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Computational Techniques for Simulation of Monolithic and Heterogeneous Structural Dynamic Systems

  • Oreste S. Bursi
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 502)

Abstract

The prediction of the transient dynamic response of monolithic structural systems, as well as of heterogeneous (numerical/ physical) subsystems, decomposed by computational or physical considerations typical of hardware-in-the-loop and pseudo-dynamic tests using numerical integration, has become an accepted practice almost to the extent that such solutions in non-linear problems often are considered to be exact solutions. It is for this reason that this chapter is placed immediately at the beginning of the book.

In light of the large body of literature on computational methods developed for both testing and control techniques applied to linear and non-linear systems, no attempt is made to cover this subject in greater depth. Rather the concepts upon which ad hoc computational methods rely are presented in a common framework along with a few applications.

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Bibliography

  1. M. Arnold and O. Brüls. Convergence of the generalized-α scheme for constrained mechanical systems. Multibody Syst Dyn, 18:185–202, 2007.zbMATHCrossRefMathSciNetGoogle Scholar
  2. M. Arnold, B. Burgermeister, and A. Eichberger. Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs. Multibody System Dynamics, 17:99–117, 2007.zbMATHCrossRefMathSciNetGoogle Scholar
  3. G. Baldo, A. Bonelli, O. Bursi, and S. Erlicher. The accuracy of the generalized method in the time integration of non linear single and two DoF forced systems. Computational Mechanics, 38:15–31, 2006.zbMATHCrossRefMathSciNetGoogle Scholar
  4. V. Bayer, U. E. Dorka, U. Füllekrug, and J. Gschwilm. On real-time pseudodynamic sub-structure testing: algorithm, numerical and experimental results. Aerospace Science and Technology, 9:223–232, 2005.CrossRefGoogle Scholar
  5. B. Biondi and G. Muscolino. Component-mode synthesis method variants in the dynamics of coupled structures. Meccanica, 35:17–38, 2000.zbMATHCrossRefGoogle Scholar
  6. A. Bonelli and O. S. Bursi. Generalized-α methods for seismic structural testing. Earthquake Engineering and Structural Dynamics, 33(10): 1067–1102, 2004.CrossRefGoogle Scholar
  7. A. Bonelli, O. S. Bursi, and M. Mancuso. Explicit predictor-multicorrector time discontinuons Galerkin methods for non-linear dynamics. Journal of Sound and Vibration, 246(4):625–652, 2001.CrossRefMathSciNetGoogle Scholar
  8. A. Bonelli, O. S. Bursi, and M. Mancuso. Explicit predictor-multicorrector time discontinuons Galerkin methods for non-linear dynamics. Journal of Sound and Vibration, 256(4):659–724, 2002.CrossRefMathSciNetGoogle Scholar
  9. A. Bonelli, O. S. Bursi, L. He, P. Pegon, and G. Magonette. Convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring. International Journal for Numerical Methods in Engineering, 2008. DOI: 10.1002/nme.2285.Google Scholar
  10. P. A. Bonnet, C. N. Lim, M. S. Williams, A. Blakeborough, S. A. Neild, D. P. Stoten, and C. A. Taylor. Real-time hybrid experiments with Newmark integration, MCSmd outer-loop control and multi-tasking strategies. Earthquake Engineering and Structural Dynamics, 36(1):577–588, 2007.CrossRefGoogle Scholar
  11. P. A. Bonnet. The development of multi-axis real-time substructure testing. PhD thesis, University of Oxford, 2006.Google Scholar
  12. O. Brüls and J. C. Golinval. On the numerical damping of time integrators for coupled mechatronic systems. Computer Methods in Applied Mechanics and Engineering, 197:577–588, 2008.CrossRefMathSciNetGoogle Scholar
