Constitutive and Geometric Nonlinear Models for the Seismic Analysis of RC Structures with Energy Dissipators

  • P. Mata
  • A. H. Barbat
  • S. Oller
  • R. Boroschek
Original Paper


Nowadays, the use of energy dissipating devices to improve the seismic response of RC structures constitutes a mature branch of the innovative procedures in earthquake engineering. However, even though the benefits derived from this technique are well known and widely accepted, the numerical methods for the simulation of the nonlinear seismic response of RC structures with passive control devices is a field in which new developments are continuously preformed both in computational mechanics and earthquake engineering. In this work, a state of the art of the advanced models for the numerical simulation of the nonlinear dynamic response of RC structures with passive energy dissipating devices subjected to seismic loading is made. The most commonly used passive energy dissipating devices are described, together with their dissipative mechanisms as well as with the numerical procedures used in modeling RC structures provided with such devices. The most important approaches for the formulation of beam models for RC structures are reviewed, with emphasis on the theory and numerics of formulations that consider both geometric and constitutive sources on nonlinearity. In the same manner, a more complete treatment is given to the constitutive nonlinearity in the context of fiber-like approaches including the corresponding cross sectional analysis. Special attention is paid to the use of damage indices able of estimating the remaining load carrying capacity of structures after a seismic action. Finally, nonlinear constitutive and geometric formulations for RC beam elements are examined, together with energy dissipating devices formulated as simpler beams with adequate constitutive laws. Numerical examples allow to illustrate the capacities of the presented formulations.


Seismic Response Stress Couple Plastic Hinge Federal Emergency Management Agency Tune Mass Damper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ahmadi HR, Muhr AH (1997) Modelling dynamic properties of filled rubber. Plast Rubber Compos Process Appl 26:451–461 Google Scholar
  2. 2.
    Aiken I (1996) Passive energy dissipation hardware and applications. In: Proceedings, Los Angeles county and SEAOSC symposium on passive energy dissipation systems for new and existing buildings, Los Angeles, July 1996 Google Scholar
  3. 3.
    Aiken I (1998) Testing of seismic isolators and dampers—considerations and limitations. In: Proceedings, structural engineering world congress, San Francisco, California, 1998 Google Scholar
  4. 4.
    Aiken ID, Kelly JM (1996) Cyclic dynamic testing of fluid viscous dampers. In: Proceedings, Caltrans fourth seismic research workshop, California Department of Transportation, Sacramento, California, USA, July 1996 Google Scholar
  5. 5.
    Aiken ID, Kelly JM, Pall AS (1968) Seismic response of a nine-story steel frame with friction damped cross-bracing. In: Proceedings, ninth world conference on earthquake engineering, Tokyo and Kyoto, Japan, August 1988 Google Scholar
  6. 6.
    Akiyama H (2003) Metodología de proyecto sismoresistente de edificios basada en el balance energético. Editorial Reverté SA, 2003 Google Scholar
  7. 7.
    Antman SS (1991) Nonlinear problems of elasticity. Springer, New York Google Scholar
  8. 8.
    Antman SS (1996) Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods. J Nonlinear Sci 6:1–18 MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Arfiadi Y, Hadi MNS (2000) Passive and active control of three-dimensional buildings. Earthquake Eng Struct Dyn 29:377–396 CrossRefGoogle Scholar
  10. 10.
    Argyris J (1982) An excursion into large rotations. Comput Methods Appl Mech Eng 32:85–155 MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Argyris J, Poterasu VF (1993) Large rotations revisited application of Lie algebra. Comput Methods Appl Mech Eng 103:11–42 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Armero F (1999) Large-scale modeling of localized dissipative mechanisms in a local continuum: applications to the numerical simulation of strain localization in rate-dependent inelastic solids. Mech Cohes-Frict Mater 4:101–131 CrossRefGoogle Scholar
  13. 13.
    Armero F, Ehrlich D (2004) An analysis of strain localization and wave propagation in plastic models of beams at failure. Comput Methods Appl Mech Eng 193:3129–3171 CrossRefzbMATHGoogle Scholar
  14. 14.
    Armero F, Ehrlich D (2005) Numerical modeling of softening hinges in the Euler-Bernoulli beams. Comput Struct 84:641–656 MathSciNetCrossRefGoogle Scholar
  15. 15.
    Armero F, Ehrlich D (2005) Finite element methods for the analysis of softening plastic hinges in beams and frames. Comput Mech 35:237–264 CrossRefzbMATHGoogle Scholar
  16. 16.
    Armero F, Romero I (2001) On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second-order methods. Comput Methods Appl Mech Eng 190:6783–6824 MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Armero F, Romero I (2003) Energy–dissipating momentum–conserving time–stepping algorithms for the dynamic of nonlinear Cosserat rods. Comput Mech 31:3–26 MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Asano M, Masahiko H, Yamamoto M (2001) The experimental study on viscoelastic material dampers and the formulation of analytical model. In: Proceedings of the 12th world conference on earthquake engineering, Paper no 1535 Google Scholar
  19. 19.
    Atluri SN, Cazzani A (1995) Rotations in computational solid mechanics. Arch Comput Methods Eng 2:49–138 MathSciNetCrossRefGoogle Scholar
  20. 20.
    Atluri SN, Vasudevan S (2001) A consistent theory of finite stretches and finite rotations, in space–curved beams of arbitrary cross section. Comput Mech 27:271–281 CrossRefzbMATHGoogle Scholar
  21. 21.
    Ayoub A, Filippou FC (2000) Mixed formulation of nonlinear steel-concrete composite beam element. J Struct Eng 126:0371–0381 CrossRefGoogle Scholar
  22. 22.
    Bairan Garcia JM, Mari Bernat AR (2006) Coupled model for the non-linear analysis of anisotropic sections subjected to general 3D loading. Part 1: theoretical formulation. Comput Struct 84:2254–2263 CrossRefGoogle Scholar
  23. 23.
    Barbat AH, Bozzo LM (1997) Seismic analysis of base isolated buildings. Arch Comput Methods Eng 4(2):153–192 CrossRefGoogle Scholar
  24. 24.
    Barbat AH, Cervera M, Hanganu A, Cirauqui C, Oñate E (1998) Failure pressure evaluation of the containment building of a large dry nuclear power plant. Nucl Eng Des 180:251–270 CrossRefGoogle Scholar
  25. 25.
    Barbat AH, Oller S, Hanganu A, Oñate E (1997) Viscous damage model for Timoshenko beam structures. Int J Solids Struct 34(30):3953–3976 CrossRefzbMATHGoogle Scholar
  26. 26.
    Barbat AH, Oller S, Mata P, Vielma JC (2007) Computational simulation of the seismic response of buildings with energy dissipating devices. In: Proceedings of the COMPDYN 2007, first international conference on computational methods in structural dynamics and earthquake engineering, Rethymno, Crete, Greece, June 13th–15th, 2007 Google Scholar
  27. 27.
