Structural Engineering and Mechanics

  • 제43권4호
  • /
  • Pages.411-437
  • /
  • 2012
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A continuum mechanics based 3-D beam finite element with warping displacements and its modeling capabilities

  • Yoon, Kyungho (Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology) ;
  • Lee, Youngyu (Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology) ;
  • Lee, Phill-Seung (Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology)
  • 투고 : 2012.02.09
  • 심사 : 2012.07.12
  • 발행 : 2012.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we propose a continuum mechanics based 3-D beam finite element with cross-sectional discretization allowing for warping displacements. The beam element is directly derived from the assemblage of 3-D solid elements, and this approach results in inherently advanced modeling capabilities of the beam element. In the beam formulation, warping is fully coupled with bending, shearing, and stretching. Consequently, the proposed beam elements can consider free and constrained warping conditions, eccentricities, curved geometries, varying sections, as well as arbitrary cross-sections (including thin/thick-walled, open/closed, and single/multi-cell cross-sections). We then study the modeling and predictive capabilities of the beam elements in twisting beam problems according to geometries, boundary conditions, and cross-sectional meshes. The results are compared with reference solutions obtained by analytical methods and solid and shell finite element models. Excellent modeling capabilities and solution accuracy of the proposed beam element are observed.

키워드

과제정보

연구 과제 주관 기관 : Korea Institute of Energy Technology Evaluation and Planning (KETEP)

참고문헌

  1. Abbott, I.H., Von Doenhoff, A.E. and Stivers, L.S. (1945), Summary of Airfoil Data, NACA report 824, Langley Field.
  2. Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, New York.
  3. Bathe, K.J. and Chaudhary, A. (1982), "On the displacement formulation of torsion of shafts with rectangular cross-section", Int. J. Numer. Meth. Eng., 18, 1565-1568. https://doi.org/10.1002/nme.1620181010
  4. Bathe, K.J., Lee, P.S. and Hiller, J.F. (2003), "Towards improving the MITC9 shell element", Comput. Struct., 81, 477-489. https://doi.org/10.1016/S0045-7949(02)00483-2
  5. Bucalem, M.L. and Bathe, K.J. (1993), "Higher-order MITC general shell elements", Int. J. Numer. Meth. Eng., 36, 3729-3754. https://doi.org/10.1002/nme.1620362109
  6. Chapelle, D. and Bathe, K.J. (2003), The Finite Element Analysis of Shells - Fundamentals, Springer.
  7. Dutta, A. and White, D.W. (1992), "Large displacement formulation of a three-dimensional beam element with cross-sectional warping", Comput. Struct., 45, 9-24. https://doi.org/10.1016/0045-7949(92)90340-6
  8. Dvorkin, E.N. and Bathe, K.J. (1984), "A continuum mechanics based four-node shell element for general nonlinear analysis", Eng. Comput., 1, 77-88. https://doi.org/10.1108/eb023562
  9. Gjelsvik, A. (1981), The Theory of Thin Walled Bars, Wiley, New York.
  10. Gonçalves, R., Ritto-Corrêa, M. and Camotim, D. (2010), "A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory", Comput., Mech., 46, 759-781. https://doi.org/10.1007/s00466-010-0512-2
  11. Gruttmann, F., Sauer, R. and Wagner, W. (1999), "Shear stresses in prismatic beams with arbitrary crosssections", Int. J. Numer. Meth. Eng., 45, 865-889. https://doi.org/10.1002/(SICI)1097-0207(19990710)45:7<865::AID-NME609>3.0.CO;2-3
  12. Lee, P.S. and Bathe, K.J. (2004), "Development of MITC isotropic triangular shell finite elements", Comput. Struct., 82, 945-962. https://doi.org/10.1016/j.compstruc.2004.02.004
  13. Lee, P.S. and Bathe, K.J. (2005), "Insight into finite element shell discretizations by use of the basic shell mathematical model", Comput. Struct., 83, 69-90. https://doi.org/10.1016/j.compstruc.2004.07.005
  14. Lee, P.S. and McClure, G. (2006), "A general 3D L-section beam finite element for elastoplastic large deformation analysis", Comput. Struct., 84, 215-229. https://doi.org/10.1016/j.compstruc.2005.09.013
  15. Lee, P.S. and McClure, G. (2007), "Elastoplastic large deformation analysis of a lattice steel tower structure and comparison with full-scale tests", Int. J. Constr. Steel Res., 63, 709-717. https://doi.org/10.1016/j.jcsr.2006.06.041
  16. Lee, P.S. and Noh, H.C. (2010), "Inelastic buckling behavior of steel members under reversed cyclic loading", Eng. Struct., 32, 2579-2595. https://doi.org/10.1016/j.engstruct.2010.04.031
  17. Lee, P.S., Noh, H.C. and Choi, C.K. (2008), "Geometry-dependent MITC method for a 2-node iso-beam element", Struct. Eng. Mech., 29(2), 203-221. https://doi.org/10.12989/sem.2008.29.2.203
  18. Lee, S.W. and Kim, Y.H. (1987), "A new approach to the finite element modelling of beams with warping effect", Int. J. Numer. Meth. Eng., 24, 2327-2341. https://doi.org/10.1002/nme.1620241207
  19. Pi, Y.L., Bradford, M.A. and Uy, B. (2005), "Nonlinear analysis of members curved in space with warping and Wagner effects", Int. J. Solids Struct., 42, 3147-3169. https://doi.org/10.1016/j.ijsolstr.2004.10.012
  20. Prokiæ, A. (1996), "New warping function for thin-walled beams. I: theory", J. Struct. Eng., 122, 1437-1442. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:12(1437)
  21. Roark, R.J. (1965), Formulas for Stress and Strain, McGraw Hill, New York.
  22. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity, McGraw Hill, New York.
  23. Vlasov, V.Z. (1961), Thin-walled Elastic Beams, Israel Program for Scientific Translations, Jerusalem.
  24. Zivkovic, M., Koji , M., Slavkovi , R. and Grujovi , N. (2001), "A general beam finite element with deformable cross-section", Comput. Meth. Appl. Mech. Eng., 190, 2651-2680. https://doi.org/10.1016/S0045-7825(00)00259-0