  13. B. Burgermeister, M. Arnold, and B. Ester. DAE time integration for realtime applications in multi-body dynamics. ZAMM Z. Angew. Math. Mech., 86(10):759–771, 2006.zbMATHCrossRefMathSciNetGoogle Scholar
  14. O. S. Bursi and M. Mancuso. Analysis and performance of a predictormulticorrector time discontinuous Galerkin method in non-linear elastodynamics. Earthquake engineering and structural dynamics, 31:1793–1814, 2002.CrossRefGoogle Scholar
  15. O. S. Bursi and P. B. Shing. Evaluation of some implicit time-stepping algorithms for pseudodynamic tests. Earthquake engineering and structural dynamics, 25:333–355, 1996.CrossRefGoogle Scholar
  16. O. S. Bursi D. P. Stoten, and L. Vulcan. Convergence and frequencydomain analysis of a discrete first-order model reference adaptive controller. Structural Control and Health Monitoring, 14:777–807, 2007.CrossRefGoogle Scholar
  17. O. S. Bursi, B. A. Gonzalez, L. Vulcan, N. A. Neild, and D. J. Wagg. Novel coupling Rosenbrock-based algorithms for real-time dynamic substructure testing. Earthquake Engineering and Structural Dynamics, 37(3): 339–360, 2008.CrossRefGoogle Scholar
  18. J. C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, 2003.Google Scholar
  19. V. Cannillo and M. Mancuso. Spurious resonances in numerical time integration methods for linear dynamics. Journal of Sound and Vibration, 238(3):389–399, 2000.CrossRefMathSciNetGoogle Scholar
  20. S. Y. Chang. Error propagation in implicit pseudodynamic testing of nonlinear systems. Journal of Engineering Mechanics, 131(12):1257–1269, 2005.CrossRefGoogle Scholar
  21. S.-Y. Chang. An improved on-line dynamic testing method. Engineering Structures, 24:587–596, 2002.CrossRefGoogle Scholar
  22. S. Y. Chu, T. T. Soong, C. C. Lin, and Y. Z. Chen. Time-delay effect and compensation on direct output feedback controlled mass damper systems. Earthquake Eng. and Struct. Dyn., 31(1):121–137, 2002.CrossRefGoogle Scholar
  23. S. Y. Chu, T. T. Soong, and A. M. Reinhorn. Active, Hybrid, and Semiactive Structural Control: A Design and Implementation Handbook. Wiley, Chichester, 2005.Google Scholar
  24. J. Chung and G. M. Hulbert. A, time integration algorithm for structural dynamics with improved numerical dissipation: the Generalized-alpha method. Journal of Applied Mechanics, 60:371–375, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  25. A. Combescure and A. Gravouil. A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis. Computer Methods in Applied Mechanics and Engineering, 191: 1129–1157, 2002.zbMATHCrossRefGoogle Scholar
  26. D. Combescure and P. Pegon. α-Operator Splitting time integration technique for pseudodynamic testing error propagation analysis. Soil Dynamics and Earthquake Engineering, 16:427–443, 1997.CrossRefGoogle Scholar
  27. J. Cuadrado, J. Cardenal, and E. Bayo. Modeling and solution methods for efficient real-time simulation of multibody dynamics. Multibody System Dynamics, 1:1897–1913, 1997.CrossRefMathSciNetGoogle Scholar
  28. G. Dahlquist. A special stability problem for linear multistep methods. BIT Numerical Mathematics, 3(1):27–43, 1963.zbMATHCrossRefMathSciNetGoogle Scholar
  29. W. J. T. Daniel. Explicit/implicit partitioning and a new explicit form of the generalized alpha method. Communications in numerical methods in engineering, 19:909–920, 2003.zbMATHCrossRefMathSciNetGoogle Scholar
  30. A. P. Darby, M. S. Williams, and A. Blakeborough. Stability and delay compensation for real-time substructure testing. Journal of Engineering Mechanics, 128(12):1276–1284, 2002.CrossRefGoogle Scholar