    Barbat AH, Rodellar J, Ryan E, Molinares N (1993) Comportamiento sísmico de edificios con un sistema no lineal de control hibrido. Rev Int Métodos Numér Cálcy Diseño Ing 9:201–220 Google Scholar
  28. 28.
    Barbat AH, Rodellar J, Ryan EP, Molinares N (1995) Active control of nonlinear base-isolated buildings. J Eng Mech 121(6):676–684 CrossRefGoogle Scholar
  29. 29.
    Barham WS, Aref AJ, Dargush GF (2005) Flexibility-based large increment method for analysis of elastic-perfectly plastic beam structures. Comput Struct 83:2453–2462 CrossRefGoogle Scholar
  30. 30.
    Barroso LR, Breneman SE, Smith HA (2002) Performance evaluation of controlled steel frames under multilevel seismic loads. J Struct Eng 128(11):1368–1378 CrossRefGoogle Scholar
  31. 31.
    Bathe KJ (1996) Finite element procedures. Prentice-Hall, Englewood Cliffs Google Scholar
  32. 32.
    Bathe KJ, Bolourchi S (1979) Large displacement analysis of three-dimensional beam structures. Int J Numer Methods Eng 14:961–986 CrossRefzbMATHGoogle Scholar
  33. 33.
    Batista Marques de Sousa J Jr, Barreto Caldas R (2005) Numerical analysis of composite steel–concrete columns of arbitrary cross section. J Eng Mech 131(11):1721–1730 Google Scholar
  34. 34.
    Battini JM, Pacoste C (2002) Co-rotational beam elements with warping effects in instability problems. Comput Methods Appl Mech Eng 191:1755–1789 CrossRefzbMATHGoogle Scholar
  35. 35.
    Bauchau OA, Choi JI (2003) The vector parameterization of motion. Nonlinear Dyn 33:165–188 MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Bauchau OA, Theron NJ (1996) Energy decaying scheme for non-linear beam models. Comput Methods Appl Mech Eng 134:37–56 MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Bauchau O, Trainelli L (2003) The vectorial parametrization of rotation. Nonlinear Dyn 32:71–92 MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Bayrak O, Sheikh SA (2001) Plastic hinge analysis. J Struct Eng 127(9):1092–1100 CrossRefGoogle Scholar
  39. 39.
    Bentz EC (2000) Sectional analysis of reinforced concrete members. PhD thesis, University of Toronto Google Scholar
  40. 40.
    Betsch P, Menzel A, Stein E (1998) On the parametrization of finite rotations in computational mechanics. A classification of concepts with application to smooth shells. Comput Methods Appl Mech Eng 155:273–305 MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Betsch P, Steinmann P (2002) Frame-indifferent beam finite element based upon the geometrically exact beam theory. Int J Numer Methods Eng 54:1775–1788 MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Betsch P, Steinmann P (2003) Constrained dynamics of geometrically exact beams. Comput Mech 31:49–59 CrossRefzbMATHGoogle Scholar
  43. 43.
    Blandford GE (1996) Large deformation analysis of inelastic space truss structures. J Struct Eng 122(4):407–415 CrossRefGoogle Scholar
  44. 44.
    Bottasso CL, Borri M (1997) Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation. Comput Methods Appl Mech Eng 143:393–415 MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Bottasso CL, Borri M, Trainelli L (2001) Integration of elastic multibody systems by invariant conserving/dissipating algorithms. II. Numerical schemes and applications. Comput Methods Appl Mech Eng 190:3701–3733 MathSciNetCrossRefGoogle Scholar
  46. 46.
    Braga F, Faggella M, Gigliotti R, Laterza M (2005) Nonlinear dynamic response of HDRB and hybrid HDRB-friction sliders base isolation systems. Bull Earthquake Eng 3:333–353 CrossRefGoogle Scholar
  47. 47.
    Bratina S, Saje M, Planinc I (2004) On materially and geometrically non-linear analysis of reinforced concrete planar frames. Int J Solids Struct 41:7181–7207 CrossRefzbMATHGoogle Scholar
  48. 48.
    Briseghella L, Majorana CE, Pellegrino C (1999) Conservation of angular momentum and energy in the integration of non-linear dynamic equations. Comput Methods Appl Mech Eng 179:247–263 MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Bruneau M, Vian D Experimental investigation of PΔ effects to collapse during earthquakes. In: 12th European conference on earthquake engineering, Elsevier Science Ltd., Amsterdam, Paper Ref. 021 Google Scholar
  50. 50.
    Budd CJ, Iserles A (1999) Geometric integration: numerical solution of differential equations on manifolds. R Soc 357:945–956 MathSciNetzbMATHGoogle Scholar
  51. 51.
    Buonsanti M, Royer-Carfagni G (2003) From 3-D nonlinear elasticity theory to 1-D bars with nonconvex energy. J Elast 70:87–100 MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Car E (2000) Modelo constitutivo continuo para el estudio del comportamiento mecánico de los materiales compuestos. PhD thesis, Universidad Politécnica de Cataluña Google Scholar
  53. 53.
    Cardona A, Gerardin M (1988) A beam finite element non-linear theory with finite rotations. Int J Numer Methods Eng 26:2403–2438 CrossRefzbMATHGoogle Scholar
  54. 54.
    Cardona A, Huespe A (1999) Evaluation of simple bifurcation points and post-critical path in large finite rotations problems. Comput Methods Appl Mech Eng 175:137–156 CrossRefzbMATHGoogle Scholar
  55. 55.
    Celledoni E, Owren B (2003) Lie group methods for rigid body dynamics and time integration on manifolds. Comput Methods Appl Mech Eng 192:421–438 MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Cesnik CES, Sutyrint VG, Hodges DH (1988) Refined theory of composite beams: the role of short-wavelength extrapolation. Int J Solids Struct 33(10):1387–1408 CrossRefGoogle Scholar
  57. 57.
    Clark P, Aiken I, Ko E, Kasai K, Kimura I (1999) Design procedures for buildings incorporating hysteretic seismic devices. In: Proceedings, 68th annual convention Santa Barbara, California, Structural Engineering Association of California, October 1999 Google Scholar
  58. 58.
    Cocchetti G, Maier G (2003) Elastic-plastic and limit-state analyses of frames with softening plastic–hinge models by mathematical programming. Int J Solids Struct 40:7219–7244 MathSciNetCrossRefzbMATHGoogle Scholar
  59. 59.
    Coleman J, Spacone E (2001) Localization issues in force-based frame elements. J Struct Eng 127(11):1257–1265 CrossRefGoogle Scholar
  60. 60.
    Connor JJ, Wada A, Iwata M, Huang YH (1997) Damage-controlled structures. I: preliminary design methodology for seismically active regions. J Struct Eng 123(4):423–431 CrossRefGoogle Scholar
  61. 61.
