Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vector mechanics-based simulation of large deformation behavior in RC shear walls using planar four-node elements

  • Zhang, Hongmei (College of Civil Engineering and Architecture, Zhejiang University) ;
  • Shan, Yufei (Department of Disaster Mitigation for Structures, Tongji University) ;
  • Duan, Yuanfeng (College of Civil Engineering and Architecture, Zhejiang University) ;
  • Yun, Chung Bang (College of Civil Engineering and Architecture, Zhejiang University) ;
  • Liu, Song (Department of Disaster Mitigation for Structures, Tongji University)
  • Received : 2018.09.13
  • Accepted : 2019.08.26
  • Published : 2020.04.10
⟨ Previous Next ⟩

Abstract

For the large deformation of shear walls under vertical and horizontal loads, there are difficulties in obtaining accurate simulation results using the response analysis method, even with fine mesh elements. Furthermore, concrete material nonlinearity, stiffness degradation, concrete cracking and crushing, and steel bar damage may occur during the large deformation of reinforced concrete (RC) shear walls. Matrix operations that are involved in nonlinear analysis using the traditional finite-element method (FEM) may also result in flaws, and may thus lead to serious errors. To solve these problems, a planar four-node element was developed based on vector mechanics. Owing to particle-based formulation along the path element, the method does not require repeated constructions of a global stiffness matrix for the nonlinear behavior of the structure. The nonlinear concrete constitutive model and bilinear steel material model are integrated with the developed element, to ensure that large deformation and damage behavior can be addressed. For verification, simulation analyses were performed to obtain experimental results on an RC shear wall subjected to a monotonically increasing lateral load with a constant vertical load. To appropriately evaluate the parameters, investigations were conducted on the loading speed, meshing dimension, and the damping factor, because vector mechanics is based on the equation of motion. The static problem was then verified to obtain a stable solution by employing a balanced equation of motion. Using the parameters obtained, the simulated pushover response, including the bearing capacity, deformation ability, curvature development, and energy dissipation, were found to be in accordance with the experimental observation. This study demonstrated the potential of the developed planar element for simulating the entire process of large deformation and damage behavior in RC shear walls.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (51578419, U1709216 and 51522811) and the National Key R&D Program of China (2018YFE0125400, 2017YFC0806100).

