DOI QR코드

DOI QR Code

Three-field mixed beam-column finite element for geometric and material nonlinear analysis

  • Ferreira, Miguel (CERIS, Instituto Superior Tecnico, University of Lisbon) ;
  • Providencia, Paulo (University of Coimbra, INESC Coimbra) ;
  • Costa, Ricardo (Civil Engineering Department, ISISE, University of Coimbra) ;
  • Gala, Pedro (DEC ESTG, INESC Coimbra, Polytechnic Institute of Leiria) ;
  • Almeida, Joao (DECivil, ICIST, CERIS, Instituto Superior Tecnico, University of Lisbon)
  • 투고 : 2020.05.11
  • 심사 : 2021.05.28
  • 발행 : 2021.07.25

초록

A mixed element (3fME) for geometric and material nonlinear finite element analysis of plane skeletal structures is presented, which can reach any predefined accuracy with only one element per structural member. This element is based on the 3-field approach-an application of the Hu-Washizu principle-directly approximating the fields of displacements, strains and stresses. The presented formulation considers both (i) geometrically nonlinear behavior-by including the second-order term in the strain-displacement relations and establishing equilibrium in the deformed configuration-and (ii) materially nonlinear elastoplastic behavior, at the fibre level, automatically handling the axial-bending interaction. The illustrative examples include both compression- and tension-bending interaction, and compare the accuracy of the novel finite element with published results.

키워드

과제정보

This work is partially supported by the Portuguese Foundation for Science and Technology under project grant UIDB/00308/2020.

