr
autor
Bibliografia
  • [1] M.S. Djoudi, H. Bahai, Strain based finite element for the vibration of cylindrical panels with opening, Thin-Walled Structures 42 (2004) 575–588.
  • [2] M.T. Belarbi, T. Maalam, On improved rectangular finite element for plane linear elasticity analysis, Revue Europeenne des Elements Finis 40 (2005) 985–997.
  • [3] M.T. Belarbi, M. Bourezane, On improved Sabir triangular element with drilling rotation, Revue Europeenne de Genie Civil 9 (2005) 1151–1175.
  • [4] M. Himeur, M. Guenfoud, Bending triangular finite element with a fictious fourth node based on the strain approach, European Journal of Computational Mechanics 20 (2012) 455–485.
  • [5] D.G. Ashwell, A.B. Sabir, T.M. Roberts, Further studies in application of curved finite elements to circular arches, International Journal of Mechanics Science 13 (1971) 507–517.
  • [6] D.G. Ashwel, A.B. Sabir, A new cylindrical shell finite element based on independent strain functions, International Journal of Mechanics Science 14 (1972) 171–183.
  • [7] A.B. Sabir, A rectangular and triangular plane elasticity element with drilling degrees of freedom, In: Proceedings of the 2nd International Conference on Variational Methods in Engineering, Southampton University, Springer-Verlag, Berlin, 1985, pp. 17–25 (Chapter 9).
  • [8] A.B. Sabir, H.Y. Salhi, A strain based finite element for general plane elasticity in polar coordinates, RES 19 (1986) 1–16.
  • [9] A.B. Sabir, A. Sfendji, Triangular and rectangular plane elasticity finite element, Thin-Walled Structures 21 (1995) 225–232.
  • [10] M.T. Belarbi, A. Charif, Developpement d’un nouvel element hexaedrique simple base sur le modele en deformation pour l’etude des plaques minces et epaisses, Revue Europeenne des Elements Finis 8 (1999) 135–157.
  • [11] A.B. Sabir, A.C. Lock, A curved cylindrical shell finite element, International Journal of Mechanical Science 14 (1972) 125–135.
  • [12] A.E. Assan, Analysis of multiple stiffened barrel shell structures by strain-based finite elements, Thin-Walled Structures 35 (1999) 233–253.
  • [13] A.B. Sabir, T.A. Charchafchi, Curved rectangular and quadrilateral shell element for cylindrical shell, in: J.R. Whiteman (Ed.), The Mathematics of Finite Elements and Application, vol. IV, Academic Press, 1982, pp. 231–239.
  • [14] L. Belounar, M. Guenfoud, A new rectangular finite element based on the strain approach for plate bending, Thin-Walled Structures 43 (2005) 47–63.
  • [15] A.B. Sabir, A.C. Lock, The application of finite element to the large deflection geometrically nonlinear behavior of cylindrical shells, International Journal of Variational Methods in Engineering (1972) 766–775 (Southampton).
  • [16 A.B. Sabir, A. Sfendji, Large deflection geometrically nonlinear finite element analysis of circular arches, International Journal of Mechanical Science 15 (1973) 33–47.
  • [17] A.B. Sabir, M.S. Djoudi, Shallow shell finite element for the large deflection geometrically non linear analysis of shells and plates, Thin-Walled Structures 21 (1995) 253–267.
  • [18] M.S. Djoudi, H. Bahai, A shallow shell finite element for the linear and nonlinear analysis of cylindrical shells, Engineering Structures 25 (2003) 769–778.
  • [19] S. Kugler, P. Fotiu, J. Murin, A highly efficient membrane finite element with drilling degrees of freedom, Acta Mechanica 213 (2010) 323–348.
  • [20] A. Madeo, G. Zagari, R. Casciaro, An isostatic quadrilateral membrane finite element with drilling rotations and no spurious modes, Finite Element in Analysis and Design 50 (2012) 21–32.
  • [21] M. Huang, Z. Zhao, C. Shen, An effective planar triangular element with drilling rotation, Finite Element in Analysis and Design 46 (2010) 1031–1036.
  • [22] R.H. Mac-Neal, R.L. Harder, A proposed standard set of problems to test finite element accuracy, Finite Element in Analysis and Design 11 (1985) 3–20.
  • [23] S. Timoshenko, J.N. Goodier, Theory of Elasticity, 2nd ed., McGraw-Hill, New York, 1951.
  • [24] D.J. Allman, A quadrilateral finite element including vertex rotations for plane elasticity analysis, International Journal for Numerical Methods in Engineering 26 (1988) 717–730.
  • [25] J-L. Batoz, G. Dhatt, Modelisation des structures par elements finis, Solides elastiques, Edition Hermes, Paris, vol. 1, 1990.
  • [26] E.L. Wilson, R. Taylor, W.P. Doherty, J. Ghaboussi, Incompatible displacement models, in: Fenves et al. (Ed.), Numerical and Computer Methods in Structural Mechanics, Academic Press, New York, 1973, pp. 43–57.
  • [27] R.L. Taylor, P.J. Beresford, E.L. Wilson, Non conforming element for stress analysis, International Journal for Numerical Methods in Engineering 10 (1976) 1211–1219.
  • [28] T.H. Pian, K. Sumihara, Rational approach for assumed stress finite elements, International Journal for Numerical Methods in Engineering 20 (1984) 1685–1695.
  • [29] R. Ayad, Elements finis de plaque et coque en formulation mixte avec projection en cisaillement, These de Doctorat, U.T.C, 1993.
  • [30] A. Ibrahimobigovic, R.L. Taylor, E.L. Wilson, A robust quadrilateral membrane finite element with drilling degrees of freedom, International Journal for Numerical Methods in Engineering 30 (1990) 445–457.
  • [31] R.L. Taylor, J.C. Simo, Bending and membrane elements for analysis of thick and thin shells, in: J. Middelton, G.N. Pande (Eds.), Proceeding Numeta, 1985, pp. 587–591.
  • [32] D.V. Griffiths, S.M. Willson, An explicit form of the plastic matrix for Mohr–Coulomb materials, Communications in Applied Numerical Methods 2 (1986) 523–529.
  • [33] I.M. Smith, D.V. Griffith, Programming the Finite Element Method, 4th ed., John Wiley & Sons, Ltd, UK, 2004.
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  • [35] P. Miaojuan, L. Dongming, C. Yumin, The complex variable element-free Galerkin (CVEFG) method for elasto-plasticity problems, Engineering Structures 33 (2011) 127–135.
  • [36] D.V. Griffth, The effect of pore fluid compressibility on failure loads in elastic plastic soil, International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985) 253–259.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-30fece8a-8c01-4fd3-bccf-07252c66e7a7
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