    Cosenza E, Manfredy G (2000) Damage indices and damage measures. Progress Struct Eng Mater 2:50–59 CrossRefGoogle Scholar
  62. 62.
    Crisfield MA (1998) Non-linear finite element analysis of solids and structures, vol 1&2. Willey, New York Google Scholar
  63. 63.
    Crisfield MA, Galvanetto U, Jelenic̀ G (1997) Dynamics of 3-D co-rotational beams. Comput Mech 20:507–519 CrossRefzbMATHGoogle Scholar
  64. 64.
    Crisfield MA, Jelenic̀ G (1999) Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. R Soc 455:1125–1147 MathSciNetzbMATHGoogle Scholar
  65. 65.
    Crisfield MA, Wills J (1988) Solution strategies and softening materials. Comput Methods Appl Mech Eng 66:267–289 CrossRefzbMATHGoogle Scholar
  66. 66.
    CSI analysis reference manual for SAP200r®, ETABs®, and SAFE™. Computers and Structures, Inc., Berkeley, California, USA, 2004 Google Scholar
  67. 67.
    Das S, Hadi MNS (1996) Non-linear finite element analysis of reinforced concrete members using MSC/NASTRAN. In: MSC world users conference, Newport Beach, CA, June 1996 Google Scholar
  68. 68.
    Davenne L (2004) Macro-element analysis in earthquake engineering. In: Multi-physics and multi-scale computer models in non-linear analysis and optimal design of engineering structures under extreme conditions, Slovenia, June 13–17, 2004 Google Scholar
  69. 69.
    Davenne L, Ragueneau F, Mazar J, Ibrahimbegović A (2003) Efficient approaches to finite element analysis in earthquake engineering. Comput Struct 81:1223–1239 CrossRefGoogle Scholar
  70. 70.
    De La Llera JC, Vásquez J, Chopra AK, Almazán JL (2000) A macro-element model for inelastic building analysis. Earthquake Eng Struct Dyn 29:1725–1757 CrossRefGoogle Scholar
  71. 71.
    Dides MA, De La Llera JC (2005) A comparative study of concentrated plasticity models in dynamic analysis of building structures. Earthquake Eng Struct Dyn 34:1005–1026 CrossRefGoogle Scholar
  72. 72.
    Driemeier L, Baroncini SP, Alves M (2005) A contribution to the numerical non-linear analysis of three-dimensional truss system considering large strains, damage and plasticity. Commun Nonlinear Sci Numer Simul 10:515–535 CrossRefzbMATHGoogle Scholar
  73. 73.
    Ehrlich D, Armero F (2005) Finite element methods for the analysis of softening plastic hinges in beams and frames. Comput Mech 35:237–264 CrossRefzbMATHGoogle Scholar
  74. 74.
    Ericksen JL, Truesdell C (1957) Exact theory of stress and strain in rods and shells. Arch Ration Mech Anal 1:295–323 MathSciNetGoogle Scholar
  75. 75.
    European Committee for Standardization (1998) Eurocode 8: design of structures for earthquake resistance–Part 1: general rules, seismic actions and rules for buildings. Final Draft, Ref No: prEN 1998-1:2003 E Google Scholar
  76. 76.
    Fajfar P, Fifchinger M, Dolšek M (2004) Macro-models and simplified methods for efficient structural analysis in earthquake engineering. In: Multi-physics and multi-scale computer models in non-linear analysis and optimal design of engineering structures under extreme conditions, Slovenia, June 13–17, 2004 Google Scholar
  77. 77.
    Faleiro J, Oller S, Barbat AH (2008) Plastic-damage seismic model for reinforced concrete frames. Comput Struct 86(7–8):581–597 CrossRefGoogle Scholar
  78. 78.
    Fardis MN (1997) Seismic analysis of RC structures. Constr Res Commun Ltd 1(1):57–67 Google Scholar
  79. 79.
    Federal Emergency Management Agency (FEMA) (2000) NEHRP recommended provisions for seismic regulations for new buildings and other structures. Report 368, Washington, DC Google Scholar
  80. 80.
    Federal Emergency Management Agency (FEMA) (2000) Prestandard and commentary for the seismic rehabilitation of buildings. Report 356, Washington, DC Google Scholar
  81. 81.
    Felippa CA, Crivelli LA, Haugen B (1994) A survey of the core-congruential formulation for geometrically nonlinear TL finite elements. Arch Comput Methods Eng 1:1–48 MathSciNetCrossRefGoogle Scholar
  82. 82.
    Fialko S (2001) Aggregation multilevel iterative solver for analysis of large-scale finite element problems of structural mechanics: linear statics and natural vibrations. In: Parallel processing and applied mathematics: 4th international conference. PPAM 2001, Naleczów, Poland, September 9–12, 2001 Google Scholar
  83. 83.
    Fraternali F, Bilotti G (1997) Nonlinear elastic stress analysis in curved composite beams. Comput Struct 62(5):837–859 CrossRefzbMATHGoogle Scholar
  84. 84.
    Freddi L, Morassi A, Paroni R (2004) Thin-walled beams: the case of the rectangular cross-section. J Elast 76:45–66 MathSciNetCrossRefzbMATHGoogle Scholar
  85. 85.
    Fu Y, Kasai K (1998) Comparative study of frames using viscoelastic and viscous dampers. J Struct Eng 124(5):513–522 CrossRefGoogle Scholar
  86. 86.
    Gerardin M, Cardona A (1989) Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra. Comput Mech 4:115–135 CrossRefGoogle Scholar
  87. 87.
    Gluck N, Reinhorn AM, Gluck J, Levy R (1996) Design of supplemental damping for control of structures. J Struct Eng 122(12):1394–1399 CrossRefGoogle Scholar
  88. 88.
    Gonzalez O, Simo JC (1996) On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry. Comput Methods Appl Mech Eng 134:197–222 MathSciNetCrossRefzbMATHGoogle Scholar
  89. 89.
    Grassia FS (1998) Practical parameterization of rotations using the exponential map. J Graphics Tools 3:29–48 Google Scholar
  90. 90.
    Gruttmann F, Sauer R, Wagner W (1998) A geometrical nonlinear eccentric 3-D beam element with arbitrary cross sections. Comput Methods Appl Mech Eng 160:383–400 MathSciNetCrossRefzbMATHGoogle Scholar
  91. 91.
    Gruttmann F, Sauer R, Wagner W (1998) Shear stresses in prismatic beams with arbitrary cross-sections. Technical Report Universität Karlsruhe (TH), Institut für Baustatik Google Scholar
  92. 92.
    Gruttmann F, Sauer R, Wagner W (2000) Theory and numerics of three-dimensional beams with elastoplastic material behavior. Int J Numer Methods Eng 48:1675–1702 CrossRefzbMATHGoogle Scholar
  93. 93.