  31. J. R. Dormand and P. J. Prince. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6:19–26, 1980.zbMATHCrossRefMathSciNetGoogle Scholar
  32. Real-time interface, Implementation guide, Release 3.2. dSPACE GmbH, Paderborn, Germany, 2001.Google Scholar
  33. S. Erlicher, L. Bonaventura, and O. S. Bursi. The analysis of generalized-α methods for non-linear dynamic problems. Computational Mechanics, 28:83–104, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  34. C. Farhat and F.-X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32:1205–1227, 1991.zbMATHCrossRefGoogle Scholar
  35. C. Farhat, P.S. Chen, and J. Mandel. A scalable Lagrange multiplier based domain decomposition method for time dependent problems. International Journal for Numerical Methods in Engineering, 38:3831–3854, 1995.zbMATHCrossRefGoogle Scholar
  36. C. Farhat, J. Cortial, C. Dastillung, and H. Bavestrello. Time-parallel implicit integrators for the near-real-time prediction of linear structural dynamic responses. International Journal for Numerical Methods in Engineering, 67:697–724, 2006.zbMATHCrossRefMathSciNetGoogle Scholar
  37. C. A. Felippa and K. C. Park. Staggered transient analysis procedures for coupled dynamic systems: formulation. Comp. Meths. Appl. Mech. Engrg., 24:61–112, 1980.zbMATHCrossRefGoogle Scholar
  38. C. A. Felippa, K.C. Park, and C. Farhat. Partitioned analysis of coupled mechanical systems. Computer Methods in Applied Mechanics and Engineering, 190:3247–3270, 2001.zbMATHCrossRefGoogle Scholar
  39. G. F. Franklin and J. D. Powell. Digital Control of Dynamic Systems. Addison-Wesley Publishing Company, New York, 1980.Google Scholar
  40. A. Gravouil and A. Combescure. Multi-time-step explicit-implicit method for non-linear structural dynamics. International Journal for Numerical Methods in Engineering, 50:199–225, 2001.zbMATHCrossRefGoogle Scholar
  41. E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer-Verlag, 1996.Google Scholar
  42. E. Hairer, S. P. Norsett, and G. Wanner. Solving Ordinary Differential Equations I. Nonstiff Problems. Springer-Verlag, 1987.Google Scholar
  43. L. He. Development of Partitioned Time Integration Schemes for Parallel Simulation of Heterogeneous Systems. PhD thesis, University of Trento, 2008.Google Scholar
  44. H. M. Hilber, T. J. R. Hughes, and R. L. Taylor. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics, 5:283–292, 1977.CrossRefGoogle Scholar
  45. T. Horiuchi, M. Inoue, T. Konno, and Namita Y. Real-time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber. Earthquake Eng. and Struct. Dyn., 28(10):1121–1141, 1999.CrossRefGoogle Scholar
  46. T. J. R. Hughes. The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1987.zbMATHGoogle Scholar
  47. T. J. R. Hughes and G. M. Hulbert. Space-time finite element methods for elastodynamics: formulations and error estimates. Computer Methods in Applied Mechanics and Engineering, 66:339–363, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  48. T. J. R. Hughes, K. S. Pister, and R. L. Taylor. Implicit-explicit finite elements in non-linear transient analysis. Computer Methods in Applied Mechanics and Engineering, 17/18:159–182, 1979.CrossRefGoogle Scholar
  49. G. M. Hulbert. Space-time finite element methods: 1970’s and Beyond, chapter An Overview of Variational Integrators, pages 116–123. CIMNE, Barcelona, Spain, 2004.Google Scholar
  50. G. M. Hulbert and J. Chung. The unimportance of the spurious root of time integration algorithms for structural dynamics. Communications in Numerical Methods in Engineering, 10:591–597, 1994.zbMATHCrossRefGoogle Scholar