참고문헌

  1. Akkose, M., Sunca, F. and Turkay, A. (2018), "Pushover analysis of prefabricated structures with various partially fixity rates", Earthq. Struct., 14(1), 21-32. https://doi.org/10.12989/eas.2018.14.1.021.
  2. Bayat, M. and Zahrai, S.M. (2017), "Seismic performance of mid-rise steel frames with semi-rigid connections having different moment capacity", Steel Compos. Struct., 25(1), 1-17. https://doi.org/10.12989/scs.2017.25.1.001.
  3. Chan, S. (1988), "Geometric and material non-linear analysis of beam-columns and frames using the minimum residual displacement method", Int. J. Numer. Meth. Eng., 26, 2657-2669. https://doi.org/10.1002/nme.1620261206.
  4. Chen, W. and Lui, E. (1991), Stability Design of Steel Frames, Taylor & Francis.
  5. Cottrell, J.A., Hughes, T.J. and Bazilevs, Y. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley & Sons.
  6. Doltsinis, L.S. (1989), "Non-linear concepts in the analysis of solids and structures", Ed. L.S. Doltsinis, Advances in Computational Nonlinear Mechanics, Chapter 1, Springer, Wien.
  7. EN 1993-1-1:2005 (2005), Eurocode 3: Design of Steel Structures-Part 1-1: General Rules and Rules for Buildings, European Committee for Standardization, Brussels.
  8. Felippa, C.A. (1994), "A survey of parametrized variational principles and applications to computational mechanics", Comput. Meth. Appl. Mech. Eng., 113(1-2), 109-139. https://doi.org/10.1016/0045-7825(94)90214-3.
  9. Ferreira, M., Andrade, A., Providencia, P. and Cabrera, F. (2018), "An efficient three-field mixed finite element model for the linear analysis of composite beams with deformable shear connection", Compos. Struct., 191, 190-201. https://doi.org/10.1016/j.compstruct.2018.02.045.
  10. Ferreira, M., Providencia, P., Gala, P. and Almeida, J. (2017), "Improved displacement based alternative to force based finite element for nonlinear analysis of framed structures", Eng. Struct., 135, 95-103. https://doi.org/10.1016/j.engstruct.2016.12.020.
  11. Gala, P. (2013), "The fictitious force method and its application to the non-linear material analysis of skeletal structures", Ph.D. Thesis, University of Coimbra, Portugal.
  12. Hadianfard, M.A., Eskandari, F. and Javid Sharifi, B. (2018), "The effects of beam-column connections on behavior of buckling-restrained braced frames", Steel Compos. Struct., 28(3), 309-318. https://doi.org/10.12989/scs.2018.28.3.309.
  13. Hjelmstad, K.D. and Taciroglu, E. (2003), "Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli Euler beams", Commun. Numer. Meth. Eng., 19(10), 809-832. https://doi.org/10.1002/cnm.622.
  14. Hjelmstad, K.D. and Taciroglu, E. (2005), "Variational basis of nonlinear flexibility methods for structural analysis of frames", J. Eng. Mech., 131(11), 1157-1169. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:11(1157).
  15. Jalilkhani, M. and Manafpour, A.R. (2018), "Evaluation of seismic collapse capacity of regular RC frames using nonlinear static procedure", Struct. Eng. Mech., 68(6), 647-660. https://doi.org/10.12989/sem.2018.68.6.647.
  16. Kondoh, K. and Atluri, S. (1986), "A simplified finite element method for large deformation, postbuckling analyses of large frame structures, using explicitly derived tangent stiffness matrices", Int. J. Numer. Meth. Eng., 23(1), 69-90. https://doi.org/10.1002/nme.1620230107.
  17. Lee, C.L. and Filippou, F.C. (2015), "Frame element with mixed formulations for composite and RC members with bond slip. i: theory and fixed-end rotation", J. Struct. Eng., 141(11), 04015039. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001273.
  18. Lui, E. (1988), "A practical P-delta analysis method for type FR and PR frames", Eng. J., AISC, 25, 85-98.
  19. McKenna, F., Scott, M.H. and Fenves, G.L. (2010), "Nonlinear finite-element analysis software architecture using object composition", J. Comput. Civil Eng., 24(1), 95-107. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000002.
  20. Moghaddam, S.H. and Masoodi, A.R. (2019), "Elastoplastic nonlinear behavior of planar steel gabled frame", Adv. Comput. Des., 4(4), 397-413. http://doi.org/10.12989/acd.2019.4.4.397.
  21. Munro, J. (1978), "Optimal plastic design of frames", Proceedings of NATO, Waterloo: Advanced Study in Engineering Plasticity by Mathematical Programming, 136-171.
  22. 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).
  23. Reddy, J. (2004), An Introduction to Nonlinear Finite Element Analysis, OUP Oxford.
  24. Sharma, V., Shrimali, M.K., Bharti, S.D. and Datt, T.K. (2020), "Evaluation of responses of semirigid frames at target displacements predicted by the nonlinear static analysis", Steel Compos. Struct., 36(4), 399-415. https://doi.org/10.12989/scs.2020.36.4.399.
  25. Simo, J.C. and Rifai, M.S. (1990), "A class of mixed assumed strain methods and the method of incompatible modes", Int. J. Numer. Meth. Eng., 29(8), 1595-1638. https://doi.org/10.1002/nme.1620290802.
  26. Souza, R. (2000), "Force-based finite element for large displacement inelastic analysis of frames", Ph.D. Thesis, University of California, Berkeley.
  27. Spacone, E., Filippou, F.C. and Taucer, F.F. (1996), "Fibre beam-column model for non-linear analysis of R/C frames: Part I. Formulation", Earthq. Eng. Struct. Dyn., 25(7), 711-725. https://doi.org/10.1002/(SICI)1096- 9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9.
  28. Taylor, R.L., Filippou, F.C., Saritas, A. and Auricchio, F. (2003), "A mixed finite element method for beam and frame problems", Comput. Mech., 31(1-2), 192-203. https://doi.org/10.1007/s00466-003-0410-y.
  29. Timoshenko, S. and Gere, J. (1961), Theory of Elastic Stability, McGraw-Hill.
  30. Wierzbicki, T. (2013), "Structural mechanics", Lecture Notes, MIT OpenCourseWare, Massachusetts.
  31. Williams, F. (1964), "An approach to the nonlinear behaviour of the members of a rigid-jointed plane framework with finite deflections", Quart. J. Mech. Appl. Math., 17(4), 451-469. https://doi.org/10.1093/qjmam/17.4.451.
  32. Wood, R. and Zienkiewicz, O. (1977), "Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells", Compos. Struct., 7(6), 725-735. https://doi.org/10.1016/0045-7949(77)90027-X.
  33. Wriggers, P. and Korelc, J. (1996), "On enhanced strain methods for small and finite deformations of solids", Comput. Mech., 18(6), 413-428. https://doi.org/10.1007/BF00350250.
  34. Zienkiewicz, O.C., Taylor, R.L. and Fox, D. (2014), The Finite Element Method for Solid and Structural Mechanics, 7th Edition, Elsevier.
  35. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (2013), The Finite Element Method: Its Basis and Fundamentals, 6th Edition, Elsevier.