    Gupta A, Krawinkler H (2000) Dynamic P-Delta effects for flexible inelastic steel structures. J Struct Eng 126(1):145–154 CrossRefGoogle Scholar
  94. 94.
    Hajjar JF (2000) Concrete-filled steel tube columns under earthquake loads. Progress Struct Eng Mater 2:72–81 CrossRefGoogle Scholar
  95. 95.
    Hanganu AD, Oñate E, Barbat AH (2002) Finite element methodology for local/global damage evaluation in civil engineering structures. Comput Struct 80:1667–1687 CrossRefGoogle Scholar
  96. 96.
    Hanson RD, Aiken ID, Nims DK, Ritchter PJ, Batchman RE (1993) State of the art and state of the practice in seismic engineering dissipation. In: Proceedings, ATC-17-1. Seminar on seismic isolation, passive energy dissipation and active control. Applied Technology Council, San Francisco, California, March 1993 Google Scholar
  97. 97.
    Highway Innovative Technology Evaluation Center (HITEC) (1996) A service center of the civil engineering research foundation (CERF). Guidelines for the testing of seismic isolation and energy dissipation devices. Technical Evaluation Report No: 96-02 Google Scholar
  98. 98.
    Highway Innovative Technology Evaluation Center (HITEC) (1999) A service center of the civil engineering research foundation (CERF). Summary of the evaluation findings for the testing of seismic isolation and passive energy dissipating devices. Technical Evaluation Report No: 40404 Google Scholar
  99. 99.
    Hjelmstad KD, Taciroglu E (2003) Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli-Euler beams. Commun Numer Methods Eng 19:809–832 CrossRefzbMATHGoogle Scholar
  100. 100.
    Hsiao KM, Lin JY, Lin WY (1999) A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams. Comput Methods Appl Mech Eng 169:1–18 CrossRefzbMATHGoogle Scholar
  101. 101.
    Hughes TJR (2000) The finite element method. Linear static and dynamic finite element analysis. Dover, New York Google Scholar
  102. 102.
    Hwang JS, Ku SW (1997) Analytical modelling of high damping rubber bearings. J Struct Eng 123:1029–1036 CrossRefGoogle Scholar
  103. 103.
    Iaura M, Atluri SN (1989) On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams. Comput Mech 4:73–78 CrossRefGoogle Scholar
  104. 104.
    Ibrahimbegović A (1995) On finite element implementation of geometrically nonlinear Reissner’s beam theory: three-dimensional curved beam elements. Comput Methods Appl Mech Eng 122:11–26 CrossRefzbMATHGoogle Scholar
  105. 105.
    Ibrahimbegović A (1997) On the choice of finite rotation parameters. Comput Methods Appl Mech Eng 149:49–71 CrossRefzbMATHGoogle Scholar
  106. 106.
    Ibrahimbegović A, Al Mikdad M (2000) Quadratically convergent direct calculation of critical points for 3D structures undergoing finite rotations. Comput Methods Appl Mech Eng 189:107–120 CrossRefzbMATHGoogle Scholar
  107. 107.
    Ibrahimbegović A, Mamouri S (2002) Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations. Comput Methods Appl Mech Eng 191:4241–4258 CrossRefGoogle Scholar
  108. 108.
    Ibrahimbegović A, Mazen AM (1998) Finite rotations in dynamics of beams and implicit time-stepping schemes. Int J Numer Methods Eng 41:781–814 CrossRefzbMATHGoogle Scholar
  109. 109.
    Ibrahimbegović A, Taylor RL, Lim H (2003) Non-linear dynamics of flexible multibody systems. Comput Struct 81:1113–1132 CrossRefGoogle Scholar
  110. 110.
    Isobe D, Tsuda M (2003) Seismic collapse analysis of reinforced concrete framed structures using the finite element method. Earthquake Eng Struct Dyn 32:2027–2046 CrossRefGoogle Scholar
  111. 111.
    Izzuddin BA (2001) Conceptual issues in geometrically nonlinear analysis of 3D framed structures. Comput Methods Appl Mech Eng 191:1029–1053 CrossRefzbMATHGoogle Scholar
  112. 112.
    Jelenic̀ G (2004) Different aspects of invariance and shear locking in 3D beam elements. In: Advanced research workshop: multi-physics and multi-scale computer models in non-linear analysis and optimal design of engineering structures under extreme conditions, Bled, Slovenia, June 13–17, 2004 Google Scholar
  113. 113.
    Jelenic̀ G, Crisfield MA (1999) Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for static and dynamics. Comput Methods Appl Mech Eng 171:141–171 MathSciNetCrossRefGoogle Scholar
  114. 114.
    Jelenic̀ G, Saje M (1995) A kinematically exact space finite strain beam model-finite element formulation by generalized virtual work principle. Comput Methods Appl Mech Eng 120:131–161 MathSciNetCrossRefGoogle Scholar
  115. 115.
    Jiang WG, Henshall JL (2002) A coupling cross-section finite element model for torsion analysis of prismatic bars. Eur J Mech A/Solids 21:513–522 CrossRefzbMATHGoogle Scholar
  116. 116.
    Kane C, Marsden JE, Ortiz M, West M (2000) Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Int J Numer Methods Eng 49:1295–1325 MathSciNetCrossRefzbMATHGoogle Scholar
  117. 117.
    Kapania RK, Li J (2003) On a geometrically exact curved/twisted beam theory under rigid cross-section assumption. Comput Mech 30:428–443 CrossRefzbMATHGoogle Scholar
  118. 118.
    Kapania RK, Li J (2003) A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations. Comput Mech 30:444–459 CrossRefzbMATHGoogle Scholar
  119. 119.
    Kappos AJ (1997) Seismic damage indices for RC buildings: evaluation of concepts and procedures. Constr Res Commun Ltd 1(1):78–87 Google Scholar
  120. 120.
    Kasai K, Fu Y, Watanabe A (1998) Passive control systems for seismic damage mitigation. J Struct Eng 124(5):501–512 CrossRefGoogle Scholar
  121. 121.
    Kelly J (1997) Earthquake-resistant design with rubber, 2nd edn. Springer, Telos Google Scholar
  122. 122.
    Kelly JM (1999) The role of damping in seismic isolation. Earthquake Eng Struct Dyn 28:3–20 CrossRefGoogle Scholar
  123. 123.
    Kikuchi M, Aiken I (1997) An analytical hysteresis model for elastomeric seismic isolation bearings. Earthquake Eng Struct Dyn 26(2):215–231 CrossRefGoogle Scholar
  124. 124.
    Kim JK, Lee TG (1993) Failure behavior of reinforced concrete frames by the combined layered and nonlayered method. Comput Struct 48(5):819–825 CrossRefGoogle Scholar
  125. 125.
    Kojima H, Yoshihide Y (1990) Performance, durability of high damping rubber bearings for earthquake protection. Rubber World 202(4) Google Scholar
  126. 126.
