DOI QR코드

DOI QR Code

Isogeometric analysis of the seismic response of a gravity dam: A comparison with FEM

  • Abdelhafid Lahdiri (Laboratory of Solid Mechanics and Systems LMSS, Department of Civil Engineering, University of Boumerdes) ;
  • Mohammed Kadri (Laboratory of Solid Mechanics and Systems LMSS, Department of Civil Engineering, University of Boumerdes)
  • Received : 2020.04.10
  • Accepted : 2024.02.19
  • Published : 2024.04.25

Abstract

Modeling and analyzing the dynamic behavior of fluid-soil-structure interaction problems are crucial in structural engineering. The solution to such coupled engineering systems is often not achievable through analytical modeling alone, and a numerical solution is necessary. Generally, the Finite Element Method (FEM) is commonly used to address such problems. However, when dealing with coupled problems with complex geometry, the finite element method may not precisely represent the geometry, leading to errors that impact solution quality. Recently, Isogeometric Analysis (IGA) has emerged as a preferred method for modeling and analyzing complex systems. In this study, IGA based on Non-Uniform Rational B-Splines (NURBS) is employed to analyze the seismic behavior of concrete gravity dams, considering fluid-structure-foundation interaction. The performance of IGA is then compared with the classical finite element solution. The computational efficiency of IGA is demonstrated through case studies involving simulations of the reservoir-foundation-dam system under seismic loading.

Keywords

Acknowledgement

This research was supported by the National Found of Research - DGRSDT, Algerian Ministry of High Education.

