Extension of Generalized Bouc-Wen Hysteresis Modeling of Wood Joints and Structural Systems
Publication: Journal of Engineering Mechanics
Volume 146, Issue 3
Abstract
A critical analysis of the hysteresis models of wooden connections has led to an alternative analytical formulation of the pinching phenomenon. Starting from the generalized Bouc-Wen model, the six-degrees-of-freedom formulation has been extended to an eight parameters formulation, which is a better representative of the connection’s cyclical degradation. The information given by the two additional parameters and also energy-dependency of the parameters provide a faithful representation of the actual hysteresis cycles of wooden connections. The model has been calibrated on experimental data, following an identification procedure, based on an Ordinary Least Squares (OLS) operator.
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Data Availability Statement
The MATLAB code implemented during this study is available from the corresponding author by request.
Acknowledgments
The authors would like to thank Prof. Asif Iqbal (University of Northern British Columbia, Canada) and Dr. Igor Gavrić (CNR IVALSA, Trento, Italy) for having kindly provided the experimental data used in the current paper.
References
Adly, A., I. Mayergoyz, and A. Bergqvist. 1991. “Preisach modeling of magnetostrictive hysteresis.” J. Appl. Phys. 69 (8): 5777–5779. https://doi.org/10.1063/1.347873.
Ahmadi, G., F. Fan, and M. Noori. 1997. “A thermodynamically consistent model for hysteretic materials.” Iran. J. Sci. Technol. 21 (3): 257–278.
Baber, T. T., and M. N. Noori. 1986. “Modeling general hysteresis behavior and random vibration application.” J. Vib. Acoust. Stress Reliab. Des. 108 (4): 411–420. https://doi.org/10.1115/1.3269364.
Baber, T. T., and Y.-K. Wen. 1981. “Random vibration hysteretic, degrading systems.” J. Eng. Mech. Div. 107 (6): 1069–1087.
Bažant, Z. P. 1978. “Endochronic inelasticity and incremental plasticity.” Int. J. Solids Struct. 14 (9): 691–714. https://doi.org/10.1016/0020-7683(78)90029-X.
Blass, H., et al. 1994. “Timber structures in seismic regions RILEM state-of-the-art report.” Mater. Struct. 27 (3): 157. https://doi.org/10.1007/BF02473030.
Bouc, R. 1967. “Forced vibrations of mechanical systems with hysteresis.” In Proc., 4th Conf. on Nonlinear Oscillations, Prague, Czechia: Academia.
Capecchi, D., and G. D. Felice. 2001. “Hysteretic systems with internal variables.” J. Eng. Mech. 127 (9): 891–898. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:9(891).
Casciati, F. 1989. “Stochastic dynamics of hysteretic media.” Struct. Saf. 6 (2–4): 259–269. https://doi.org/10.1016/0167-4730(89)90026-X.
Casciati, F., and L. Faravelli. 1987. “Stochastic equivalent linearization in 3-D hysteretic frames.” In Proc., Transactions of the 9th Int. Conf. on Structural Mechanics in Reactor Technology, edited by F. H. Wittmann. Rotterdam, Netherlands: A.A. Balkema.
Ceccotti, A. 2008. “New technologies for construction of medium-rise buildings in seismic regions: The xlam case.” Struct. Eng. Int. 18 (2): 156–165. https://doi.org/10.2749/101686608784218680.
Ceccotti, A., M. Follesa, and M. P. Lauriola. 2007. Le strutture di legno in zona sismica: criteri e regole per la progettazione e il restauro. Torino, Italy: CLUT.
Ceccotti, A., and A. Vignoli. 1989. “A hysteretic behavioural model for semi-rigid joints.” Eur. Earthquake Eng. 3 (3): 3–9.
Chui, Y. H., C. Ni, and L. Jiang. 1998. “Finite-element model for nailed wood joints under reversed cyclic load.” J. Struct. Eng. 124 (1): 96–103. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:1(96).
Der Kiureghian, A. 2000. “The geometry of random vibrations and solutions by FORM and SORM.” Probab. Eng. Mech. 15 (1): 81–90. https://doi.org/10.1016/S0266-8920(99)00011-9.
Dolan, J. D. 1989. “The dynamic response of timber shear walls.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of British Columbia.
Dominguez, A., R. Sedaghati, and I. Stiharu. 2006. “A new dynamic hysteresis model for magnetorheological dampers.” Smart Mater. Struct. 15 (5): 1179. https://doi.org/10.1088/0964-1726/15/5/004.
Erlicher, S., and O. S. Bursi. 2008. “Bouc–wen-type models with stiffness degradation: Thermodynamic analysis and applications.” J. Eng. Mech. 134 (10): 843–855. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:10(843).
Foliente, G. C. 1995. “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng. 121 (6): 1013–1022. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:6(1013).
Foschi, R. O. 2000. “Modeling the hysteretic response of mechanical connections for wood structures.” In Proc., 6th World Conf. on Timber Engineering. Vancouver, BC, Canada: Univ. of British Columbia.
Gavric, I., M. Fragiacomo, and A. Ceccotti. 2015. “Cyclic behavior of CLT wall systems: Experimental tests and analytical prediction models.” J. Struct. Eng. 141 (11): 04015034. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001246.
Gelman, A., H. S. Stern, J. B. Carlin, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. London: Chapman and Hall.
Gulkan, P., and M. A. Sozen. 1974. “Inelastic responses of reinforced concrete structure to earthquake motions.” J. Proc. 71 (12): 604–610.
