Triangular Layered Finite Element Method for Reinforced Concrete Slabs

Cover Page

Cite item

Full Text

Abstract

This study presents an advanced layered triangular finite element method for modeling reinforced concrete (RC) slabs, incorporating material nonlinearity based on a refined global-local plate theory. The RC slab's cross-section is discretized into concrete and steel layers, each modeled as an individual plate element with distinct material properties. The proposed formulation independently considers displacement field variables and out-of-plane stress components, enabling precise nodal stress determination through constitutive relationships. A three-node triangular element maintaining C1-continuity is employed for spatial discretization, with governing equations derived using a triangular layered plate theory. Benchmark verification studies confirm the method’s computational accuracy and efficiency, with ultimate deflection predictions exhibiting errors ranging from 2.59% (minimum) to 11.2% (maximum). Comprehensive numerical tests demonstrate that the proposed triangular layered finite element approach delivers high-precision solutions while significantly reducing computational expense.

About the authors

Dara A. Mawlood

Siberian Federal University

Author for correspondence.
Email: dara.mawloud@univsul.edu.iq
ORCID iD: 0009-0003-2819-3107

Master student, Department of Building Structures and Controlled Systems, Institute of Civil Engineering

79 Svobodny аv., 660041, Krasnoyarsk, Russian Federation

Alexandr A. Koyankin

Siberian Federal University

Email: KoyankinAA@mail.ru
ORCID iD: 0000-0001-5271-9904
SPIN-code: 2779-8314

Candidate of Technical Sciences, Associate Professor of the Department of Building Structures and Controlled Systems, Institute of Civil Engineering