References

  1. Altunisik, A.C. and Sesli, H.A.S.A.N. (2015), "Dynamic response of concrete gravity dams using different water modelling approaches: Westergaard, Lagrange and Euler", Comput. Concr., 16(3), 429-448. http://doi.org/10.12989/cac.2015.16.3.429
  2. Altunisik, A.C., Kalkan, E. and Basaga, H.B. (2018), "Development of engineering software to predict the structural behavior of arch dams", Adv. Comput. Des., 3(1), 87-112. https://doi.org/10.12989/acd.2018.3.1.087 87
  3. Amin Abbasi, E.A. and Barani, G.A. (2018), "Seismic analysis of the arch dams", Irrig. Water En., 8(3), 13-23.
  4. Auricchio, F., Da Veiga, L.B., Hughes, T.J., Reali, A. and Sangalli, G. (2012), "Isogeometric collocation for elastostatics and explicit dynamics", Comput. Meth. Appl. Mech. Eng., 249, 2-14. http://doi.org/10.1016/j.cma.2012.03.026
  5. Bazilevs, Y. and Akkerman, I. (2010), "Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method. Journal of Computational Physics, 229(9), 3402-3414. http://doi.org/10.1016/j.jcp.2010.01.008
  6. Bazilevs, Y., Calo, V.M., Hughes, T.J. and Zhang, Y. (2008), "Isogeometric fluid-structure interaction: theory, algorithms, and computations", Comput. Mech., 43, 3-37. https://doi.org/10.1007/s00466-008-0315-x
  7. Bazilevs, Y., Calo, V.M., Zhang, Y. and Hughes, T.J. (2006), "Isogeometric fluid-structure interaction analysis with applications to arterial blood flow", Comput. Mech., 38, 310-322. https://doi.org/10.1007/s00466-006-0084-3
  8. Bazilevs, Y., Gohean, J.R., Hughes, T.J.R., Moser, R.D. and Zhang, Y. (2009), "Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device", Comput. Meth. Appl. Mech. Eng., 198(45-46), 3534-3550. https://doi.org/10.1016/j.cma.2009.04.015
  9. Bazilevs, Y., Hsu, M.C. and Scott, M. (2012), "Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines", Comput. Meth. Appl. Mech. Eng., 249, 28-41. http://doi.org/10.1016/j.cma.2012.03.028
  10. CGS (2003), National Center for Resaerch in Seismic Eginineering, Hussein Dey, Algiers, Algeria. https://www.cgs-dz.org
  11. Chakrabarti, P. and Chopra, A.K. (1973), "Earthquake analysis of gravity dams including hydrodynamic interaction", Earthq. Eng. Struct. Dyn., 2(2), 143-160.
  12. Cottrell, J.A., Hughes, T.J. and Bazilevs, Y. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley & Sons.
  13. Cottrell, J.A., Reali, A., Bazilevs, Y. and Hughes, T.J. (2006), "Isogeometric analysis of structural vibrations. Computer methods in applied mechanics and engineering, 195(41-43), 5257-5296. http://doi.org/10.1016/j.cma.2005.09.027
  14. Cox, M.G. (1971), "The numerical evaluation of B-Splines, national physical laboratory", DNAC, 4.
  15. Dalcin, L., Collier, N., Vignal, P., Cortes, A.M.A. and Calo, V.M. (2016), "PetIGA: A framework for high-performance isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 308, 151-181. https://doi.org/10.1016/j.cma.2016.05.011
  16. De Boor, C. (1972), "On calculating with B-splines", J. Approxim. Theor., 6(1), 50-62.
  17. De Falco, C., Reali, A. and Vazquez, R. (2011), "GeoPDEs: a research tool for isogeometric analysis of PDEs", Adv. Eng. Softw., 42(12), 1020-1034. https://doi.org/10.1016/j.advengsoft.2011.06.010
  18. Duval, A., Elguedj, T., Al-Akhras, H. and Maurin, F. (2015), "abqNURBS : Implementation d'elements isogeometriques dans Abaqus et outils de pre-et post-traitement dedies", Proceedings of the 12e Colloque National en Calcul des Structures, Giens, France, May.
  19. Evans, J.A., Bazilevs, Y., Babuska, I. and Hughes, T.J. (2009), "n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method", Comput. Meth. Appl. Mech. Eng., 198(21-26), 1726-1741. https://doi.org/10.1016/j.cma.2009.01.021.
  20. Fakhye, R.J.M., Junior, G.C.B. and Machado, R.D. (2016), "Dynamic Response of Gravity Dam Model using Isogeometric Analysis", Int. J. Comput. Appl., 151(4), "https://doi.org/10.5120/ijca2016911731
  21. Gomez, H., Hughes, T.J., Nogueira, X. and Calo, V.M. (2010), "Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations", Comput. Meth. Appl. Mech. Eng., 199(25-28), 1828-1840. https://doi.org/10.1016/j.cma.2010.02.010.
  22. Hartmann, S., Benson, D.J. and Lorenz, D. (2011, May), "About Isogeometric Analysis and the new NURBS-based Finite Elements in LS-DYNA", Proceedings of the 8th European LS-DYNA Users Conference, Strasbourg, France, May.
