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Analysis of plates and shells using an edge-based smoothed finite element method

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Abstract

In this paper, an approach to the analysis of arbitrary thin to moderately thick plates and shells by the edge-based smoothed finite element method (ES-FEM) is presented. The formulation is based on the first order shear deformation theory, and Discrete Shear Gap (DSG) method is employed to mitigate the shear locking. Triangular meshes are used as they can be generated automatically for complicated geometries. The discretized system equations are obtained using the smoothed Galerkin weak form, and the numerical integration is applied based on the edge-based smoothing domains. The smoothing operation can provide a much needed softening effect to the FEM model to reduce the well-known “overly stiff” behavior caused by the fully compatible implementation of the displacement approach based on the Galerkin weakform, and hence improve significantly the solution accuracy. A number of benchmark problems have been studied and the results confirm that the present method can provide accurate results for both plate and shell using triangular mesh.

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References

  1. Pugh ED, Hinton E, Zienkiewicz OC (1978) A study of triangular plate bending element with reduced integration. Int J Numer Methods Eng 12: 1059–1078

    Article  MATH  Google Scholar 

  2. Belytschko T, Stolarski H, Carpenter N (1984) A C0 triangular plate element with one-point quadrature. Int J Numer Methods Eng 20: 787–802

    Article  MATH  Google Scholar 

  3. Stricklin J, Haisler W, Tisdale P, Gunderson R (1969) A rapidly converging triangular plate bending element. AIAA J 7: 180–181

    Article  MATH  Google Scholar 

  4. Dhatt G (1969) Numerical analysis of thin shells by curved triangular elements based on discrete Kirchhoff hypothesis. In: Proceedings of the ASCE symposium on applications of FEM in civil engineering. Vanderbilt University, Nashville, pp 255–278

  5. Dhatt G (1970) An efficient triangular shell element (Kirchhoff triangular shell element design via linear shell theory). AIAA J. 8: 2100–2102

    Article  Google Scholar 

  6. Batoz JL, Bathe KJ, Ho LW (1980) A study of three-node triangular plate bending elements. Int J Numer Methods Eng 15: 1771–1812

    Article  MATH  Google Scholar 

  7. Bathe KJ, Brezzi F (1989) The MITC7 and MITC9 plate bending element. Comput Struct 32: 797–814

    Article  MATH  Google Scholar 

  8. Lee PS, Bathe KJ (2004) Development of MITC isotropic triangular shell finite elements. Comput Struct 82: 945–962

    Article  Google Scholar 

  9. Lee PS, Noh HC, Bathe KJ (2007) Insight into 3-node triangular shell finite element: the effects of element isotropy and mesh patterns. Comput Struct 85: 404–418

    Article  Google Scholar 

  10. Ayad R, Dhatt G, Batoz JL (1998) A new hybrid-mixed variational approach for Reissner–Mindlin plates, the MiSP model. Int J Numer Methods Eng 42: 1149–1479

    Article  MATH  MathSciNet  Google Scholar 

  11. Sze KY, Zhu D (1999) A quadratic assumed natural strain shell curved triangular element. Comp Methods Appl Mech Eng 174: 57–71

    Article  MATH  Google Scholar 

  12. Kim JH, Kim YH (2002) Three-node macro triangular shell element based on the assumed natural strains. Comput Mech 29: 441–458

    Article  MATH  Google Scholar 

  13. Kim JH, Kim YH (2002) A three-node C0 ANS element for geometrically non-linear structural analysis. Comp Methods Appl Mech Engrg 191: 4035–4059

    Article  Google Scholar 

  14. Chen WJ, Cheung YK (2001) Refined 9-Dof triangular Mindin plate elements. Int J Numer Methods Eng 51: 1259–1281

    Article  MATH  Google Scholar 

  15. Chen WJ (2004) Refined 15-DOF triangular discrete degenerated shell element. Int J Numer Methods Eng 60: 1817–1846

    Article  MATH  Google Scholar 

  16. Bletzinger KU, Bischoff M, Ramm E (2000) A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput Struct 75: 321–334

    Article  Google Scholar 

  17. Liu GR (2008) A generalized gradient smoothing technique and smoothed bilinear form for Galerkin formulation of a wide class of computational methods. Int J Comput Methods 5(2): 199–236

    Article  MathSciNet  Google Scholar 

  18. Liu GR (2009) A G space theory and weakened weak (W2) form for a unified formulation of compatible and incompatible methods, Part I: theory and part II: applications to solid mechanics problems. Int J Numer Methods Eng. doi:10.1002/nme.2719 (published online)

  19. Chen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerkin meshfree methods. Int J Numer Methods Eng 50: 435–466

    Article  MATH  Google Scholar 

  20. Liu GR, Zhang GY, Dai KY, Wang YY, Zhong ZH, Li GY, Han X (2005) A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems. Int J Comput Methods 2: 645–665

    Article  MATH  Google Scholar 

  21. Liu GR, Zhang GY (2008) Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM). Int J Numer Methods Eng 74: 1128–1161

