DOI QR코드

DOI QR Code

Innovative displacement-based beam-column element with shear deformation and imperfection

  • Tang, Yi-Qun (Department of Engineering Mechanics, Jiangsu Key Laboratory of Engineering Mechanics, Southeast University) ;
  • Ding, Yue-Yang (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Liu, Yao-Peng (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Chan, Siu-Lai (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Du, Er-Feng (Department of Engineering Mechanics, Jiangsu Key Laboratory of Engineering Mechanics, Southeast University)
  • Received : 2020.07.14
  • Accepted : 2021.11.20
  • Published : 2022.01.10

Abstract

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.

Keywords

Acknowledgement

The authors are grateful for financial support from the National Natural Science Foundation of China (52008094) and Natural Science Foundation of Jiangsu Province (SBK20200402). The authors are also grateful for financial support from the Research Grant Council of the Hong Kong SAR Government on the project "Joint-based second order direct analysis for domed structures allowing for finite joint stiffness (PolyU 152039/18E)" and Innovation and Technology Fund for the project "A new membrane-flood gate system for extreme weather hazardous mitigations for use in Hong Kong and worldwide (K-ZPD1)".

References

  1. Alsafadie, R., Hjiaj, M. and Battini, J.M. (2011), "Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation", Thin-Walled Struct., 49(4), 523-533. https://doi.org/10.1016/j.tws.2010.12.002.
  2. Argyris, J. (1982), "An excursion into large rotations", Comput. Methods Appl. Mech. Eng., 32(1), 85-155. https://doi.org/10.1016/0045-7825(82)90069-X.
  3. Batoz, J.L. and Dhatt, G. (2010), "Incremental displacement algorithms for nonlinear problems", Int. J. Numer. Meth. Eng., 14(8), 1262-1267. https://doi.org/10.1002/nme.1620140811.
  4. Battini, J.M. (2002), Co-Rotational Beam Elements in Instability Problems, Technical Report, Royal Institute of Technology, Department of Mechanics, SE-100 44 Stockholm, Sweden.
  5. Chan, S.L. (1991), "A generalized numerical procedure for nonlinear analysis of frames exhibiting a limit or a bifurcation point", Int. J. Space Struct., 6(2), 99-114. https://doi.org/10.1177/026635119100600203.
  6. Chan, S.L. (1992), "Large deflection kinematic formulations for three-dimensional framed structures", Comput. Methods Appl. Mech. Eng., 95(1), 17-36. https://doi.org/10.1016/0045-7825(92)90079-Y.
  7. Chan, S.L. and Gu, J.X. (2000), "Exact tangent stiffness for imperfect beam-column members", J. Struct. Eng., 126(9), 491-493. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:9(1094).
  8. Chan, S.L. and Zhou, Z.H. (1994), "Pointwise equilibrating polynomial element for nonlinear analysis of Frames", J. Struct. Eng., 120(6), 1703-1717. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:6(1703).
  9. Chan, S.L. and Zhou, Z.H. (1995), "Second-order elastic analysis of frames using single imperfect element per member", J. Struct. Eng., 121(6), 939-945. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:6(939).
  10. Chan J.L.Y. and Lo, S.H. (2019), "Direct analysis of steel frames with asymmetrical semi-rigid joints", Steel Comp. Struct., 31(1), 99-112. https://doi.org/10.12989/scs.2019.31.1.099.
  11. Chiorean, C.G. (2009), "A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks", Eng. Struct., 31(12), 3016-3033. https://doi.org/10.1016/j.engstruct.2009.08.003.
  12. Crisfield, M.A. (1983), "An arc-length method including line searches and accelerations", Int. J. Numer. Meth. Eng., 19(9), 1269-1289. https://doi.org/10.1002/nme.1620190902.
  13. Du, Z.L., Liu, Y.P. and Chan, S.L. (2017), "A second-order flexibility-based beam-column element with member imperfection", Eng. Struct., 143, 410-426. https://doi.org/10.1016/j.engstruct.2017.04.023.
  14. Du, Z.L., Liu, Y.P. and Chan, S.L. (2018), "A force-based element for direct analysis using stress-resultant plasticity model", Steel Comp. Struct., 29(2), 175-186. https://doi.org/10.12989/scs.2018.29.2.175.