  51. G. M. Hulbert and T. J. R. Hughes. An error analysis of truncated starting conditions in step-by-step time integration: Consequences for structural dynamics. Earthquake Engineering and Structural Dynamics, 15:901–910, 1987.CrossRefGoogle Scholar
  52. G. M. Hulbert and J. Chung. Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Computer Methods in Applied Mechanics and Engineering, 137:175–188, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  53. R. Y. Jung, P. B. Shing, E. Stauffer, and B. Thoen. Performance of a real-time pseudodynamic test system considering nonlinear structural response. Earthquake Engineering and Structural Dynamics, 32:1785–1809, 2007.CrossRefGoogle Scholar
  54. R. Kübler and W. Schiehlen. Modular simulation in multibody system dynamics. Multibody System Dynamics, 4:107–127, 2004.CrossRefGoogle Scholar
  55. Y. N. Kyrychko, K. B. Blyuss, A. Gonzalez-Buelga, S. J. Hogan, and D. J. Wagg. Real-time dynamic substructuring in a coupled oscillatorpendulum system. Proceedings of the Royal Society A, 462:1271–1294, 2006.zbMATHCrossRefMathSciNetGoogle Scholar
  56. L. M. Lacoma and I. Romero. Error estimation for hht method in non-linear solid dynamics. Computers and structures, 85:158–169, 2007.CrossRefMathSciNetGoogle Scholar
  57. J. D. Lambert. Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley, 1991.Google Scholar
  58. X. D. Li and N. E. Wiberg. Structural dynamic analysis by a time-discontinuous galerkin finite element method. International Journal for Numerical Methods in Engineering, 39:2131–2152, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  59. C. N. Lim, S.A. Neild, D. P. Stoten, and D. Drury. Real-time dynamic substructure testing via an adaptive control strategy. 1st International Conference on Advances in Experimental Structural Engineering, Nagoya, Japan, pages 393–400, 2005.Google Scholar
  60. F. Lopez-Almansa, A. H. Barbat, and J. Rodellar. SSP algorithm for linear and non-linear dynamic response simulation. International Journal for Numerical Methods in Engineering, 26(12):2687–2706, 1998.CrossRefGoogle Scholar
  61. Simulink: simulation and model-based design. The Math Works, Natick, MA, 2005.Google Scholar
  62. W. E. Misselhorn, N. J. Theron, and P. S. Els. Investigation of hardware-in-the-loop for use in suspension development. Vehicle System Dynamics, 44:65–81, 2006.CrossRefGoogle Scholar
  63. C. Moler and C. Van Loan. Nineteen dubious ways to compute the exponential of a matrix. SIAM Review, 45:1–46, 1978.Google Scholar
  64. G. Mosqueda, B. Stojadinovic, and S.A. Mahin. Real-time error monitoring for hybrid simulation. part I: Methodology and experimental verification. Journal of Structural Engineering, ASCE, 133(8):1100–1108, 2007a.CrossRefGoogle Scholar
  65. G. Mosqueda, B. Stojadinovic, and S.A. Mahin. Real-time error monitoring for hybrid simulation. part II: Structural response modification due to error. Journal of Structural Engineering, ASCE, 133(8):1109–1117, 2007b.CrossRefGoogle Scholar
  66. A. Mugan and G. M. Hulbert. Alternative characterization of time integration schemes. International Journal for Numerical Methods in Engineering, 51(3):351–376, 2001.zbMATHCrossRefGoogle Scholar
  67. M. Nakashima, T. Kaminosomo, M. Ishida, and K. Ando. Integration techniques for substructuring pseudodynamic test. In fourth U.S. National Conference on Earthquake Engineering, volume 2, Palm Springs, California, 1990.Google Scholar
  68. P. Nawrotzki and C. Eller. Numerical stability analysis in structural dynamics. Comput. Methods Appl. Mech. Engrg., 189:915–929, 2000.zbMATHCrossRefGoogle Scholar