피인용 문헌

  1. Error estimation for the automated multi-level substructuring method vol.106, pp.11, 2016, https://doi.org/10.1002/nme.5161
  2. Modeling the warping displacements for discontinuously varying arbitrary cross-section beams vol.131, 2014, https://doi.org/10.1016/j.compstruc.2013.10.013
  3. One-dimensional finite element formulation with node-dependent kinematics vol.192, 2017, https://doi.org/10.1016/j.compstruc.2017.07.008
  4. An experimental and numerical investigation on the effect of longitudinal reinforcements in torsional resistance of RC beams vol.47, pp.2, 2013, https://doi.org/10.12989/sem.2013.47.2.247
  5. Nonlinear performance of continuum mechanics based beam elements focusing on large twisting behaviors vol.281, 2014, https://doi.org/10.1016/j.cma.2014.07.023
  6. An enhanced AMLS method and its performance vol.287, 2015, https://doi.org/10.1016/j.cma.2015.01.004
  7. The MITC3 shell finite element enriched by interpolation covers vol.134, 2014, https://doi.org/10.1016/j.compstruc.2013.12.003
  8. An efficient warping model for elastoplastic torsional analysis of composite beams vol.178, 2017, https://doi.org/10.1016/j.compstruct.2017.07.041
  9. Torsional analysis of a single-bent leaf flexure vol.54, pp.1, 2015, https://doi.org/10.12989/sem.2015.54.1.189
  10. A mixed beam model with non-uniform warpings derived from the Saint Venànt rod vol.121, 2013, https://doi.org/10.1016/j.compstruc.2013.03.017
  11. A higher order beam model for thin-walled structures with in-plane rigid cross-sections vol.84, 2015, https://doi.org/10.1016/j.engstruct.2014.11.008
  12. Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects vol.132, 2015, https://doi.org/10.1016/j.compstruct.2015.07.024
  13. Modeling of helically stranded cables using multiple beam finite elements and its application to torque balance design vol.151, 2017, https://doi.org/10.1016/j.conbuildmat.2017.06.052
  14. Simple Expression of the Ultimate Lateral Resistance of Piles on Sand based on Active Pile Length vol.71, pp.4, 2015, https://doi.org/10.2208/jscejseee.71.I_329
  15. Nonlinear torsional analysis of 3D composite beams using the extended St. Venant solution vol.62, pp.1, 2017, https://doi.org/10.12989/sem.2017.62.1.033
  16. 동시회전의 화이버 단면 보 요소를 이용한 평면 구조물의 재료 및 기하 비선형 해석 vol.30, pp.3, 2012, https://doi.org/10.7734/coseik.2017.30.3.255
  17. Ballasting plan optimization for operation of a 2D floating dry dock vol.74, pp.4, 2020, https://doi.org/10.12989/sem.2020.74.4.521
  18. Towards improving finite element solutions automatically with enriched 2D solid elements vol.76, pp.3, 2012, https://doi.org/10.12989/sem.2020.76.3.379
  19. Simulation of bending and torsion tests of non-welded and welded direct-formed rectangular hollow sections vol.1001, pp.None, 2012, https://doi.org/10.1088/1757-899x/1001/1/012069
  20. FEM simulation of bending and torsion tests of similar size RHS but of the different production options vol.234, pp.None, 2012, https://doi.org/10.1051/e3sconf/202123400079
  21. Strategy to Improve Edge-Based Smoothed Finite Element Solutions Using Enriched 2D Solid Finite Elements vol.11, pp.8, 2012, https://doi.org/10.3390/app11083476
  22. A new solid-beam approach based on first or higher-order beam theories for finite element analysis of thin to thick structures vol.200, pp.None, 2012, https://doi.org/10.1016/j.finel.2021.103655