Ha, J.-L., Y.-S. Kung, R.-F. Fung, and S.-C. Hsien. 2006. “A comparison of fitness functions for the identification of a piezoelectric hysteretic actuator based on the real-coded genetic algorithm.” Sens. Actuators 132 (2): 643–650. https://doi.org/10.1016/j.sna.2006.02.022.
Han, Y., S. Lim, H. Lee, S. Choi, and H. Choi. 2003. “Hysteresis identification of polymethylaniline-based ER fluid using Preisach model.” Mater. Des. 24 (1): 53–61. https://doi.org/10.1016/S0261-3069(02)00088-2.
Haupt, R. L., S. E. Haupt, and S. E. Haupt. 1998. Vol. 2 of Practical genetic algorithms. New York: Wiley.
Iqbal, A., M. Fragiacomo, S. Pampanin, and A. Buchanan. 2018. “Seismic resilience of plywood-coupled LVL wall panels.” Eng. Struct. 167 (2018): 750–759. https://doi.org/10.1016/j.engstruct.2017.09.053.
Ismail, M., F. Ikhouane, and J. Rodellar. 2009. “The hysteresis Bouc-Wen model, a survey.” Arch. Comput. Methods Eng. 16 (2): 161–188. https://doi.org/10.1007/s11831-009-9031-8.
Karray, M., and R. Bouc. 1989. “Étude dynamique d’un systeme d’isolation antisismique.” Annales 3 (1): 43–60.
Kivell, B., P. Moss, and A. Carr. 1981. “Hysteretic modelling of moment-resisting nailed timber joints.” Earthquake Eng. 14 (4): 233–243.
Kunnath, S. K., J. B. Mander, and L. Fang. 1997. “Parameter identification for degrading and pinched hysteretic structural concrete systems.” Eng. Struct. 19 (3): 224–232. https://doi.org/10.1016/S0141-0296(96)00058-2.
Lubarda, V., and D. Krajcinovic. 1993. “Damage tensors and the crack density distribution.” Int. J. Solids Struct. 30 (20): 2859–2877. https://doi.org/10.1016/0020-7683(93)90158-4.
Ma, F., H. Zhang, A. Bockstedte, G. C. Foliente, and P. Paevere. 2004. “Parameter analysis of the differential model of hysteresis.” J. Appl. Mech. 71 (3): 342–349. https://doi.org/10.1115/1.1668082.
Macki, J. W., P. Nistri, and P. Zecca. 1993. “Mathematical models for hysteresis.” SIAM Rev. 35 (1): 94–123. https://doi.org/10.1137/1035005.
Mayergoyz, I. 1991. “The classical preisach model of hysteresis.” In Mathematical models of hysteresis, 1–63. Berlin: Springer.
Mostaghel, N. 1999. “Analytical description of pinching, degrading hysteretic systems.” J. Eng. Mech. 125 (2): 216–224. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:2(216).
Nabavi-Noori, M., and T. T. Baber. 1984. “Random vibration of degrading systems with general hysteresis.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Virginia.
Park, Y., Y. Wen, and A. H.-S. Ang. 1986. “Random vibration of hysteretic systems under bi-directional ground motions.” Earthquake Eng. Struct. Dyn. 14 (4): 543–557. https://doi.org/10.1002/eqe.4290140405.
Pires, J. A., and M. Tang. 1990. “Statistics of hysteretic energy dissipated under random dynamic loading.” J. Eng. Mech. 116 (8): 1706–1722. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1706).
Rinaldin, G., C. Amadio, and M. Fragiacomo. 2013. “A component approach for the hysteretic behaviour of connections in cross-laminated wooden structures.” Earthquake Eng. Struct. Dyn. 42 (13): 2023–2042. https://doi.org/10.1002/eqe.2310.
Song, J., and A. Der Kiureghian. 2006. “Generalized Bouc–Wen model for highly asymmetric hysteresis.” J. Eng. Mech. 132 (6): 610–618. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:6(610).
Spencer Jr., B., and L. Bergman. 1985. “On the reliability of a simple hysteretic system.” J. Eng. Mech. 111 (12): 1502–1514. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:12(1502).
Stewart, W. 1987. The seismic design of plywood sheathed shear walls. Christchurch, New Zealand: Univ. of Canterbury.
Sues, R., S. Mau, and Y.-K. Wen. 1988. “Systems identification of degrading hysteretic restoring forces.” J. Eng. Mech. 114 (5): 833–846. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:5(833).
Suzuki, Y., and R. Minai. 1988. “Application of stochastic differential equations to seismic reliability analysis of hysteretic structures.” Probab. Eng. Mech. 3 (1): 43–52. https://doi.org/10.1016/0266-8920(88)90007-0.
Thyagarajan, R. and W. Iwan. 1990. “Performance characteristics of a widely used hysteretic model in structural dynamics.” In Proc., 4th US National Conf. on Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute.
Volterra, V. 1928. “Sur la théorie mathématique des phénomenes héréditaires.” J. mathématiques pures appliquées 7 (1): 249–298.
Wen, Y.-K. 1976. “Method for random vibration of hysteretic systems.” J. Eng. Mech. Div. 102 (2): 249–263.
Yar, M., and J. Hammond. 1987. “Parameter estimation for hysteretic systems.” J. Sound Vib. 117 (1): 161–172. https://doi.org/10.1016/0022-460X(87)90442-1.
Yi, F., S. Dyke, S. Frech, and J. Carlson. 1998. “Investigation of magnetorheological dampers for earthquake hazard mitigation.” In Vol. 2 of Proc., 2nd World Conf. on Structural Control, 349–358. Hoboken, NJ: Wiley.
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Journal of Engineering Mechanics
Volume 146 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Nov 20, 2018
Accepted: Jul 11, 2019
Published online: Jan 9, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 9, 2020
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