  15. Felippa, C.A. and Haugen, B. (2005), "A unified formulation of small-strain corotational finite elements: I. Theory", Comput. Methods Appl. Mech. Eng., 194(21), 2285-2335. https://doi.org/10.1016/j.cma.2004.07.035.
  16. Jola, E.J., Vu, Q.V. and Kim, S.E. (2020), "Effect of residual stress and geometric imperfection on the strength of steel box girders", Steel Comp. Struct., 34(3), 423-440. https://doi.org/10.12989/scs.2020.34.3.423.
  17. Kitipornchai, S. and Al-Bermani, F.G.A. (1990), "Nonlinear analysis of thin-walled structures using least element/member", J. Struct. Eng., 116(1), 215-234. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:1(215).
  18. Liu, S.W., Chan, J.L.Y., Bai, Y. and Chan, S.L. (2018), "Curved-quartic-function elements with end-springs in series for direct analysis of steel frames", Steel Comp. Struct., 29(5), 623-633. https://doi.org/10.12989/scs.2018.29.5.623.
  19. Meek, J.L. and Tan, H.S. (1984), "Geometrically nonlinear analysis of space frames by an incremental iterative technique", Comput. Methods Appl. Mech. Eng., 47(3), 261-282. https://doi.org/10.1016/0045-7825(84)90079-3.
  20. Meek, J.L. and Tan, H.S. (1983), Large Deflection and Post-Buckling Analysis of Two and Three Dimensional Elastic Spatial Frames, Research Report No. CE49, Dept. of Civil Engineering, University of Queensland, Brisbane, Australia.
  21. Neuenhofer, A. and Filippou, F.C. (1997), "Evaluation of nonlinear frame finite-element models", J. Struct. Eng., 123(7), 958-966. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:7(958).
  22. Neuenhofer, A. and Filippou, F.C. (1998), "Geometrically nonlinear flexibility-based frame finite element", J. Struct. Eng., 124(6), 704-711. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:6(704).
  23. Nguyen, P.C. and Kim S.E. (2016), "Advanced analysis for planar steel frames with semi-rigid connections using plastic-zone method", Steel Comp. Struct., 21(5), 1121-1144. https://doi.org/10.12989/scs.2016.21.5.1121.
  24. NIDA (Nonlinear Integrated Design and Analysis) User's Manual (2020), "NIDA 10.0 HTML Online Documentation", http://www.nidacse.com.
  25. Oran, C. (1973), "Tangent stiffness in space frames", J. Struct. Div., 99(6), 987-1001. https://doi.org/10.1061/JSDEAG.0003548
  26. Pacoste, C. and Eriksson, A. (1997), "Beam elements in instability problems", Comput. Methods Appl. Mech. Eng., 144(1-2), 163-197. https://doi.org/10.1016/S0045-7825(96)01165-6.
  27. So, A.K.W. and Chan, S.L. (1995), "Buckling and geometrically nonlinear analysis of frames using one element/member", J. Constr. Steel. Res., 32(2), 227-230. https://doi.org/10.1016/0143-974X(91)90078-F.
  28. Tang, Y.Q., Liu, Y.P., Chan, S.L. and Du, E.F. (2019), "An innovative co-rotational pointwise equilibrating polynomial element based on Timoshenko beam theory for second-order analysis", Thin-Walled Struct., 141, 15-27. https://doi.org/10.1016/j.tws.2019.04.001.
  29. Tang, Y.Q., Zhou, Z.H. and Chan, S.L. (2015), "Nonlinear beam-column element under consistent deformation", Int. J. Struct. Stab. Dy., 15(05), 1450068. https://doi.org/10.1142/S0219455414500680.
  30. Tang, Y.Q., Zhou, Z.H. and Chan, S.L. (2017), "A simplified co-rotational method for quadrilateral shell elements in geometrically nonlinear analysis", Int. J. Numer. Meth. Eng., 112(11), 1519-1538. https://doi.org/10.1002/nme.5567.
  31. Thai, H.T., Kim, S.E. and Kim, J. (2017), "Improved refined plastic hinge analysis accounting for local buckling and lateral-torsional buckling", Steel Comp. Struct., 24(3), 339-349. https://doi.org/10.12989/scs.2017.24.3.339.
  32. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, (2nd Edition), McGraw-Hill, New York, U.S.A.
  33. Trahair, N. (2018), "Trends in the code design of steel framed structures", Adv. Steel Constr., 14(1), 37-56. https://doi.org/10.18057/IJASC.2018.14.1.3.
  34. Zhou, Z.H. and Chan, S.L. (1995), "Self-equilibrating element for second-order analysis of semirigid jointed frames", J. Eng. Mech., 121(8), 896-902. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:8(896).