DOI QR코드

DOI QR Code

Computationally efficient 3D finite element modeling of RC structures

  • Markou, George (Alhosn University, Department of Civil Engineering) ;
  • Papadrakakis, Manolis (Institute of Structural Analysis & Seismic Research, National Technical University of Athens)
  • Received : 2012.04.04
  • Accepted : 2013.05.02
  • Published : 2013.10.25

Abstract

A detailed finite element modeling is presented for the simulation of the nonlinear behavior of reinforced concrete structures which manages to predict the nonlinear behavior of four different experimental setups with computational efficiency, robustness and accuracy. The proposed modeling method uses 8-node hexahedral isoparametric elements for the discretization of concrete. Steel rebars may have any orientation inside the solid concrete elements allowing the simulation of longitudinal as well as transverse reinforcement. Concrete cracking is treated with the smeared crack approach, while steel reinforcement is modeled with the natural beam-column flexibility-based element that takes into consideration shear and bending stiffness. The performance of the proposed modeling is demonstrated by comparing the numerical predictions with existing experimental and numerical results in the literature as well as with those of a commercial code. The results show that the proposed refined simulation predicts accurately the nonlinear inelastic behavior of reinforced concrete structures achieving numerical robustness and computational efficiency.

Keywords

References

  1. Argyris, J., Tenek, L. and Olofsson, L. (1997), "TRIC: a simple but sophisticated 3-node triangular element based on 6 rigid-body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells", Comput. Methods Appl. Mech. Eng., 145, 11-85. https://doi.org/10.1016/S0045-7825(96)01233-9
  2. Argyris, J.H., Balmer, H., Doltsinis, J.S., Dunne, P.C., Haase, M., Kleiber, M., Malejannakis, G.A., Mlejnek, H.P., Muller, M. and Scharf, D.W. (1979), "Finite element method - the natural approach", Comput. Methods Appl. Mech. Eng., 17(18), 1-106.
  3. Argyris, J.H., Tenek, L. and Mattsson, A. (1998), "BEC: A 2-node fast converging shear-deformable isotropic and composite beam element based on 6 rigid-body and 6 straining modes", Comput. Methods Appl. Mech. Eng., 152, 281-336. https://doi.org/10.1016/S0045-7825(97)00144-8
  4. Armero, F. and Oller, S. (2000), "A general framework for continuum damage models. I. Infinitesimal plastic damage models in stress space", Int. J. Solids Struct., 37(48-50), 7409-7436. https://doi.org/10.1016/S0020-7683(00)00205-5
  5. Balan, T.A., Spacone, E. and Kwon, M. (2001), "A 3D hypoplastic model for cyclic analysis of concrete structures", Eng. Struct., 23(4), 333-342. https://doi.org/10.1016/S0141-0296(00)00048-1
  6. Barzegar, F. and Maddipudi, S. (1994), "Generating reinforcement in FE modeling of concrete structures", J. Struct. Eng., 120, 1656-1662. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:5(1656)
  7. Bathe, K.J. (1995), Finite Element Procedures, Prentice Hall Inc., Upper Saddle River, New Jersey, USA.
  8. Bažant, Z.P. and Oh, B.H. (1983), "Crack band theory for fracture of concrete", Mater. Construct., 16(3),155-177. https://doi.org/10.1007/BF02486267
  9. Bažant, Z.P. and Zdenek, P. (1983), "Comment on orthotropic models for concrete and Geomaterials", J. Eng. Mech., 109(3), 849-865. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:3(849)
  10. Bertero, V.V., Aktan, A., Charney, F. and Sause, R. (1985), "Earthquake simulator tests and associated experimental analytical and correlation studies of one-fifth scale model", Earthq. Effects on Reinforced Concrete Structures, ACI, SP, Detroit, 375-424.