79 Svobodny аv., 660041, Krasnoyarsk, Russian Federation

References

  1. Le C.V., Ho V.Q., Ho P.L.H., Nguyen P.H. Limit state analysis of thin plates and slabs by a numerical pseudo-lower yield design approach. Thin-Walled Structures. 2022;172:108852. https://doi.org/10.1002/suco.202100532 EDN: BXJDTD
  2. Issa M.S., Metwally I.M., Elzeiny S.M. Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars. Engineering Structures. 2011;33:1754-1763. https://doi.org/10.1016/j.engstruct.2011.02.014
  3. Amirkhani S., Lezgy Nazargah M. Nonlinear finite element analysis of reinforced concrete columns: Evaluation of different modeling approaches for considering stirrup confinement effects. Structural Concrete. 2022;23:2820-2836. https://doi.org/10.1002/suco.202100532 EDN: BXJDTD
  4. Yeganeh-Salman A., Lezgy-Nazargah M. Evaluating the accuracy of mass scaling method in non-linear quasi-static finite element analysis of RC structures. Structural Engineering and Mechanics. 2023;85:485-500. https://doi.org/10.12989/SEM.2023.85.4.485
  5. Szilard R. Theories and applications of plate analysis: classical, numerical, and engineering methods. Hoboken, NJ: John Wiley; 2004.
  6. Werkle H. Finite elements in structural analysis: Theoretical concepts and modeling procedures in statics and dynamics of structures. Cham: Springer International Publ.; 2021. https://doi.org/10.1007/978-3-030-49840-5
  7. Harmon T.G., Zhangyuan N. Shear strength of reinforced concrete plates and shells determined by finite element analysis using layered elements. J Struct Eng. 1989;115:1141-1157. https://doi.org/10.1061/(ASCE)0733-9445(1989)115: 5(1141)
  8. Polak M.A. Modeling punching shear of reinforced concrete slabs using layered finite elements. SJ. 1998;95(1): 71-80. https://doi.org/10.14359/528
  9. Mahmood D., Rafiq S., Adbullah M. Nonlinear 3D Finite element model for square composite columns under various parameters. Iraqi Journal of Civil Engineering. 2022;16:19-28. https://doi.org/10.37650/ijce.2022.172882 EDN: NRXGDK
  10. Mawlood D., Rafiq S. Nonlinear 3D Finite element model for round composite columns under various eccentricity loads. Engineering and Technology Journal. 2022;40:1605-1614. https://doi.org/10.30684/etj.2022.133106.1168 EDN: QTWLPF
  11. Mittelstedt C. Basics of elasticity theory. Theory of plates and shells. Berlin, Heidelberg: Springer Berlin Heidelberg; 2023. p. 3-57. https://doi.org/10.1007/978-3-662-66805-4_1
  12. Timošenko S.P., Woinowsky-Krieger S. Theory of plates and shells. 2nd. ed., [Nachdr.]. New York: McGraw-Hill; 1996.
  13. Oñate E. Structural analysis with the finite element method: linear statics. Dordrecht London: Springer; 2009.
  14. Jiang J., Mirza F.A. Nonlinear analysis of reinforced concrete slabs by a discrete finite element approach. Computers & Structures. 1997;65:585-592. https://doi.org/10.1016/S0045-7949(94)E0269-8
  15. Saiah B., Bachene M., Guemana M., Chiker Y., Attaf B. On the free vibration behavior of nanocomposite laminated plates contained piece-wise functionally graded graphene-reinforced composite plies. Engineering Structures. 2022; 253:113784. https://doi.org/10.1016/j.engstruct.2021.113784 EDN: IKFKRC
  16. Rodrigues Da Silva A., Paulo De Souza Rosa J. Nonlinear numerical analysis of prestressed concrete beams and slabs. Engineering Structures. 2020;223:111187. https://doi.org/10.1016/j.engstruct.2020.111187 EDN: AYEZIR
  17. Van Vinh P., Avcar M., Belarbi M.-O., Tounsi A., Quang Huy L. A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates. Structures. 2023;47:1595-1612. https://doi.org/10.1016/j.istruc.2022.11.113 EDN: GLXCXE
  18. Cinefra M., Kumar S.K., Carrera E. MITC9 Shell elements based on RMVT and CUF for the analysis of laminated composite plates and shells. Composite Structures. 2019;209:383-90. https://doi.org/10.1016/j.compstruct.2018.10.039 EDN: WUDZCK
  19. Moleiro F., Mota Soares C.M., Mota Soares C.A., Reddy J.N. A layerwise mixed least-squares finite element model for static analysis of multilayered composite plates. Computers & Structures. 2011;89:1730-1742. https://doi.org/10.1016/j.compstruc.2010.10.008
  20. Liguori F.S., Corrado A., Bilotta A., Madeo A. A layer-wise plasticity-based approach for the analysis of reinforced concrete shell structures using a mixed finite element. Engineering Structures. 2023;285:116045. https://doi.org/10.1016/j.engstruct.2023.116045 EDN: XEVDXS
  21. Wang R., Fang Z., Lezgy-Nazargah M., Khosravi H. Nonlinear analysis of reinforced concrete slabs using a quasi-3D mixed finite element formulation. Engineering Structures. 2023;294:116781. https://doi.org/10.1016/j.engstruct.2023. 116781 EDN: HKKQXZ
  22. Zhang Y.-G., Lu M.-W., Hwang K.-C. Finite element modeling of reinforced concrete structures. Finite Elements in Analysis and Design. 1994;18:51-8. https://doi.org/10.1016/0168-874X(94)90089-2
  23. Zhang Y.X., Bradford M.A., Gilbert R.I. A new triangular layered plate element for the non-linear analysis of reinforced concrete slabs. Commun Numer Meth Engng. 2005;22:699-709. https://doi.org/10.1002/cnm.840
  24. Willam K., Pramono E., Sture S. Fundamental issues of smeared crack models. In: Shah SP, Swartz SE, editors. Fracture of Concrete and Rock. New York, NY: Springer New York; 1989. p. 142-157. https://doi.org/10.1007/978-1-4612-3578-1_15
  25. Mohamed M.S., Thamboo J.A., Jeyakaran T. Experimental and numerical assessment of the flexural behaviour of semi-precast-reinforced concrete slabs. Advances in Structural Engineering. 2020;23:1865-1879. https://doi.org/10.1177/1369433220904011 EDN: GDQHBJ
  26. Nurmi S., Hoult N.A., Howell S.D. Distributed strain monitoring of two-way slabs. Engineering Structures. 2019;189:580-588. https://doi.org/10.1016/j.engstruct.2019.04.002
  27. Xiao Y., Li B., Fujikake K. Experimental study of reinforced concrete slabs under different loading rates. ACI Structural Journal. 2016;113. https://doi.org/10.14359/51688067

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).