    Kwak H-G, Filippou FC (1990) Finite element analysis of reinforced concrete structures under monotonic loads. Technical Report n: UCB/SEMM–90/14. Department of Civil Engineering, University of California Berkeley, California, USA Google Scholar
  127. 127.
    Kwak H-G, Kim S-P (2001) Nonlinear analysis of RC beam subject to cyclic loading. J Struct Eng 127(12):1436–1444 CrossRefGoogle Scholar
  128. 128.
    Lafortune S, Goriely A, Tabor M (2006) The dynamics of stretchable rods in the inertial case. Nonlinear Dyn 43:173–195 MathSciNetCrossRefzbMATHGoogle Scholar
  129. 129.
    Lee T, Leok M, McClamroch NH (2007) Lie group variational integrators for the full body problem. Comput Methods Appl Mech Eng 196:2907–2924 MathSciNetCrossRefzbMATHGoogle Scholar
  130. 130.
    Lee D, Taylor DP (2001) Viscous damper development and future trends. Struct Des Tall Build 10:311–320 CrossRefGoogle Scholar
  131. 131.
    Lens EV, Cardona A, Géradin M (2004) Energy preserving time integration for constrained multibody systems. Multibody Syst Dyn 11:41–61 MathSciNetCrossRefzbMATHGoogle Scholar
  132. 132.
    Lew A, Marsden JE, Ortiz M, West M (2004) An overview of variational integrators. In: Franca LP (ed) Finite element methods: 1970’s and beyond. CIMNE, Barcelona Google Scholar
  133. 133.
    Lew A, Marsden JE, Ortiz M, West M (2004) Variational time integrators. Int J Numer Methods Eng 60:153–212 MathSciNetCrossRefzbMATHGoogle Scholar
  134. 134.
    Li J (2000) A geometrically exact curved beam theory and its finite element formulation/implementation. MSc thesis, Virginia Polytechnic Institute and State University Google Scholar
  135. 135.
    Lim CW, Chung TY, Moon SJ (2003) Adaptive bang-bang control for the vibration control of structures under earthquakes. Earthquake Struct Dyn 32:1977–1994 CrossRefGoogle Scholar
  136. 136.
    Lin YY, Chang KC (2003) Study on damping reduction factors for buildings under earthquake ground motions. J Struct Eng 129:206–214 CrossRefGoogle Scholar
  137. 137.
    Lin WH, Chopra AK (2003) Asymmetric one-storey elastic system with non-linear viscous and viscoelastic dampers: earthquake response. Earthquake Eng Struct Dyn 32:555–577 CrossRefGoogle Scholar
  138. 138.
    Lin WH, Chopra AK (2003) Asymmetric one-storey elastic system with non-linear viscous and viscoelastic dampers: simplified analysis and supplemental damping system design. Earthquake Eng Struct Dyn 32:579–596 CrossRefGoogle Scholar
  139. 139.
    Liu JY, Hong JZ (2004) Dynamics of three-dimensional beams undergoing large overall motion. Eur J Mech A/Solids 23:1051–1068 CrossRefzbMATHGoogle Scholar
  140. 140.
    López Almansa F, Barbat AH, Rodellar J (1988) SSP algorithm for linear and non-linear dynamic response simulation. Int J Numer Methods Eng 26(12):2687–2706 CrossRefzbMATHGoogle Scholar
  141. 141.
    Love AEHA (1996) Treatise on the mathematical theory of elasticity. Dover, New York Google Scholar
  142. 142.
    Lu Y (2002) Comparative study of seismic behavior of multistory reinforced concrete framed structures. J Struct Eng 128(2):169–178 CrossRefGoogle Scholar
  143. 143.
    Lubliner J (1972) On the thermodynamic foundations of non-linear solid mechanics. Int J Non-Linear Mech 7:237–254 CrossRefzbMATHGoogle Scholar
  144. 144.
    Lubliner J (1985) Thermomechanics of deformable bodies, Technical Report, Department of Civil Engineering, University of California at Berkeley Google Scholar
  145. 145.
    Lubliner J (2008) Plasticity theory. Dover, New York Google Scholar
  146. 146.
    Lubliner J, Oliver J, Oller S, Oñate E (1989) A plastic-damage model for concrete. Int J Solids Struct 25:299–326 CrossRefGoogle Scholar
  147. 147.
    Luccioni BM, Rougier VC (2005) A plastic damage approach for confined concrete. Comput Struct 83:2238–2256 CrossRefGoogle Scholar
  148. 148.
    Magalhães de Souza R, Filippou FC, Maués Brabo Pereira A, Aranha GYR Jr (2003) Force formulation of a non-prismatic Timoshenko beam finite element for dynamic analysis of frames. In: CILAMNE, XXIV Iberian Latin–American congress on computational methods in engineering, Ouro Preto/MG Brasil Google Scholar
  149. 149.
    Mäkinen J (2001) Critical study of Newmark-scheme on manifold of finite rotations. Comput Methods Appl Mech Eng 191:817–828 CrossRefzbMATHGoogle Scholar
  150. 150.
    Mäkinen J (2004) A formulation for flexible multibody mechanics. Lagrangian geometrically exact beam elements using constrain manifold parametrization. PhD thesis, Tampere University of Technology, Institute of Applied Mechanics and Optimization Google Scholar
  151. 151.
    Mäkinen J (2007) Total Lagrangian Reissner’s geometrically exact beam element without singularities. Int J Numer Methods Eng 70:1009–1048 CrossRefGoogle Scholar
  152. 152.
    Mäkinen J, Marjamäki H (2005) Total Lagrangian parametrization of rotation manifold. In: ENOC, Hedinhoven, Netherlands, pp 522–530 Google Scholar
  153. 153.
    Makris N, Burton SA, Hill D, Jordan M (1996) Analysis and design of ER damper for seismic protection of structures. J Mech Eng 122(10):1003–1011 CrossRefGoogle Scholar
  154. 154.
    Makris N, Changt SP (2000) Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures. Earthquake Eng Struct Dyn 29:85–107 CrossRefGoogle Scholar
  155. 155.
    Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Cliffs Google Scholar
  156. 156.
    Marsden JE, Hughes TJR (1983) Mathematical foundations of elasticity. Prentice-Hall, Englewood Cliffs zbMATHGoogle Scholar
  157. 157.
    Marsden JE, Wendlandt JM (1997) Mechanical systems with symmetry, variational principles, and integration algorithms. In: Alber M, Hu B, Rosenthal J (eds) Current and future directions in applied mathematics. Birkhäuser, Basel, pp 219–261 Google Scholar
  158. 158.
    Marsden JE, West M (2001) Discrete mechanics and variational integrators. Acta Numer 10:357–514 MathSciNetCrossRefzbMATHGoogle Scholar
  159. 159.
    Martínez Franklin CE (1997) A theoretical and numerical evaluation of nonlinear beam elements. Master of science thesis, Massachusetts Institute of Technology Google Scholar
  160. 160.