    Article  MATH  Google Scholar 

  22. Liu GR, Dai KY, Nguyen TT (2007) A smoothed finite element method for mechanics problems. Comput Mech 39: 859–877

    Article  MATH  Google Scholar 

  23. Dai KY, Liu GR, Nguyen TT (2007) An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics. Finite Elem Anal Des 43: 847–860

    Article  MathSciNet  Google Scholar 

  24. Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71: 902–930

    Article  MathSciNet  Google Scholar 

  25. Cui XY, Liu GR, Li GY, Zhao X, Nguyen TT, Sun GY (2008) A smoothed finite element method (SFEM) for linear and geometrically nonlinear analysis of plates and shells. CMES Comput Model Eng Sci 28(2): 109–126

    MathSciNet  Google Scholar 

  26. Nguyen-Xuan H, Rabczuk T, Bordas S, Debongnie JF (2008) A smoothed finite element method for plate analysis. Comp Methods Appl Mech Eng 197: 1184–1203

    Article  MATH  Google Scholar 

  27. Bathe KJ, Dvorkin EH (1985) A four-node plate bending element based on Mindlin–Reissner plate theory and mixed interpolation. Int J Numer Methods Eng 21: 367–383

    Article  MATH  Google Scholar 

  28. Liu GR (2009) On the G space theory. Int J Comput Methods 6(2): 257–289

    Article  MathSciNet  Google Scholar 

  29. Liu GR, Nguyen TT, Dai KY, Lam KY (2008) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analysis. J Sound Vib 320: 1100–1130

    Article  Google Scholar 

  30. Cui XY, Liu GR, Li GY, Zhang GY, Sun GY (2009) Analysis of elastic–plastic problems using edge-based smoothed finite element. Int J Press Vessel Pip 86: 711–718

    Article  Google Scholar 

  31. Timoshenko S, Woinowsky-Krieger S (1940) Theory of plates and shells. McGraw-Hill, New York

    MATH  Google Scholar 

  32. Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth Heinemann, Oxford

    MATH  Google Scholar 

  33. Zienkiewicz OC, Taylor RL (2000) The finite element method. In: Solid Mechanics, 5th edn, vol. 2. Butterworth-Heinemann, Oxford

  34. Clough RW, Tocher JL (1965) Finite element stiffness matrices for analysis of plates in bending. In: Proceedings of conference on matrix methods in structural mechanics. Air Force Institute of Technology, Wright-Patterson A. F. Base, Ohio, pp 515–545

  35. Alwood RJ, Cornes GM (1969) A polygonal finite element for plate bending problems using the assumed stress approach. Int J Numer Methods Eng 1: 135–149

    Article  Google Scholar 

  36. Bazeley GP, Cheung YK, Irons BM, Zienkiewicz OC (1965) Triangular elements in plate bending conforming and non-conforming solutions. In: Proceedings of conference on matrix methods in structural mechanics. Air Force Institute of Technology, Wright-Patterson A. F. Base, Ohio, pp 547–577

  37. Batoz JL (1982) An explicit formulation for an efficient triangular plate-bending element. Int J Numer Methods Eng 18: 1077–1089

    Article  MATH  Google Scholar 

  38. Batoz JL, Katili I (1992) On a simple triangular Reissner/ Mindlin plate element based on incompatible modes and discrete constraints. Int J Numer Methods Eng 35: 1603–1632

    Article  MATH  Google Scholar 

  39. Batoz JL, Lardeur P (1989) A discrete shear triangular nine dof element for the analysis of thick to very thin plates. Int J Numer Methods Eng 28: 533–560

    Article  MATH  MathSciNet  Google Scholar 

  40. Ugural AC (1981) Stresses in plates and shells. McGraw-Hill, New York

    Google Scholar 

  41. Belytschko T, Stolarski H, Carpenter NA (1984) C0 triangular plate element with one point quadrature. Int J Numer Methods Eng 20: 787–862

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, 410082, Changsha, People’s Republic of China

    Xiangyang Cui, Guang-yao Li & Gang Zheng

  2. Department of Mechanical Engineering, Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, 9 Engineering Drive 1, Singapore, 117576, Singapore

    Xiangyang Cui & Gui-Rong Liu

  3. Singapore-MIT Alliance (SMA), E4-04-10, 4 Engineering Drive 3, Singapore, 117576, Singapore

    Gui-Rong Liu & GuiYong Zhang

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  1. Xiangyang Cui
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  2. Gui-Rong Liu
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  3. Guang-yao Li
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  4. GuiYong Zhang
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  5. Gang Zheng
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Correspondence to Guang-yao Li.

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Cui, X., Liu, GR., Li, Gy. et al. Analysis of plates and shells using an edge-based smoothed finite element method. Comput Mech 45, 141–156 (2010). https://doi.org/10.1007/s00466-009-0429-9

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  • DOI: https://doi.org/10.1007/s00466-009-0429-9

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