  69. S. A. Neild, D. P. Stoten, D. Drury, and D. J. Wagg. Control issues relating to real-time substructuring experiments using a shaking table. Earthquake Engineering and Structural Dynamics, 34(9):1171–1192, 2005.CrossRefGoogle Scholar
  70. N. M. Newmark. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division ASCE, 85:67–94, 1959.Google Scholar
  71. K. C. Park and Carlos A. Felippa. A variational principle for the formulation of partitioned structural systems. Int. J. Numer. Meth. Engng., 47:395–418, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  72. P. Pegon. Alternative characterization of time integration schemes. Computer Methods in Applied Mechanics and Engineering, 190(20):2707–2727, 2001.zbMATHCrossRefGoogle Scholar
  73. P. Pegon. Continuous psd testing with substructuring. In O. S. Bursi and D. J. Wagg, editors, Modern Testing Techniques for Structural Systems, Dynamics and Control. CISM, 2008.Google Scholar
  74. P. Pegon and G. Magonette. Continuous PSD testing with non-linear substructuring: Presentation of, a stable parallel inter-field procedure. Technical Report I.02.167, E.C., JRC, ELSA Ispra, Italy, 2005.Google Scholar
  75. P. Pegon and G. Magonette Continuous PsD testing with non-linear substructuring: using the operator splitting technique to avoid iterative procedures. Technical Report SPI.05.30, E.C., JRC, ELSA, Ispra, Italy, 2005.Google Scholar
  76. A. V. Pinto, P. Pegon, G. Magonette, and G. Tsionis. Pseudo-dynamic testing of bridges using non-linear substructuring. Earthquake Engineering and Structural Dynamics, 33:1125–1146, 2004.CrossRefGoogle Scholar
  77. V. M. Popov. Hyperstability of Automatic control systems. Springer-Verlag, New York, 1973.Google Scholar
  78. A. Preumont. Frequency domain analysis of time integration operators. Earthquake Engineering and Structural Dynamics, 10(5):691–697, 1982.CrossRefGoogle Scholar
  79. AM. Reinhorn, MV. Sivaselvan, Z. Liang, and X. Shao. Real-time dynamic hybrid testing of structural systems. In Proceeding of the 13th World Conference on Earthquake Engineering Vancouver, Canada, 2004.Google Scholar
  80. H. H. Rosenbrock. Some general implicit processes for the numerical solution of differential equations. Computer Journal, 5:329–330, 1963.zbMATHCrossRefMathSciNetGoogle Scholar
  81. J. C. Samin, O. Brüls, J. F. Collard, L. Sass, and P. Fisette. Multiphysics modeling and optimization of mechatronic multibody systems. Multibody System Dynamics, 18:345–373, 2007.zbMATHCrossRefGoogle Scholar
  82. J. D. Sherrick. Concepts In Systems and Signals. Prentice Hall, 2004.Google Scholar
  83. P. B. Shing. Real-time hybrid testing techniques. In O. S. Bursi and D. J. Wagg, editors, In Modern Testing Techniques for Structural Systems, Dynamics and Control. CISM, 2008.Google Scholar
  84. P. B. Shing and M. T. Vannan. On the accuracy of an implicit time integration for pseudodynamic tests. Earthquake Engineering and Structural Dynamics, 19:631–651, 1990.CrossRefGoogle Scholar
  85. P. B. Shing, M. T. Vannan, and E. Cater. Implicit time integration for pseudodynamic tests. Earthquake Engineering and Structural Dynamics, 20:551–576, 1991.CrossRefGoogle Scholar
  86. P. B. Shing, O. S. Bursi, and M.T. Vannan. Pseudodynamic tests of a concentrically braced frame using substructuring techniques. J. of Construct. Steel Research, 29:121–148, 1994.CrossRefGoogle Scholar
  87. A. Soroushian, P. Wriggers, and J. Farjoodi. On practical integration of semi-discretized equations of motion part 1: reasons for probable instability and improper convergence. Journal of Sound and Vibration, 18: 705–731, 2005.CrossRefMathSciNetGoogle Scholar