  11. Borja, R.I., Sama, K.M. and Sanz, P.F. (2003), "On the numerical integration of three-invariant elastoplastic constitutive models", Comput. Methods Appl. Mech. Eng., 192, 1227-1258. https://doi.org/10.1016/S0045-7825(02)00620-5
  12. Bresel, B. and Scordelis, A.C. (1963), Shear strength of reinforced concrete beams, ACI J., 60, 51-74.
  13. Cedolin, L. and Dei, P.S. (1977), "Finite element studies of shear-critical R/C beams", ASCE, J. Eng. Mech. Div., 103(3), 395-410.
  14. Cervenka, J. and Papanikolaou, V.K. (2008), "Three dimensional combined fracture-plastic material model for concrete", Int. J. Plasticity, 24(12), 2192-2220. https://doi.org/10.1016/j.ijplas.2008.01.004
  15. Cervenka, V. (1970), Inelastic finite element analysis of reinforced concrete panels under plane loads, Ph.D., University of Colorado, University Microfilms, Inc., Michigan.
  16. Cervenka, V., Jendele, L., Cervenka, J. (2008), ATENA program documentation. Part 1: Theory, Cervenka Consulting, Prague, Czech Republic.
  17. Cervera, M., Hinton, E. and Hassan, O. (1987), "Nonlinear Analysis of RC plate and shell structures using 20-noded isoparametric brick elements", Comput. Struct., 25, 845-869. https://doi.org/10.1016/0045-7949(87)90200-8
  18. Ciampi, V. and Nicoletti, M. (1986), "Parameter identification for cyclic constitutive models with stiffness and strength degradation", Procceding of the 8th European Conference on Earthquake Engineering, Lisbon.
  19. Clough, R.W., Benuska, K.L. and Wilson, E.L. (1965), "Inelastic earthquake response of tall buildings", Proceeding of the 3th World Conference on Earthquake Engineering, New Zealand, 11, New Zealand.
  20. Cotsovos,, D.M., Zeris, C.A. and Abas, A.A. (2009), "Finite Element Modeling of Structural Concrete", ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2009, Rhodes, Greece.
  21. Darwin, D. and Pecknold, D.A. (1976), "Analysis of RC shear panels under cyclic loading", J. Struct. Div., ASCE, 102(2), 355-369.
  22. Desmorat, R., Gatuingt, F. and Ragueneau, F. (2007), "Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials", Eng. Fracture Mech., 74(10), 1539-1560. https://doi.org/10.1016/j.engfracmech.2006.09.012
  23. Elwi, A.E. and Hrudey, T.M. (1989), "Finite element model for curved embedded reinforcement", J. Eng. Mech., 115, 740-754. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:4(740)
  24. Fardis, M.N., Alibe, B. and Tasoulas, J.L. (1983), "Monotonic and cyclic constitutive law for concrete", J. Eng. Mech., ASCE, 109, 516-536. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:2(516)
  25. Girard, C. and Bastien, J. (2002), "Finite element bond slip model for concrete columns under cyclic loads", J. Struct. Eng., ASCE, 128, 1502-1510. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:12(1502)
  26. Gonzalez-Vidosa, F., Kotsovos, M.D. and Pavlovic, M.N. (1988), "On the numerical instability of the smeared-crack approach in the nonlinear modeling of concrete structures", Commun. Appl. Num. Meth. Engng, 4, 799-806. https://doi.org/10.1002/cnm.1630040614
  27. Gonzalez-Vidosa, F., Kotsovos, M.D. and Pavlovic, M.N. (1991), "A three-dimensional nonlinear finite-element model for structural concrete; Part 1: main features and objectivity study and Part 2: generality study", Proceedings of the Institution of Civil Engineers, Part 2, Research and Theory, 91, 517-544. https://doi.org/10.1680/iicep.1991.15628
  28. Hartl, H. and Handel, C.H. (2002), "3D finite element modeling of reinforced concrete structures", fib 2002, Osaka Congress, Japan.