References

  1. Amir, Ayoub, and Filippou C.F. (1998), "Nonlinear finite-element analysis of RC shear panels and walls", J. Struct. Eng., 124(3), 298-308. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:3(298).
  2. Bathe, K.J. and Wilson, E.L. (1976), Numerical methods in finite element analysis, Prentice Hall, Englewood Cliffs, NJ, USA.
  3. Darwin, D. and Pecknold, D. A. (1977), "Nonlinear biaxial stress-strain law for concrete", ASCE J. Eng. Mech. Division, 103(2): 229-241. https://doi.org/10.1061/JMCEA3.0002220
  4. Dong, Y.G. and Lu, X.L. (2007), "Study on axial compression ratio calculation and limit value for steel reinforced concrete walls", J. Earthq. Eng. Eng. Vib., 27(1), 80-85. https://doi.org/10.3969/j.issn.1000-1301.2007.01.012
  5. Duan, Y.F., He, K., Zhang, H.M., Ting, E.C., Wang, C.Y., Chen, S.K. and Wang, R.Z. (2014), "Entire-process simulation of earthquake-induced collapse of a mockup cable-stayed bridge by vector form intrinsic finite element (VFIFE) Method", Adv. Struct. Eng., 17(3), 347-360. https://doi.org/10.1260/1369-4332.17.3.347.
  6. Duan, Y.F., Wang, S.M., Wang, R.Z., Wang, C.Y., Shih, J.Y., Yun, C.B. (2018), "Vector form intrinsic finite-element analysis for train and bridge dynamic interaction", J. Bridge Eng., 23(1), https://doi.org/10.1061/(ASCE)BE.1943-5592.0001171.
  7. Duan, Y.F., Wang, S.M., Wang, R.Z., Wang, C.Y., and Ting, E.C. (2017), "Vector form intrinsic finite element based approach to simulate crack propagation", J. Mech., 33(6), 1-16. https://doi.org/10.1017/jmech.2017.85.
  8. GB 50011-2010 (2010), Code for seismic design of buildings, Industry Standard of the People's Republic of China; Beijing, China.
  9. Gulsan, M.E., Albegmprli, H.M. and Cevik, A. (2018), "Finite element and design code assessment of reinforced concrete haunched beams", Struct. Eng. Mech., 66(4), 423-438. https://doi.org/10.12989/sem.2018.66.4.423.
  10. Hillerborg, A., Modeer, M., and Peterson, P.E. (1976), "Analysis of crack formation and crack grouth in concrete by means of fracture mechanics and finite element", Cement Concrete Res., 6(6):773-782. https://doi.org/10.1016/0008-8846(76)90007-7.
  11. Jiang, J.Q., Lu, X.Z., and Ye, L.P. (2005), Finite Element Analysis of Concrete Structures, Tsinghua University Press, Beijing, China.
  12. Kupfer, H. and Gerstle, K. (1973), "Behavior of Concrete under Biaxial Stress", ASCE J. Eng. Mech. Division, 66(8), 853-866. https://doi.org/10.1061/JMCEA3.0001789
  13. Lefas, I.D., Kotsovos, M.D., Ambraseys, N.N. (1990), "Behavior of reinforced-concrete structural walls - strength, deformation characteristics, and failure mechanism", ACI Struct. J., 87(1), 23-31.
  14. Lu, Xilin, Zhang, Ying, Zhang, Hongmei, Zhang Hanshu.(2018), "Experimental study on seismic performance of steel fiber reinforced high strength concrete composite shear walls with different steel fiber volume fractions", Eng. Struct., 171(2018), 247-259. https://doi.org/10.1016/j.engstruct.2018.05.068.
  15. Luo, Y . Z, and Yang, C. (2014), "A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling", J. Zhejiang University-Sci. A,15(5), 331-350. https://doi.org/10.1631/jzus.A1300248.
  16. Mattiasson, K. (1981), "Numerical results from large deflection beam and frame problems analyzed by beans of elliptic integrals", J. Numerical Methods Eng., 17(1), 145-153. https://doi.org/10.1002/nme.1620170113.
  17. Messaoudi, K., Boukhalfa, A. and Beldjelili, Y. (2018), "Three dimensional finite elements modeling of FGM plate bending using UMAT", Struct. Eng. Mech., 66(4), 487-494. https://doi.org/10.12989/sem.2018.66.4.487.
  18. Shih, C., Wang, Y.K. and Ting, E.C. (2004), "Fundamentals of a vector form intrinsic finite element: Part 3 Connected material frame and examples", J. Mech., 20(2), 133-143. https://doi.org/10.1017/S172771910000335X.
  19. Saenz, L. P. (1964), Discussion of "Equation for the stress-strain curve of concrete", Proceeding of American Concrete Institute. 61, 1229-1235.
  20. Thomsen, J.H. and Wallace, J.W. (2004), "Displacement-based design of slender reinforced concrete structural walls-experimental verification", J. Struct. Eng., 130(4), 618-630. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(618).
  21. Ting, E.C., Shih, C. and Wang, Y.K. (2004a), "Fundamentals of a vector form intrinsic finite element: Part 1 Basic procedure and a plane frame element", J. Mech., 20(2), 113-122. https://doi.org/10.1017/S1727719100003336.
  22. Ting, E.C., Shih, C. and Wang, Y.K. (2004b), "Fundamentals of a vector form intrinsic finite element: Part 2 Plane solid element", J. Mech., 20(2), 123-132. https://doi.org/10.1017/S1727719100003348.
  23. Ting, E.C., Wang, C.Y., Wu, T.Y., Wang, R.Z. and Chuang, C.C. (2006), "Motion analysis and vector form intrinsic finite element", Report No. CBER-2006-W-001, National Central University.
  24. Ting, E.C., Duan, Y.F and Wu, T.Y. (2012), Vector mechanics of Structures, Science Press, Beijing, China. (in Chinese).
  25. Wang, M.C.,and Shao, M.(1997), Basic Principles and Numerical Methods of Finite Element Method, Tsinghua University Press, Beijing, China.
  26. Wu, T. Y. and Ting, E. C. (2008), "Large deflection analysis of 3d membrane structures by a 4-node quadrilateral intrinsic element", Thin-Walled Struct., 46(3), 261-275. https://doi.org/10.1016/j.tws.2007.08.043.
  27. Wu, T. Y., Wang, R. Z. and Wang, C. Y. (2006), "Large deflection analysis of flexible planar frames", J. Chinese Institute Eng., 29(4), 593-606. https://doi.org/10.1080/02533839.2006.9671156.
  28. Wang, R. Z., Tsai, K. C. and Lin, B. Z. (2011), "Extremely large displacement dynamic analysis of elastic- plastic plane frames", Earthq. Eng. Struct. Dynam., 40(13), 1515-1533. https://doi.org/10.1002/eqe.1102.
  29. Wu, T. Y. (2013), "Dynamic nonlinear analysis of shell structures using a vector form intrinsic finite element", Eng. Struct., 56(2013), 2028-2040. https://doi.org/10.1016/j.engstruct.2013.08.009.
  30. Yu, Y. and Luo, Y Z. (2009a), "Motion analysis of deployable structures based on the rod hinge element by the finite particle method", Proceedings, 223(7), 955-964. https://doi.org/10.1243/09544100JAERO498.
  31. Yu, Y . and Luo, Y Z. (2009b), "Finite particle method for kinematically indeterminate bar assemblies", J. Zhejiang University Sci. A, 10(5), 667-676. https://doi.org/10.1631/jzus.A0820494.
  32. Yang, C., Shen, Y . B. and Luo, Y . Z. (2014), "An efficient numerical shape analysis for light weight membrane structures", J. Zhejiang University-Sci. A, 15(4), 255-271. https://doi.org/10.1631/jzus.A1300245.
  33. Zhang, H.M., Lu, X.L., Duan Y.F. and Zhu, Y. (2014), "Experimental study on failure mechanism of rc walls with different boundary elements under vertical and lateral loads", Adv. Struct. Eng., 17(3), 361-379. https://doi.org/10.1260%2F1369-4332.17.3.361. https://doi.org/10.1260/1369-4332.17.3.361
  34. Zhang, H.M., Lu, X.L. and Wu X.H. (2010b), "Experimental study and numerical simulation of the reinforced concrete walls with different stirrup in the boundary element", J. Asian Architecture and Build. Eng., 17(2), 447-454. https://doi.org/10.3130/jaabe.9.447.
  35. Zhang, H.M., Lu, X.L. and Lu, L. (2007), "Influence of boundary element on seismic behavior of reinforced concrete shear walls", J. Earthq. Eng. Eng. Vib., 27(1), 92-98. https://doi.org/10.3969/j.issn.1000-1301.2007.01.014
  36. Zhang, H.X., Liu, H. and Li, G.C. (2019), "Seismic performance of encased steel plate-reinforced gangue concrete composite shear walls", KSCE J. Civil Eng., 23(7), 2919-2932. https://doi.org/10.1007/s12205-019-0286-9.
  37. Zhu, B.L. and Dong, Z.X. (1985), Nonlinear Analysis of Reinforced Concrete, Tongji University Press, Shanghai, China. (in Chinese)