  88. D. P. Stoten and H. Benchoubane. Empirical studies of an mrac algorithm with minimal controller synthesis. International Journal of Control, 51(4):823–849, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  89. D. P. Stoten and S. A. Neild. The error-based minimal control synthesis algorithm with integral action. Proc. of the Institetion of Mechanical Engineers, Part I: Journal of systems and Control Engineering, 217:187–201, 2003.CrossRefGoogle Scholar
  90. C. R. Thewalt and S. A. Mahin. Hybrid solution techniques for generalized pseudodynamic testing. Technical Report No. UCB/EERC-87/09, Earthquake Engineering Research Center, University of California Berkeley, CA, 1987.Google Scholar
  91. R. J. Vaccaro. Digital Control — A State-Space Approach. McGraw-Hill, New York, 1995.Google Scholar
  92. V. R. Vasquez and W. B. Whiting. Accounting for both random errors and systematic errors in uncertainty propagation analysis of computer models involving experimental measurements with monte carlo methods. Risk Analysis, 25(6):1669–1681, 2006.CrossRefGoogle Scholar
  93. L. Vulcan. Discrete-time analysis of integrator algorithms applied to S.I.S.O adaptive controllers with minimal control systhesis PhD thesis, University of Trento, Italy, 2006.Google Scholar
  94. D. J. Wagg, S. A. Neild, and P. Gawthrop. Real-time testing with dynamic substructuring. In O. S. Bursi and D. J. Wagg, editors, Modern Testing Techniques for Structural Systems, Dynamics and Control. CISM, 2008.Google Scholar
  95. M.I. Wallace, J. Sieber, S.A. Neild, D.J. Wagg, and B. Krauskopf. Stability analysis of real-time dynamic substructuring using delay differential equation models. Earthquake Engineering and Structural Dynamics, 34(15):1817–1832, 2004.CrossRefGoogle Scholar
  96. M. I. Wallace, D. J. Wagg, and S. A. Neild An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring. Proceedings of the Royal Society A, 2064(461):3807–3826, 2005.CrossRefMathSciNetGoogle Scholar
  97. N. E. Wiberg and X. D. Li. A post-processing technique and an a posteriori error estimate for the Newmark method in dynamic analysis. Earthquake Engineering and Structural Dynamics, 22(6):465–489, 1993.CrossRefGoogle Scholar
  98. M. S. Williams and A. Blakeborough. Laboratory testing of structures under dynamic loads: an introductory review. Philosophical Transactions of the Royal Society of London, Series A, 359(1786):1651–1670, 2001.CrossRefGoogle Scholar
  99. B. Wu, H. Bao, J. Ou, and S. Tian. Stability and accuracy analysis of the central difference method for real-time substructure testing. Earthquake Engineering and Structural Dynamics, 34(7):705–718, 2005.CrossRefGoogle Scholar
  100. B. Wu, G. Xu Q. Wang, and M. S. Williams. Operator-splitting method for real-time substructure testing. Earthquake Engineering and Structural Dynamics, 35(3):293–314, 2006.CrossRefGoogle Scholar
  101. D. M. Young. Iterative Solution of Large Linear System. Academic Press, Orlando, 1971.Google Scholar
  102. Q. Zhang and T. Hisada. Studies of the strong coupling and weak coupling methods in fsi analysis. International Journal for Numerical Methods in Engineering, 60:2013–2029, 2004.zbMATHCrossRefGoogle Scholar
  103. Y. Zhang, R. Sause, J. M. Ricles, and C. J. Naito. Modified predictorcorrector numerical scheme for real-time pseudo dynamic tests using state-space formulations. Earthquake Engineering and Structural Dynamics, 34(3):271–288, 2005.CrossRefGoogle Scholar

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© CISM, Udine 2008

Authors and Affiliations

  • Oreste S. Bursi
    • 1
  1. 1.Department of Mechanical and Structural EngineeringUniversity of TrentoTrentoItaly

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