    Martinez X, Oller S, Rastellini F, Barbat AH (2008) Numerical procedure for the computation of RC structures reinforced with FRP using the serial/parallel mixing theory. Comput Struct 86(15–16):1604–1618 CrossRefGoogle Scholar
  161. 161.
    Mata P, Boroschek R, Barbat AH (2004) Analytical model for high damping elastomers applied to energy dissipating devices. Numerical study and experimental validation. In: 3CSC third European conference on structural control, Vienna, July 12–15, 2004 Google Scholar
  162. 162.
    Mata P, Boroschek R, Barbat AH, Oller S (2007) High damping rubber model for energy dissipating devices. J Earthquake Eng 11(2):231–256 Google Scholar
  163. 163.
    Mata P, Oller S, Barbat AH (2007) Static analysis of beam structures under nonlinear geometric and constitutive behavior. Comput Methods Appl Mech Eng 196:4458–4478 MathSciNetCrossRefGoogle Scholar
  164. 164.
    Mata P, Oller S, Barbat AH (2008) Dynamic analysis of beam structures considering geometric and constitutive nonlinearity. Comput Methods Appl Mech Eng 197:857–878 MathSciNetCrossRefzbMATHGoogle Scholar
  165. 165.
    Mata P, Barbat AH, Oller S, Boroschek R (2008) Nonlinear seismic analysis of RC structures with energy dissipating devices. Int J Numer Methods Eng, 2008, submitted Google Scholar
  166. 166.
    Mazars J, Kotronis P, Ragueneau F, Casaux G (2006) Using multifiber beams to account for shear and torsion. Applications to concrete structural elements. Comput Methods Appl Mech Eng 195:7264–7281 CrossRefzbMATHGoogle Scholar
  167. 167.
    Mazzolani FM (2001) Passive control technologies for seismic-resistant buildings in Europe. Progress Struct Eng Mater 3:277–287 CrossRefGoogle Scholar
  168. 168.
    Meek JL, Loganathan S (1989) Large displacement analysis of space-frame structures. Comput Methods Appl Mech Eng 72:57–75 CrossRefzbMATHGoogle Scholar
  169. 169.
    Miyazakyi M, Mitsusaka Y (1992) Design of a building with 20% or greater damping. In: Tenth world conference on earthquake engineering, Madrid, Spain, pp 4143–4148 Google Scholar
  170. 170.
    Monti G, Spacone E (2000) Reinforced concrete fiber beam element with bond-slip. J Struct Eng 126:654–661 CrossRefGoogle Scholar
  171. 171.
    Neuenhofer A, Filippou FC (1997) Evaluation of the nonlinear frame finite-element models. J Struct Eng 123(7):958–966 CrossRefGoogle Scholar
  172. 172.
    Neuenhofer A, Filippou FC (1998) Geometrically nonlinear flexibility–based frame finite element. J Struct Eng 124(6):704–711 CrossRefGoogle Scholar
  173. 173.
    Nukala PKVV, White DW (2004) A mixed finite element for three-dimensional nonlinear analysis of steel frames. Comput Methods Appl Mech Eng 193:2507–2545 CrossRefzbMATHGoogle Scholar
  174. 174.
    Oliver J (1996) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng 39:3575–3600 CrossRefzbMATHGoogle Scholar
  175. 175.
    Oliver J, Cervera M, Oller S, Lubliner J (1990) Isotropic damage models and smeared crack analysis of concrete. In: Proceedings 2nd ICCAADCS, vol 2, Zell Am See, Austria. Pineridge Press, pp 945–958 Google Scholar
  176. 176.
    Oliver J, Huespe AE (2004) Continuum approach to material failure in strong discontinuity settings. Comput Methods Appl Mech Eng 193:3195–3220 MathSciNetCrossRefzbMATHGoogle Scholar
  177. 177.
    Oller S (2001) Fractura mecánica. Un enfoque global. International Center for Numerical Methods in Engineering, CIMNE Google Scholar
  178. 178.
    Oller S, Barbat AH (2006) Moment-curvature damage model for bridges subjected to seismic loads. Comput Methods Appl Mech Eng 195:4490–4511 CrossRefzbMATHGoogle Scholar
  179. 179.
    Oller S, Luccioni B, Barbat AH (1996) Un método de evaluación del daño sísmico en pórticos de hormigón armado. Rev Int Métodos Numér Cálc Diseño Ing 12:215–238 Google Scholar
  180. 180.
    Oller S, Oñate E, Miquel J (1996) Mixing anisotropic formulation for the analysis of composites. Commun Numer Methods Eng 12:471–482 CrossRefzbMATHGoogle Scholar
  181. 181.
    Oller S, Oñate E, Miquel J, Botello S (1996) A plastic damage constitutive model for composites materials. Int J Solids Struct 33(17):2501–2518 CrossRefzbMATHGoogle Scholar
  182. 182.
    O’Reilly OM (1998) On constitutive relations for elastic rods. Int J Solids Struct 35:1009–1024 MathSciNetCrossRefzbMATHGoogle Scholar
  183. 183.
    Ovesy HR, Loughlan J, GhannadPour SAM (2006) Geometric non-linear analysis of channel sections under end shortening, using different versions of the finite strip method. Comput Struct 84:855–872 CrossRefGoogle Scholar
  184. 184.
    Papaioannou I, Fragiadakis M, Papadrakakis M (2005) Inelastic analysis of framed structures using the fiber approach. In: 5ht GRACM international congress on computational mechanics Google Scholar
  185. 185.
    Park MS, Lee BC (1996) Geometrically non-linear and elastoplastic three-dimensional shear flexible beam element of Von-Mises-type hardening material. Int J Numer Methods Eng 39:383–408 MathSciNetCrossRefzbMATHGoogle Scholar
  186. 186.
    Parulekar YM, Reddy GR, Vaze KK, Kushwaha HS (2004) Lead extrusion dampers for reducing seismic response of coolant channel assembly. Nucl Eng Des 227:175–183 CrossRefGoogle Scholar
  187. 187.
    Petrolo AS, Casciaro R (2004) 3D beam element based on Saint Venànt’s rod theory. Comput Struct 82:2471–2481 CrossRefGoogle Scholar
  188. 188.
    Pielorz A (2004) Nonlinear equations for a thin beam. Acta Mech 167:1–12 CrossRefzbMATHGoogle Scholar
  189. 189.
    Popescu B, Hodges DH (2000) On asymptotically correct Timoshenko-like anisotropic beam theory. Int J Solids Struct 37:535–558 MathSciNetCrossRefzbMATHGoogle Scholar
  190. 190.
    Rasouli SK, Yahyai M (2002) Control of response of structures with passive and active tuned mass dampers. Struct Des Tall Build 11:1–14 CrossRefGoogle Scholar
  191. 191.