  29. Ile, N. and Reynouard, J.M. (2000), "Nonlinear analysis of reinforced concrete shear wall under earthquake loading", J. Earthq. Eng., 4(2), 183-213.
  30. Jason, L., Huerta, A., Pijaudier-Cabot, G. and Ghavamian, S. (2006), "An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model", Comput. Methods Appl. Mech. Eng., 195(52), 7077-7092. https://doi.org/10.1016/j.cma.2005.04.017
  31. Jendele, L. and Červenka, J. (2009), "On the solution of multi-point constraints - Application to FE analysis of reinforced concrete structures", Comput. Struct., 87, 970-980. https://doi.org/10.1016/j.compstruc.2008.04.018
  32. Jiràsek, M. and Rolshoven, S. (2003), "Comparison of integral-type nonlocal plasticity models for strain-softening materials", Int. J. Eng. Sci., 41, 1553-1602. https://doi.org/10.1016/S0020-7225(03)00027-2
  33. Kolleger, J. and Mehlhorn, G. (1987), "Material model for cracked reinforced concrete", IABSE Colloquium on Computational Mechanics of Concrete Structures-Advances and Applications, Delft, 63-74.
  34. Kotsovos, M.D. (1979), "A mathematical description of the strength properties of concrete under generalized stress", Mag. Concrete Res., 31(108), 151-158. https://doi.org/10.1680/macr.1979.31.108.151
  35. Kotsovos, M.D. (1983), "Effect of Testing Techniques on the Post-Ultimate Behavior of Concrete in Compression", Mater. Struct., RILEM, 16(91), 3-12.
  36. Kotsovos, M.D. (1984), "Concrete. A brittle fracturing material", RILEM Mater. Struct., 17, 107-115.
  37. Kotsovos, M.D. and Pavlovic, M.N. (1995), Structural concrete. Finite Element Analysis for Limit State Design, Thomas Telford, London.
  38. Kwak, H.G. and Kim, D.Y. (2001), "Nonlinear analysis of RC shear walls considering tension-stiffening effect", Comput. Struct., 79, 499-517. https://doi.org/10.1016/S0045-7949(00)00157-7
  39. Kwak, H.G. and Kim, D.Y. (2001), "Nonlinear analysis of RC shear walls considering tension-stiffening effect", Comput. Struct., 79, 499-517. https://doi.org/10.1016/S0045-7949(00)00157-7
  40. Kwak, H.G. and Kim, D.Y. (2004), "Material nonlinear analysis of RC shear walls subject to cyclic loadings", Eng. Struct., 26, 1423-1436. https://doi.org/10.1016/j.engstruct.2004.05.014
  41. Kwak, H.G. and Kim, D.Y. (2006), "Cracking behavior of RC panels subject to biaxial tensile stresses", Comput. Struct., 84, 305-317. https://doi.org/10.1016/j.compstruc.2005.09.020
  42. Kwan, W.P. and Billington, S.L. (2001), "Simulation of structural concrete under cyclic load", J. Struct. Eng., 127, 1391-1401. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:12(1391)
  43. Lee, J. and Fenves, G.L. (2001), "A return-mapping algorithm for plastic-damage models: 3D and plane stress formulation", Int. J. Numer. Methods Eng., 50(2), 487-506. https://doi.org/10.1002/1097-0207(20010120)50:2<487::AID-NME44>3.0.CO;2-N
  44. Lefas, I. (1988), Behavior of reinforced concrete walls and its implication for ultimate limit state design, Ph.D., University of London.
  45. Lefas, I.D. and Kotsovos, M.D. (1990), "Strength and deformation characteristics of reinforced concrete walls under load reversals", ACI Struct. J., 87(6), 716-726.
  46. Lubliner, J., Oliver, J., Oller, S. and Onate, E. (1989), "A plastic-damage model for concrete", Int. J. Solids Struct., 3, 299-326.