  23. Hughes, T.J., Reali, A. and Sangalli, G. (2008), "Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS", Comput. Meth. Appl. Mech. Eng., 197(49-50), 4104-4124. https://doi.org/10.1016/j.cma.2008.04.006
  24. Hughes, T.J., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194(39-41), 4135-4195. https://doi.org/1016/j.cma.2004.10.008 1016/j.cma.2004.10.008
  25. Lahdiri, A. and Kadri, M. (2022), "Free vibration behavior of multi-directional functionally graded imperfect plates using 3D isogeometric approach", Earthq. Struct., 22(5), 538. https://doi.org/10.12989/eas.2022.22.5.527
  26. Lai, Y., Zhang, Y.J., Liu, L., Wei, X., Fang, E. and Lua, J. (2017), "Integrating CAD with Abaqus: a practical isogeometric analysis software platform for industrial applications", Comput. Math. Appl., 74(7), 1648-1660. https://doi.org/10.1016/j.camwa.2017.03.032
  27. Ledoux, M. and El Hami, A. (2017), Propulsion Compressible et Approche Numerique en Mecanique des Fluides (Vol. 3), ISTE Group, France.
  28. Piegl, L. and Tiller, W. (2012), "The NURBS Book. Springer Science & Business Media.
  29. Lin, G., Zhang, Y., Wang, Y. and Hu, Z.Q. (2012), "A time-domain coupled scaled boundary isogeometric approach for earthquake response analysis of dam-reservoir-foundation system. In 15th world conference on earthquake engineering.
  30. Ma, C., Chen, W.Z. and Sun, J.Y. (2016), "Numerical implementation of spatial elastoplastic damage model of concrete in the framework of isogeometric analysis Approach", Math. Probl. Eng., 2016. https://doi.org/10.1155/2016/4273024
  31. Maghsoodi, R., Amini, R. and Z Moghaddam, N. (2014), "Using isogeometric method for dam break modeling by Lagrangian approach", J. Solid Fl. Mech., 4(3), 45-55. https://doi.org/10.22044/jsfm.2014.339
  32. Mandal, A. and Maity, D. (2019), "Seismic analysis of dam-foundation-reservoir coupled system using direct coupling method", Coupl. Syst. Mech., 8(5), 393-414. https://doi.org/10.12989/csm.2019.8.5.393
  33. Nielsen, P.N., Gersborg, A.R., Gravesen, J. and Pedersen, N.L. (2011), "Discretizations in isogeometric analysis of Navier-Stokes flow", Comput. Meth. Appl. Mech. Eng., 200(45-46), 3242-3253. https://doi.org/10.1016/j.cma.2011.06.007
  34. Ouzandja, D. and Tiliouine, B. (2015), "Effects of dam-foundation contact conditions on seismic performance of concrete gravity dams", Arab. J. Sci. Eng., 40, 3047-3056. https://doi.org/10.1007/s13369-015-1770-2
  35. Ouzandja, D., Tiliouine, B., Belharizi, M. and Kadri, M. (2017), "Three-dimensional nonlinear seismic response of Oued Fodda concrete gravity dam considering contact elements at dam-reservoir interaction interface", Asian J. Civil Eng., 18(6), 977-992.
  36. Reali, A. (2006), "An isogeometric analysis approach for the study of structural vibrations", J. Earthq. Eng., 10(1), 1-30. https://doi.org/10.1142/S1363246906002700
  37. Sevim, B. (2018), "Geometrical dimensions effects on the seismic response of concrete gravity dams", Adv. Concr. Constr., 6(3), 269. https://doi.org/10.12989/acc.2018.6.3.269
  38. Shahrbanozadeh, M., Barani, G.A. and Shojaee, S. (2015), "Simulation of flow through dam foundation by isogeometric method", Eng. Sci. Technol., 18(2), 185-193. https://doi.org/10.1016/j.jestch.2014.11.001
  39. Simpson, R.N., Bordas, S.P., Lian, H. and Trevelyan, J. (2013), "An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects", Comput. Struct., 118, 2-12. https://doi.org/10.1016/j.compstruc.2012.12.021
  40. Simpson, R.N., Bordas, S.P., Trevelyan, J. and Rabczuk, T. (2012), "A two-dimensional isogeometric boundary element method for elastostatic analysis", Comput. Meth. Appl. Mech. Eng., 209, 87-100. https://doi.org/10.1016/j.cma.2011.08.008
  41. Thai, C.H., Nguyen-Xuan, H., Nguyen-Thanh, N., Le, T.H., Nguyen-Thoi, T. and Rabczuk, T. (2012), "Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach", Int. J. Numer. Meth. Eng., 91(6), 571-603. http://doi.org/10.1002/nme.4282
  42. Varughese, J.A. and Nikithan, S. (2016), "Seismic behavior of concrete gravity dams", Adv. Comput. Des., 1(2), 195-206. http://doi.org/10.12989/acd.2016.1.2.195
  43. Xu, J., Yuan, S. and Chen, W. (2019), "Isogeometric analysis of gradient-enhanced damaged plasticity model for concrete", Comput. Concr., 23(3), 171-188.
  44. Zhang, M., Li, M., Shen, Y. and Zhang, J. (2019), "Isogeometric shape optimization of high RCC gravity dams with functionally graded partition structure considering hydraulic fracturing", Eng. Struct., 179, 341-352. https://doi.org/10.1016/j.engstruct.2018.11.005