    Reismann H (2001) Finite deformation of slender beams. ZAMM J Appl Math Mech 81:481–488 CrossRefzbMATHGoogle Scholar
  192. 192.
    Reissner E (1972) On one-dimensional finite-strain beam theory: the plane problem. J Appl Math Phys 23:795–804 CrossRefzbMATHGoogle Scholar
  193. 193.
    Reissner E (1973) On one-dimensional large-displacement finite-strain beam theory. Stud Appl Math LII:287–295 Google Scholar
  194. 194.
    Reznikov BS (1991) Analysis of the nonlinear deformation of composites with allowance for finite rotations of structural elements. Translated from Zh Prikl Mekh Tekhn Fiz 4:161–165 Google Scholar
  195. 195.
    Riley MA, Sadek F, Mohraz B (1999) Guidelines for testing passive energy dissipation devices. In: Proceedings, US/Japan Bridge engineering workshop, 15th, Tsukuba city, Japan Google Scholar
  196. 196.
    Ritto-Corrëa M, Camotin D (2002) On the differentiation of the Rodriguez formula and its significance for the vector-like parametrization of Reissner-Simo beam theory. Int J Numer Methods Eng 55:1005–1032 CrossRefzbMATHGoogle Scholar
  197. 197.
    Robinson WH, Greenbank LR (2006) An extrusion energy absorber suitable for the protection of structures during an earthquake. Earthquake Eng Struct Dyn 4:251–259 CrossRefGoogle Scholar
  198. 198.
    Romero I (2004) The interpolation of rotations and its application to finite element models of geometrically exact rods. Comput Mech 34:121–133 MathSciNetCrossRefzbMATHGoogle Scholar
  199. 199.
    Romero I, Armero F (2002) An objective finite element approximation of the kinematics and geometrically exact rod and its use in the formulation of an energy-momentum conserving scheme in dynamics. Int J Numer Methods Eng 54:1683–1716 MathSciNetCrossRefzbMATHGoogle Scholar
  200. 200.
    Rosen A, Sabag M, Givoli G (1996) A general nonlinear structural model of a multirod (multibeam) system-I. Theoretical derivations. Comput Struct 61:617–632 CrossRefzbMATHGoogle Scholar
  201. 201.
    Rubin MB (2007) A simplified implicit Newmark integration scheme for finite rotations. Comput Math Appl 53:219–231 MathSciNetCrossRefzbMATHGoogle Scholar
  202. 202.
    Ryan KR, Chopra AK (2004) Estimating the seismic displacement of friction pendulum isolators based on non-linear response history analysis. Earthquake Struct Dyn 33:359–373 CrossRefGoogle Scholar
  203. 203.
    Salomón O, Oller S, Barbat AH (1999) Finite element analysis of base isolated buildings subjected to earthquake loads. Int J Numer Methods Eng 46(10):1741–1761 CrossRefzbMATHGoogle Scholar
  204. 204.
    Salomón O, Oller S, Barbat AH (2000) Análisis sísmico de edificios con dispositivos de aislamiento de base elastoméricos. Rev Int Métodos Num Cálc Diseño Ing 16:281–304 zbMATHGoogle Scholar
  205. 205.
    Schimizze AM (2001) Comparison of P–Δ analyses of plane frames using commercial structural analysis programs and current AISC design specifications. Master of science thesis, Virginia Polytechnic Institute and State University, USA Google Scholar
  206. 206.
    Schulz M, Filippou F (2001) Non-linear spatial Timoshenko beam element with curvature interpolation. Int J Numer Methods Eng 50:761–785 CrossRefzbMATHGoogle Scholar
  207. 207.
    Scott MH, Fenves GL (2006) Plastic hinge integration methods for the force-based beam-column elements. J Struct Eng 132(2):244–252 CrossRefGoogle Scholar
  208. 208.
    Shao Y, Aval S, Mirmiran A (2005) Fiber-element model for cyclic analysis of concrete-filled fiber reinforced polymer tubes. J Struct Eng 131(2):292–303 CrossRefGoogle Scholar
  209. 209.
    Shen KL, Soong TT (2005) Design of energy dissipation devices based on concept of damage control. J Struct Eng 122(1):76–82 CrossRefGoogle Scholar
  210. 210.
    Shi G, Atluri SN (1988) Elasto-plastic large deformation analysis of space–frames: a plastic hinge and stress–based explicit derivation of tangent stiffness. Int J Numer Methods Eng 26:589–615 CrossRefzbMATHGoogle Scholar
  211. 211.
    Simmonds JG (2005) A simple nonlinear thermodynamic theory of arbitrary elastic beams. J Elast 81:51–62 MathSciNetCrossRefzbMATHGoogle Scholar
  212. 212.
    Simo JC (1985) A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput Methods Appl Mech Eng 49:55–70 CrossRefzbMATHGoogle Scholar
  213. 213.
    Simo JC (1992) The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation. Comput Methods Appl Mech Eng 96:189–200 MathSciNetCrossRefzbMATHGoogle Scholar
  214. 214.
    Simo JC, Hjelmstad KD, Taylor RL (1984) Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear. Comput Methods Appl Mech Eng 42:301–330 CrossRefzbMATHGoogle Scholar
  215. 215.
    Simo JC, Hughes TJR (1997) Computational inelasticity. Springer, New York Google Scholar
  216. 216.
    Simo JC, Ju J (1987) Strain and stress based continuum damage models–Part I: formulation. Int J Solids Struct 23:281–301 Google Scholar
  217. 217.
    Simo JC, Tarnow N, Doblare M (1992) Non-linear dynamics of three–dimensional rods: exact energy and momentum conserving algorithms. Int J Numer Methods Eng 34:117–164 CrossRefzbMATHGoogle Scholar
  218. 218.
    Simo JC, Tarnow N, Wong KK (1992) Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Comput Methods Appl Mech Eng 100:63–116 MathSciNetCrossRefzbMATHGoogle Scholar
  219. 219.
    Simo JC, Vu-Quoc L (1986) A three-dimensional finite-strain rod model. Part II: computational aspects. Comput Methods Appl Mech Eng 58:79–116 CrossRefzbMATHGoogle Scholar
  220. 220.
    Simo JC, Vu-Quoc L (1988) On the dynamics in space of rods undergoing large motions—a geometrically exact approach. Comput Methods Appl Mech Eng 66:125–161 MathSciNetCrossRefzbMATHGoogle Scholar
  221. 221.
    Simo JC, Vu-Quoc L (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int J Solids Struct 27:371–393 MathSciNetCrossRefzbMATHGoogle Scholar
  222. 222.
    Sivaselvan MV, Reinhorn AM (2002) Collapse analysis: large inelastic deformations analysis of planar frames. J Struct Eng ASCE 128(12):1575–1583 CrossRefGoogle Scholar
  223. 223.
    Soong TT, Dargush GF (1997) Passive energy dissipation systems in structural engineering. Wiley, New York Google Scholar
  224. 224.