  47. Lykidis, G. (2007), Static and dynamic analysis of reinforced concrete structures with 3D finite elements and the smeared crack approach, Ph.D. Thesis, NTUA, Greece.
  48. Markou, G. (2010), ReConAn v1.00. Finite Element Analysis Software Manual, Institute of Structural Analysis and Seismic Research, Technical University of Athens, Greece.
  49. Markou, G. (2011), Detailed Three-Dimensional Nonlinear Hybrid Simulation for the Analysis of Large-Scale Reinforced Concrete Structures, Ph.D. Thesis, National Technical University of Athens.
  50. Markou, G. and Papadrakakis, M. (2012), "An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations", Adv. Eng. Soft. ADES, 45(1), 175-187. https://doi.org/10.1016/j.advengsoft.2011.09.025
  51. Mazars, J., Kotronis, P., Ragueneau, F. and Casaux, G. (2006), "Using multifiber beams to account for shear and torsion. Applications to concrete structural elements", Comput. Mathod Appl. Mech., 195, 7264-7281. https://doi.org/10.1016/j.cma.2005.05.053
  52. Mazars, J., Ragueneau, F., Casaux, G., Colombo, A. and Kotronis, P. (2004), "Numerical modeling for earthquake engineering: the case of lightly RC structural walls", Int. J. Numer. Anal. Methods Geom., 28, 857-874. https://doi.org/10.1002/nag.363
  53. Menegotto, M. and Pinto, P.E. (1973), "Method of analysis for cyclically loaded reinforced concrete plane frames Including changes in geometry and non-elastic behavior of elements under combined normal force and bending", Proceedings, IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, Lisbon.
  54. Mergos, P.E. and Kappos, A.J. (2008), "A distributed shear and flexural flexibility model with shear-flexure interaction for R/C members subjected to seismic loading", Earthq. Eng. Struct. Dyn., 37 1349-1370. https://doi.org/10.1002/eqe.812
  55. Mirzabozorg, H. and Ghaemian, M. (2005), "Nonlinear behavior of mass concrete in 3d problems using a smeared crack approach", Earthq. Eng. Struct. Dyn., 34, 247-269. https://doi.org/10.1002/eqe.423
  56. Mitchell, W.F. (1997), "A Fortran 90 Interface for OpenGL", NISTIR 5985.
  57. Navarro, G.J., Miguel, S.P., Fernandez, P.M.A. and Filippou, F.C. (2007), "A 3D numerical model for reinforced and prestressed concrete elements subjected to combined axial, bending, shear and torsion loading", Eng. Struct., 29, 3404-3419. https://doi.org/10.1016/j.engstruct.2007.09.001
  58. Nechnech, W., Meftah, F. and Reynouard, J.M. (2002), "An elasto-plastic damage model for plain concrete subjected to high temperatures", Eng. Struct., 24(5) 597-611.
  59. Oliver, J., Linero, D.L., Huespe, A.E. and Manzoli, O.L. (2008), "Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach", Comput. Methods Appl. Mech. Eng., 197, 332-348. https://doi.org/10.1016/j.cma.2007.05.017
  60. Oliver, J. (1989), "Consistent characteristic length for smeared cracking models", Int. J. Numer. Methods Eng., 28(2), 461-474. https://doi.org/10.1002/nme.1620280214
  61. Ozbolt, J. and Li, Y.J. (2001), "Three dimensional cyclic analysis of compressive diagonal shear failure", Finite Element Anal. RC Struct., Eds. (Willam, K., Tanabe, T.), ACI, SP, 205(4) , 61-79.
  62. Papachristidis, A., Fragiadakis, M., and Papadrakakis, M. (2009), "A shear-deformable fiber beam-column element for seismic analysis of steel structures", Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN), Rhodes.
