Structural Engineering and Mechanics

  • 제11권3호
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  • Pages.325-340
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  • 2001
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A direct modification method for strains due to non-conforming modes

  • Choi, Chang-Koon (Department of Civil Engineering, Korea Advanced Institute of Science and Technology) ;
  • Chung, Keun-Young (Department of Civil Engineering, Korea Advanced Institute of Science and Technology) ;
  • Lee, Tae-Yeol (Department of Civil Engineering, Korea Advanced Institute of Science and Technology)
  • 발행 : 2001.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper addresses an efficient modification method that eliminates the undesirable effects of strains due to various non-conforming modes so that the non-conforming element can pass the patch test unconditionally. The scheme is incorporated in the element formulation to establish new types of non-conforming hexahedral elements designated as NHx and NVHx for the regular element and variable node element, respectively. Non-conforming displacement modes are selectively added to the ordinary (conforming) element displacement assumptions to improve the bending behavior of the distorted solid element. To verify the validation of proposed direct modification method and the improvement of element behavior, several numerical tests are carried out. Test results show that the proposed method is effective and its applications to non-conforming solid elements guarantee for the element to pass the patch test.

키워드

참고문헌

  1. Choi, C.K. and Schnobrich, W.C. (1975), "Non conforming finite element analysis of shells", J. Eng. Mech. Div. ASCE, 1, 447-464.
  2. Choi, C.K. and Lee, N.H. (1993), "Three dimensional solid elements for adaptive mesh gradation", Structural Engineering and Mechanics, 1(1), 61-74. https://doi.org/10.12989/sem.1993.1.1.061
  3. Choi, C.K., Chung, K.Y. and Lee, N.H. (1996), "Three-dimensional non-conforming 8-node solid elements with Rotational Degrees of Freedom", Structural Engineering and Mechanics, 4(5), 569-586. https://doi.org/10.12989/sem.1996.4.5.569
  4. Choi, C.K., Kim, S.H., Park, Y.M. and Chung, K.Y. (1998), "Two dimensional nonconforming finite elements: A state of the art", Structural Engineering and Mechanics, 6(1), 41-61. https://doi.org/10.12989/sem.1998.6.1.041
  5. Choi, C.K., Chung, K.Y. and Lee, E.J. (2001), "Mixed formulated 13-node elements with rotational degrees of freedom: MR-H13 Elements", Structural Engineering and Mechanics, 11(1), 105-122. https://doi.org/10.12989/sem.2001.11.1.105
  6. Hughes, T.J.R. (1987), The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
  7. Ibrahimbegovic, A., Taylor, R.L. and Wilson, E.L. (1990), "A robust quadrilateral membrane element with rotational degrees of freedom", Int. J. Numer. Methods Eng. 30, 445-457. https://doi.org/10.1002/nme.1620300305
  8. Ibrahimbegovic, A. and Wilson, E.L. (1991), "Thick shell and solid finite elements with independent rotation Fields", Int. J. Numer. Methods Eng., 31, 1393-1414. https://doi.org/10.1002/nme.1620310711
  9. Iura, M. and Atluri, S.N. (1992), "Formulation of a membrane finite element with drilling degrees of freedom", Computational Mechanics, 9, 417-428. https://doi.org/10.1007/BF00364007
  10. Irons, B. and Razaque, A. (1972), "Experience with the patch test for convergence of finite element methods", Math. Foundations of the Finite Element Method (Ed. A. K. Aziz), Academic Press, 557-587.
  11. Irons, B. and Ahmad, S. (1980), Techniques of Finite Elements, Ellis Horwood, Chichester, U.K.
  12. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Fnite Element in Analysis and Design, 1, 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  13. Taylor, R.L., Bersesford, P.J. and Wilson, E.L. (1976), "A non-conforming element for stress analysis", Int. J. Numer. Methods Eng., 10(6), 1211-1219. https://doi.org/10.1002/nme.1620100602
  14. Taylor, R.L., Simo, J.C., Zienkiewicz, O.C. and Chan, A.C.H. (1986), "The patch test-a condition for assessing FEM convergence", Int. J. Numer. Methods Eng., 22, 39-62. https://doi.org/10.1002/nme.1620220105
  15. Wilson, E.L. and Taylor, R.L., Dherty, W.P. and Ghaboussi, J. (1971), "Incompatible displacement modes", ONR Symposium on Numerical and Computer Methods in Structural Mechanics, University of Illinois, Urbana.
  16. Wilson, E.L. and Ibrahimbegovic, A. (1990), "Use of incompatible displacement modes for the calculation of element stiffnesses or stresses", Finite Elements in Analysis and Design, 31, 229-241.
  17. Yunus, S.M. and Pawlak, T.P. (1991), "Solid elements with rotational degrees of freedom. Part I: Hexahedron elements", Int. J. Numer. Methods Eng., 31, 573-592. https://doi.org/10.1002/nme.1620310310

피인용 문헌

  1. Non-conforming modes for improvement of finite element performance vol.14, pp.5, 2002, https://doi.org/10.12989/sem.2002.14.5.595
  2. Variable-node non-conforming membrane elements vol.16, pp.4, 2003, https://doi.org/10.12989/sem.2003.16.4.479
  3. Reliability analysis for the uncertainties in vehicle and high-speed railway bridge system based on an improved response surface method for nonlinear limit states vol.59, pp.1-2, 2010, https://doi.org/10.1007/s11071-009-9521-0
  4. A new quadrilateral 5-node non-conforming membrane element with drilling DOF vol.14, pp.6, 2002, https://doi.org/10.12989/sem.2002.14.6.699
  5. Dynamic analysis of guideway structures by considering ultra high-speed Maglev train-guideway interaction vol.29, pp.4, 2008, https://doi.org/10.12989/sem.2008.29.4.355
  6. Incompatible Bubbles: A non-conforming finite element formulation for linear elasticity vol.196, pp.9-12, 2007, https://doi.org/10.1016/j.cma.2006.09.010
  7. Direct modification for non-conforming elements with drilling DOF vol.55, pp.12, 2002, https://doi.org/10.1002/nme.550
  8. A new three-dimensional finite element analysis model of high-speed train–bridge interactions vol.25, pp.13, 2003, https://doi.org/10.1016/S0141-0296(03)00133-0
  9. A Four-node General Shell Element with Drilling DOFs vol.16, pp.4, 2012, https://doi.org/10.5000/EESK.2012.16.4.037