Computers and Concrete

  • 제18권5호
  • /
  • Pages.1019-1039
  • /
  • 2016
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A dynamic analysis algorithm for RC frames using parallel GPU strategies

  • Li, Hongyu (School of Civil and Environment Engineering, Shenzhen Graduate School, Harbin Institute of Technology) ;
  • Li, Zuohua (School of Civil and Environment Engineering, Shenzhen Graduate School, Harbin Institute of Technology) ;
  • Teng, Jun (School of Civil and Environment Engineering, Shenzhen Graduate School, Harbin Institute of Technology)
  • 투고 : 2015.11.25
  • 심사 : 2016.08.03
  • 발행 : 2016.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a parallel algorithm of nonlinear dynamic analysis of three-dimensional (3D) reinforced concrete (RC) frame structures based on the platform of graphics processing unit (GPU) is proposed. Time integration is performed using Newmark method for nonlinear implicit dynamic analysis and parallelization strategies are presented. Correspondingly, a parallel Preconditioned Conjugate Gradients (PCG) solver on GPU is introduced for repeating solution of the equilibrium equations for each time step. The RC frames were simulated using fiber beam model to capture nonlinear behaviors of concrete and reinforcing bars. The parallel finite element program is developed utilizing Compute Unified Device Architecture (CUDA). The accuracy of the GPU-based parallel program including single precision and double precision was verified in comparison with ABAQUS. The numerical results demonstrated that the proposed algorithm can take full advantage of the parallel architecture of the GPU, and achieve the goal of speeding up the computation compared with CPU.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Natural Scientific Research Innovation Foundation in Harbin Institute of Technology

참고문헌

  1. Adeli, H. (2000), "High-performance computing for large-scale analysis, optimization, and control", J. Aerospace Eng., 13(1), 1-10. https://doi.org/10.1061/(ASCE)0893-1321(2000)13:1(1)
  2. Bathe, K.J. and Wilson, E. (1976), Numerical mthods in finite eement analysis, Prentice-Hall, Englewood Cliffs, New Jersey.
  3. Belytschko, T. (1983), "An overview of semidiscretization and time integration procedures", Computational methods for transient analysis(A 84-29160 12-64), Amsterdam, North-Holland, 1-65.
  4. Benzi, M. and Tuma, M. (1999), "A comparative study of sparse approximate inverse preconditioners", Appl. Numer. Math., 30(2), 305-340. https://doi.org/10.1016/S0168-9274(98)00118-4
  5. Blakely, R.W.G. and Park, R. (1973), "Prestressed concrete sections with cyclic flexure", J. Struct. Div., 99(8), 1717-1742.
  6. Bryan, B.A. (2013), "High-performance computing tools for the integrated assessment and modelling of social-ecological systems", Environ. Modell. Softw., 39, 295-303. https://doi.org/10.1016/j.envsoft.2012.02.006
  7. Chetverushkin, B.N., Shilnikov, E.V. and Davydov, A.A. (2013), "Numerical simulation of the continuous media problems on hybrid computer systems", Adv. Eng. Softw., 60-61, 42-47. https://doi.org/10.1016/j.advengsoft.2013.02.003
  8. Eklund, A., Dufort, P., Forsberg, D. and LaConte, S.M. (2013), "Medical image processing on the GPU-Past, present and future", Med. Image Anal., 17(8), 1073-1094. https://doi.org/10.1016/j.media.2013.05.008
  9. Fahmy, M.W. and Namini, A.H. (1994), "A survey of parallel nonlinear dynamic analysis methodologies", Comput. Struct., 53(4), 1033-1043. https://doi.org/10.1016/0045-7949(94)90390-5
  10. Farhat, C. and Roux, F.X. (1991), "A method of finite element tearing and interconnecting and its parallel solution algorithm", Int. J. Numer. Meth. Eng., 32(6), 1205-1227. https://doi.org/10.1002/nme.1620320604
  11. Fung, T.C. (1997), "A precise time-step integration method by step‐response and impulsive‐response matrices for dynamic problems", Int. J. Numer. Methods Eng., 40(24), 4501-4527. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4501::AID-NME266>3.0.CO;2-U
  12. Fung, T.C. (1997), "Third-order time-step integration methods with controllable numerical dissipation", Commun. Numer. Meth. Eng., 13(4), 307-315. https://doi.org/10.1002/(SICI)1099-0887(199704)13:4<307::AID-CNM64>3.0.CO;2-2
  13. Galoppo, N., Govindaraju, N.K., Henson, M. and Manocha, D. (2005), "LU-GPU: Efficient algorithms for solving dense linear systems on graphics hardware", Proceedings of the 2005 ACM/IEEE Conference on Supercomputing, IEEE Computer Society, November.