  63. Papachristidis, A., Fragiadakis, M., and Papadrakakis, M. (2010), "A 3D fibre beam-column element with shear modeling for the inelastic analysis of steel structures", Comput. Mech., 45(6), 553-572. https://doi.org/10.1007/s00466-010-0470-8
  64. Papaioannou, I., Fragiadakis, M. and Papadrakakis, M. (2005), "Inelastic analysis of framed structures using the fiber approach", Proceeding of the 5th International Congress on Computational Mechanics, GRACM 05, Limassol, Cyprus, 1, 231-238.
  65. Papanikolaou, V.K. and Kappos, A.J. (2009), "Numerical study of confinement effectiveness in solid and hollow reinforced concrete bridge piers: Part 1: Methodology", Eng. Struct., 87(21-22), 1427-1439.
  66. Papanikolaou, V.K. and Kappos, A.J. (2009), "Numerical study of confinement effectiveness in solid and hollow reinforced concrete bridge piers: Part 2: Analysis results and discussion", Eng. Struct., 87(21-22), 1427-1439.
  67. Papanikolopoulos, K. (2003), Investigation of the non-linear behavior of reinforced concrete members with finite elements, Postgraduate Thesis, National Technical University of Athens, Athens.
  68. Park, H. and Kim, J.Y. (2005), "Hybrid plasticity model for reinforced concrete in shear", Eng. Struct., 27, 35-48. https://doi.org/10.1016/j.engstruct.2004.08.013
  69. Rashid, Y.M. (1968), "Ultimate strength analysis of prestressed concrete vessels", Nucl. Eng. Des., 7, 334-344. https://doi.org/10.1016/0029-5493(68)90066-6
  70. Saritas, A. and Filippou, F.C. (2009), "Numerical integration of a class of 3d plastic-damage concrete models and condensation of 3d stress-strain relations for use in beam finite elements", Eng. Stuct., 31(10), 2327-2336. https://doi.org/10.1016/j.engstruct.2009.05.005
  71. Sato, Y. and Naganuma, K. (2007), "Discrete-like crack simulation by smeared crack-based FEM for reinforced concrete", Earthq. Eng. Struct. Dyn., 36, 2137-2152. https://doi.org/10.1002/eqe.720
  72. Siemens PLM Software (2009), World-class finite element analysis (FEA) solution for the Windows desktop, Siemens Product Lifecycle Management Software Inc.
  73. Simo, J.C. and Ju, J.W. (1987), "Strain-based and stress-based continuum damage models.1. formulation", Int. J. Solids Struct., 23(7), 821-840. https://doi.org/10.1016/0020-7683(87)90083-7
  74. Spacone, E., Filippou, F.C. and Taucer, F.F. (1996), "Fibre beam-clumn model for nonlinear analysis of R/C frames Part I: formulation", Earthq. Eng. Struct. Dyn., 25, 711-725. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9
  75. Spiliopoulos, K.V. and Lykidis, G. (2006), "An efficient three-dimensional solid finite element dynamic analysis of reinforced concrete structures", Earthq. Eng. Struct. Dyn., 35, 137-157. https://doi.org/10.1002/eqe.510
  76. Takizawa, H. (1976), "Notes on some basic problems in inelastic analysis or planar RC structures", Trans. Arch. Inst. Japan, 240, Part I, 51-62, Part II, 65-77.
  77. Taucer, F.F., Spacone, E. and Filippou, F.C. (1991), A Fiber beam-column element for seismic response analysis of reinforced concrete structures, Report No. UCB/EERC-91/17, University of California, Berkeley.