    Soong TT, Spencer BF Jr (2002) Supplemental energy dissipation: state-of-the-art and state-of-the-practice. Eng Struct 24:243–259 CrossRefGoogle Scholar
  225. 225.
    Spacone E, El-Tawil S (2004) Nonlinear analysis of steel–concrete composite structures: state of the art. J Struct Eng ASCE 130(2):159–168 CrossRefGoogle Scholar
  226. 226.
    Spencer BF Jr, Nagarajajah S (2003) State of the art of structural control. J Struct Eng 129(7):845–856 CrossRefGoogle Scholar
  227. 227.
    Spiliopoulos KV, Lykidis GC (2005) An efficient three–dimensional solid finite element dynamic analysis of reinforced concrete structures. Earthquake Eng Struct Dyn 35(2):137–157 CrossRefGoogle Scholar
  228. 228.
    Stammers CW, Sireteanu T (2000) Control of building seismic response by means of three semi-active friction dampers. J Sound Vib 237(5):745–759 CrossRefGoogle Scholar
  229. 229.
    Stuelpnagel J (1964) On the parametrization of the three–dimensional rotation group. SIAM Rev 6:422–430 MathSciNetCrossRefzbMATHGoogle Scholar
  230. 230.
    Taucer FF, Spacone E, Filipou FC (1991) A fiber beam-column element for seismic response analysis of reinforced concrete structures. Technical Report No UCB/EERC-91/17. Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley Google Scholar
  231. 231.
    Thanoon WA, Hamed AMM, Noorzaei J, Jaafar MS, Al-Silayvani BJ (2004) Inelastic analysis of composite sections. Comput Struct 82:1649–1656 CrossRefGoogle Scholar
  232. 232.
    Towashiraporn P, Park J, Goodno BJ, Craig JI (2002) Passive control methods for seismic response modification. Progress Struct Eng Mater 4:47–86 Google Scholar
  233. 233.
    Trainelli L (2002) The vectorial parametrization of rotation and motion. Technical Report, Politecnico di Milano, Dipartimento de Ingegneria Aerospaziale Google Scholar
  234. 234.
    Uriz P, Whittaker AS (2001) Retrofit of the pre-Northridge steel moment-resisting frames using fluid viscous dampers. Struct Des Tall Build 10:371–390 CrossRefGoogle Scholar
  235. 235.
    Valles RE, Reinhorn AM, Kunnath SK, Li C, Madan A (1996) IDARC 2D version 4.0: a program for the inelastic damage analysis of buildings. Technical Report NCEER-96-0010. National Center for Earthquake Engineering Research, State University of New York at Buffalo, January 8 Google Scholar
  236. 236.
    Vignjevic R (1997) A hybrid approach to the transient collapse analysis of thin walled frameworks I. Comput Methods Appl Mech Eng 148:407–421 CrossRefzbMATHGoogle Scholar
  237. 237.
    Vignjevic R (1997) A hybrid approach to the transient collapse analysis of thin walled frameworks II. Comput Methods Appl Mech Eng 148:423–437 CrossRefGoogle Scholar
  238. 238.
    Vu-Quoc L, Li S (1995) Dynamics of sliding geometrically-exact beams: large angle maneuver and parametric resonance. Comput Methods Appl Mech Eng 120:65–118 MathSciNetCrossRefzbMATHGoogle Scholar
  239. 239.
    Wada A, Huang Y-H, Iwata M (2000) Passive damping technology for buildings in Japan. Progress Struct Eng Mater 2:335–350 CrossRefGoogle Scholar
  240. 240.
    Wagner W, Gruttmann F (2001) Finite element analysis of Saint-Venant torsion problem with exact integration of the elastic-plastic constitutive equations. Comput Methods Appl Mech Eng 190:3831–3848 CrossRefzbMATHGoogle Scholar
  241. 241.
    Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech Div 102:249–263 Google Scholar
  242. 242.
    Williamson EB (2003) Evaluation of damage and PΔ effects for systems under earthquake excitation. J Struct Eng 129(8):1036–1046 CrossRefGoogle Scholar
  243. 243.
    Wolfe RW, Masri SF, Caffrey J (2002) Some structural health monitoring approaches for nonlinear hydraulic dampers. J Struct Control 9:5–18 CrossRefGoogle Scholar
  244. 244.
    Yang JN, Kim Y-H, Agrawal AK (2000) Reseting semiactive stiffness damper for seismic response control. J Struct Eng 126(12):1427–1433 CrossRefGoogle Scholar
  245. 245.
    Yeung N, Pan ADE (1998) The effectiveness of viscous-damping walls for controlling wind vibrations in multi-story buildings. J Wind Eng Ind Aerodyn 77&78:337–348 CrossRefGoogle Scholar
  246. 246.
    Youssef N (2001) Viscous dampers at multiple levels for the historic preservation of the Los Angeles City Hall. Struct Des Tall Build 10:339–350 CrossRefGoogle Scholar
  247. 247.
    Yu W, Hodges DH (2004) Elasticity solutions versus asymptotic sectional analysis of homogeneous, isotropic, prismatic beams. J Appl Mech 71:15–23 CrossRefzbMATHGoogle Scholar
  248. 248.
    Yu W, Volovoi VV, Hodges DH, Hong X (2002) Validation of the variational asymptotic beam sectional analysis. J Am Inst Aeronaut Astronaut 40(10):2105–2112 Google Scholar
  249. 249.
    Yu AM, Yang XG, Nie GH (2006) Generalized coordinate for warping of naturally curved and twisted beams with general cross–sectional shapes. Int J Solids Struct 43:2853–2867 CrossRefzbMATHGoogle Scholar
  250. 250.
    Zupan D, Saje M (2003) Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures. Comput Methods Appl Mech Eng 192:5209–5248 MathSciNetCrossRefGoogle Scholar
  251. 251.
    Zupan D, Saje M (2003) The three-dimensional beam theory: finite element formulation based on curvature. Comput Struct 81:1875–1888 CrossRefGoogle Scholar
  252. 252.
    Zupan D, Saje M (2005) Analytical integration of stress field and tangent material moduli over concrete cross-sections. Comput Struct 83:2368–2380 CrossRefGoogle Scholar
  253. 253.
    Zupan D, Saje M (2006) The linearized three-dimensional beam theory of naturally curved and twisted beams: the strain vectors formulation. Comput Methods Appl Mech Eng 195:4557–4578 CrossRefzbMATHGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2008

Authors and Affiliations

  • P. Mata
    • 1
  • A. H. Barbat
    • 1
  • S. Oller
    • 1
  • R. Boroschek
    • 2
  1. 1.Department of Structures and Strength of MaterialsTechnical University of Catalonia, UPCBarcelonaSpain
  2. 2.Department of Civil EngineeringUniversity of ChileSantiagoChile

Personalised recommendations