  14. Georgescu, S., Chow, P. and Okuda, H. (2013), "GPU acceleration for FEM-based structural analysis", Arch. Comput. Method E., 20(2), 111-121. https://doi.org/10.1007/s11831-013-9082-8
  15. Goddeke, D. (2010), "Fast and accurate finite-element multigrid solvers for PDE simulations on GPU clusters", Ph.D. Dissertation, Technische Universit at Dortmund, Fakultat fur Mathematik,.
  16. Goddeke, D. (2011), Fast and accurate finite-element multigrid solvers for PDE simulations on GPU clusters (Logos Verlag Berlin GmbH ).
  17. Golley, B.W. (1996), "A time-stepping procedure for structure dynamics using gauss point collocation", Int. J. Numer. Meth. Eng., 39(23), 3985-3998. https://doi.org/10.1002/(SICI)1097-0207(19961215)39:23<3985::AID-NME33>3.0.CO;2-7
  18. Helfenstein, R. and Koko, J. (2012), "Parallel preconditioned conjugate gradient algorithm on GPU", J. Comput. Appl. Math., 236(15), 3584-3590. https://doi.org/10.1016/j.cam.2011.04.025
  19. Huthwaite, P. (2014), "Accelerated finite element elastodynamic simulations using the GPU", J. Comput. Phys., 257, 687-707. https://doi.org/10.1016/j.jcp.2013.10.017
  20. Kang, D.K., Kim, C. W. and Yang, H.I. (2014), "GPU-based parallel computation for structural dynamic response analysis with CUDA", J. Mech. Sci. Technol., 28(10), 4155-4162. https://doi.org/10.1007/s12206-014-0928-2
  21. Kent, D.C. and Park, R. (1971), "Flexural members with confined concrete", J. Struct. Div., 97(7), 1969-1990.
  22. Khronos Group (2014), The OpenCL Specification Version 2.0, Khronos OpenCL Working Group.
  23. Komatitsch, D., Erlebacher, G., Goddeke, D. and Michea, D. (2010), "High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster", J. Comput. Phys., 229(20), 7692-7714. https://doi.org/10.1016/j.jcp.2010.06.024
  24. Komatitsch, D., Michea, D. and Erlebacher, G. (2009), "Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA", J. Parallel. Distr. Com., 69(5), 451-460. https://doi.org/10.1016/j.jpdc.2009.01.006
  25. Li, H.Y., Teng, J., Li, Z.H. and Zhang, L. (2015), "Nonlinear dynamic analysis efficiency by using a GPU parallelization", Eng. Lett., 23(4), 232-238.
  26. Mafi, R. and Sirouspour, S. (2014), "GPU-based acceleration of computations in nonlinear finite element deformation analysis", Int. J. Numer. Methods in Bio., 30(3), 365-381.
  27. Manjuprasad, M., Gopalakrishnan, S. and Appa Rao, T.V.S.R. (2001), "Non-linear dynamic response of a reinforced concrete secondary containment shell subjected to seismic load", Eng. Struct., 23(5), 397-406. https://doi.org/10.1016/S0141-0296(00)00070-5
  28. Menegotto, M. and Pinto P.E. (1977), "Slender R.C. Compressed members in biaxial bending", J. Struct. Div., 103(3), 587-605.
  29. Miao, X., Jin, X. and Ding, J. (2015), "A new hybrid solver with two-level parallel computing for largescale structural analysis", Concurr. Comp-Pract. E., 27(14), 3661-3675. https://doi.org/10.1002/cpe.3361
  30. Mullapudi, T.R.S. and Ayoub, A. (2013), "Analysis of reinforced concrete columns subjected to combined axial, flexure, shear, and torsional loads", J. Struct. Eng., 139(4), 561-573. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000680
  31. Nathan, M.N. (1959), "A method for computation of structural dynamics", J. Eng. Mech., 85(3), 67-94.
  32. Noor, A.K. (1997), "New computing systems and future high-performance computing environment and their impact on structural analysis and design", Comput. Struct., 64(1), 1-30. https://doi.org/10.1016/S0045-7949(96)00369-0
  33. nVidia Corporation (2013a), CUDA C Programming Guide.