  78. Van, Mier, J.G.M. (1986), "Multiaxial strain-softening of concrete", Mater. Struct., RILEM, 19(111), 179-200. https://doi.org/10.1007/BF02472034
  79. Van Mier, J.G.M., Shah, S.P., Arnaud, M., Balayssac, J.P., Bassoul, A., Choi, S., Dasenbrock, D., Ferrara, G., French, C., Gobbi, M.E., Karihaloo, B.L., Konig, G., Kotsovos, M.D., Labnz, J., Lange-Kornbak, D., Markeset, G., Pavlovic, M.N., Simsch, G., Thienel, K.C., Turatsinze, A., Ulmer M., van Vliet, M.R.A. and Zissopoulos, D. (1997), "Test methods for the strain-softening of concrete), Strain-softening of concrete in uniaxial compression", Mater. Struct., RILEM, 30(198), 195-209. https://doi.org/10.1007/BF02486177
  80. Viwathenatepa, S., Popov, E.P. and Bertero, V.V. (1979), Effects of Generalized Loadings on Bond of Reinforcing Bars Embedded in Confined Concreteblocks, Report to National Science Foundation, University of California Berkeley, California.
  81. Zeris, C.A. and Mahin, S. (1988), "Analysis of reinforced concrete beam-columns under uniaxial excitation", J. Struct. Eng., ASCE, 114(4), 804-820. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:4(804)

Cited by

  1. A computationally efficient model for the cyclic behavior of reinforced concrete structural members vol.141, 2017, https://doi.org/10.1016/j.engstruct.2017.03.012
  2. A simplified and efficient hybrid finite element model (HYMOD) for non-linear 3D simulation of RC structures vol.32, pp.5, 2015, https://doi.org/10.1108/EC-11-2013-0269
  3. A quantification of the modelling uncertainty of non-linear finite element analyses of large concrete structures vol.64, 2017, https://doi.org/10.1016/j.strusafe.2016.08.003
  4. Non-linear analysis of shear-critical reinforced concrete beams using the softened membrane model vol.16, pp.4, 2015, https://doi.org/10.1002/suco.201400093
  5. 3D nonlinear constitutive modeling for dynamic analysis of reinforced concrete structural members vol.199, 2017, https://doi.org/10.1016/j.proeng.2017.09.030
  6. Non-linear finite element analyses applicable for the design of large reinforced concrete structures 2017, https://doi.org/10.1080/19648189.2017.1348993
  7. Modelling the flexural behaviour of fibre reinforced concrete beams with FEM vol.99, 2015, https://doi.org/10.1016/j.engstruct.2015.05.028
  8. Towards a better understanding of the ultimate behaviour of LWAC in compression and bending vol.151, 2017, https://doi.org/10.1016/j.engstruct.2017.08.063
  9. 3D Finite Element Modeling of GFRP-Reinforced Concrete Deep Beams without Shear Reinforcement vol.15, pp.02, 2018, https://doi.org/10.1142/S0219876218500019
  10. Computing intersections between non-compatible curves and finite elements vol.56, pp.3, 2015, https://doi.org/10.1007/s00466-015-1181-y
  11. Computationally Efficient and Robust Nonlinear 3D Cyclic Modeling of RC Structures Through a Hybrid Finite Element Model (HYMOD) pp.1793-6969, 2019, https://doi.org/10.1142/S0219876218501256
  12. A numerical-experimental evaluation of beams composed of a steel frame with welded and conventional stirrups vol.22, pp.1, 2013, https://doi.org/10.12989/cac.2018.22.1.027
  13. Finite Element Analysis of RC Beams by the Discrete Model and CBIS Model Using LS-DYNA vol.2021, pp.None, 2013, https://doi.org/10.1155/2021/8857491
  14. Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures vol.14, pp.7, 2013, https://doi.org/10.3390/ma14071578
  15. New fundamental period formulae for soil-reinforced concrete structures interaction using machine learning algorithms and ANNs vol.144, pp.None, 2013, https://doi.org/10.1016/j.soildyn.2021.106656
  16. Finite element modelling of plain and reinforced concrete specimens with the Kotsovos and Pavlovic material model, smeared crack approach and fine meshes vol.30, pp.6, 2013, https://doi.org/10.1177/1056789520986601
  17. A new damage factor for seismic assessment of deficient bare and FRP-retrofitted RC structures vol.248, pp.None, 2021, https://doi.org/10.1016/j.engstruct.2021.113152