  34. nVidia Corporation (2013b), CUBLAS library.
  35. Ohsaki, M., Miyamura, T., Kohiyama, M., Hori, M., Noguchi, H., Akiba, H. and Koichi, K. (2009), "Highprecision finite element analysis of elastoplastic dynamic responses of super-high-rise steel frames", Earthq. Eng. Struct. D., 38(5), 635-654. https://doi.org/10.1002/eqe.900
  36. Phoon, K.K., Toh, K.C., Chan, S.H. and Lee, F.H. (2002), "An efficient diagonal preconditioner for finite element solution of Biot's consolidation equations", Int. J. Numer. Meth. Eng., 55(4), 377-400. https://doi.org/10.1002/nme.500
  37. Sasani, M. and Kropelnicki, J. (2008), "Progressive collapse analysis of an RC structure", Struct. Des. Tall Spec., 17(4), 757-771. https://doi.org/10.1002/tal.375
  38. Scott, B.D., Park, R. and Priestley, M.J.N. (1982), "Stress-strain behaviour of concrete confined by overlapping hoops at low and high strain rates", ACI J., 79(1), 13-27.
  39. Smolinski, P. (1990), "Convergence of multi-time step integration methods", Comput. Struct., 35(6), 719-724. https://doi.org/10.1016/0045-7949(90)90416-Y
  40. Spacone, E., Fillippou, F.C. and Taucer, F.F. (1996), "Fiber beam-column model for nonlinear analysis of RC frames: Part I. Formulation", Earthq. Eng. Struct. D., 25(7), 711-725. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9
  41. Stroud, A.H. and Secrest, D. (1966), Gaussian quadrature formulas, Prentice-Hall, Englewood Cliffs, New Jersey.
  42. Turek, S., Goddeke, D., Becker, C., Buijssen, S.H. and Wobker, H. (2010), "FEAST-realization of hardwareoriented numerics for HPC simulations with finite elements", Concurr. Comput.-Pract. E., 22(16), 2247-2265. https://doi.org/10.1002/cpe.1584
  43. Walpole, W.R. and Shepherd, R. (1969), "Elasto-plastic seismic response of reinforced concrete frame", J. Struct. Div., 95(ST10), 2031-2055.
  44. Weber, D., Bender, J., Schnoes, M., Stork, A. and Fellner, D. (2013), "Efficient GPU data structures and methods to solve sparse linear systems in dynamics applications", Comput. Graph. Forum., 32(1), 16-26. https://doi.org/10.1111/j.1467-8659.2012.03227.x
  45. Wei, C. and Luca, C. (2015), "New GPU computing algorithm for wind load uncertainty analysis on highrise systems", Wind Struct., 21(5), 461-487. https://doi.org/10.12989/was.2015.21.5.461
  46. Wilson, E.L., Farhoomand, I. and Bathe, K.J. (1972), "Nonlinear dynamic analysis of complex structures", Earthq. Eng. Struct. D., 1(3), 241-252. https://doi.org/10.1002/eqe.4290010305
  47. Yagawa, G., Soneda, N. and Yoshimura, S. (1991), "A Large scale finite element analysis using domain decomposition method on a parallel computer", Comput. Struct., 38(5-6), 615-625. https://doi.org/10.1016/0045-7949(91)90013-C
  48. Yamada, T., Ohbo, N. and Itami, H. (2008), "Three-dimensional analysis method of seismic resistance of large tunnel structure using large-scale numerical computation of soil-tunnel system", Proceedings of the World Tunnel Congress 2008, Agra, India, September.
  49. Yang, D.P., Peterson, G.D. and Li, H.S. (2012), "Compressed sensing and Cholesky decomposition on FPGAs and GPUs", Parallel Comput., 38(8), 421-437. https://doi.org/10.1016/j.parco.2012.03.001
  50. Yang, Y.S., Hsieh, S.H. and Hsieh, T.J. (2011), "Improving parallel substructuring efficiency by using a multilevel approach", J. Comput. Civil Eng., 26(4), 457-464. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000142
  51. Yang, Y.S., Yang, C.M. and Hsieh, T.J. (2014), "GPU parallelization of an object-oriented nonlinear dynamic structural analysis platform", Simul. Modell. Prac.Theo., 40, 112-121. https://doi.org/10.1016/j.simpat.2013.09.004
  52. Yassin, M.H.M. (1994), "Nonlinear analysis of prestressed concrete structures under monotonic and cycling loads", Ph.D. Dissertation, University of California, Berkeley.