Small and Large Displacement Dynamic Analysis of Frame Structures Based on Hysteretic Beam Elements
Publication: Journal of Engineering Mechanics
Volume 138, Issue 1
Abstract
In this work, a beam element is proposed for the nonlinear dynamic analysis of frame structures. The classical Euler-Bernoulli formulation for the elastic beam is extended by implicitly defining new hysteretic degrees of freedom, subjected to evolution equations of the Bouc-Wen type with kinematic hardening. A linear interpolation field is employed for these new degrees of freedom, which are regarded as hysteretic curvatures and hysteretic axial deformations. By means of the principle of virtual work, an elastoplastic hysteretic stiffness relation is derived, which together with the hysteretic evolution equations fully describes the behavior of the element. The elemental stiffness equations are assembled to form a system of linear global equations of motion that also depend on the introduced hysteretic variables. The solution is obtained by simultaneously solving the entire set of governing equations, namely the linear global equations of motion with constant coefficient matrices, and the nonlinear local constitutive equations for every element converted into a state-space form. Numerical results are presented to demonstrate the efficiency of the method as compared to existing methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abaqus Version 6.1 [Computer software]. HKS Publications, New York.
Baber, T. T., and Noori, M. N. (1985). “Random vibration of degrading, pinching systems.” J. Eng. Mech., 111(8), 1010–1026.
Barham, W. S., Aref, A. J., and Dargush, G. F. (2005). “Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading.” Int. J. Solids Struct., 42(26), 6586–6609.
Barham, W. S., Aref, A. J., and Dargush, G. F. (2008). “On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach.” Int. J. Solids Struct., 45(22–23), 5688–5704.
Bathe, K. J. (2007). Finite element procedures, Prentice-Hall, New York.
Bazant, S., and Bhat, P. (1977). “Prediction of hysteresis of reinforced concrete members.” J. Struct. Eng., 103(1), 153–167.
Bonnet, P. A., Williams, M. S., and Blakeborough, A. (2008). “Evaluation of numerical time-integration schemes for real-time hybrid testing.” Earthquake Eng. Struct. Dyn., 37(13), 1467–1490.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proc., 4th Conf. on Non-linear Oscillation, Institute of Radio Engineering and Electronics for the Czechoslovak Academy of Sciences.
Chao, S. H., and Loh, C. H. (2007). “Inelastic response analysis of reinforced concrete structures using modified force analogy method.” Earthquake Eng. Struct. Dyn., 36(12), 1659–1683.
Charalampakis, A. E., and Koumousis, V. K. (2008a). “Identification of Bouc–Wen hysteretic systems by a hybrid evolutionary algorithm.” J. Sound Vib., 314(3–5), 571–585.
Charalampakis, A. E., and Koumousis, V. K. (2008b). “Ultimate strength analysis of composite sections under biaxial bending and axial load.” Adv. Eng. Softw., 39(11), 923–936.
Charalampakis, A. E., and Koumousis, V. K. (2009). “A Bouc Wen model compatible with plasticity postulates.” J. Sound Vib., 322(4–5), 954–968.
Chatzi, E. N., and Smyth, A. W. (2009). “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Struct. Contr. Health Monit., 16(1), 99–123.
Chatzi, E. N., Smyth, A. W., and Masri, S. F. (2010). “Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty.” J. Struct. Safety, 32(5), 326–337.
Chiang, D.-Y. (1999). “The generalized Masing models for deteriorating hysteresis and cyclic plasticity.” Appl. Math. Modell., 23(11), 847–863.
Chopra, A. (2006). Dynamics of structures, Prentice-Hall, New York.
De Souza, R. M. (2000). “Force-based finite element for large displacement inelastic analysis of frames.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA.
Der Kiureghian, A., and Fujimura, K. (2009). “Nonlinear stochastic dynamic analysis for performance-based earthquake engineering.” Earthquake Eng. Struct. Dyn., 38(5), 719–738.
Dobson, S., Noori, M., Hou, Z., Dimentberg, M., and Baber, T. (1997). “Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis.” Int. J. Non-linear Mech., 32(4), 669–680.
Erlicher, S., and Bursi, O. (2008). “Bouc-Wen-type models with stiffness degradation: Thermodynamic analysis and applications.” J. Eng. Mech., 134(10), 843–855.
Erlicher, S., and Point, N. (2004). “Thermodynamic admissibility of Bouc-Wen type hysterisis models.” C.R. Mécanique, 332(1), 51–57.
Foliente, G. C. (1995). “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng., 121(6), 1013–1022.
Grange, S., Kotronis, P., and Mazars, J. (2009). “A macro-element to simulate 3D soil-structure interaction considering plasticity and uplift.” Int. J. Solids Struct., 46(20), 3651–3663.
Guggenberger, J., and Grundmann, H. (2005). “Stochastic response of large FEM models with hysteretic behavior in beam elements.” Comp. Methods Appl. Mech. Eng., 194(12–16), 1739–1756.
Khandelwal, K., El-Tawil, S., Kunnath, K. S., and Lew, H. S. (2008). “Macromodel-based simulation of progressive collapse: Steel frame structures.” J. Struct. Eng., 134(7), 1070–1078.
Málaga-Chuquitaype, C., Elghazouli, A. Y., and Bento, R. (2009). “Rigid-plastic models for the seismic design and assessment of steel framed structures.” Earthquake Eng. Struct. Dyn., 31, 2540–2553.
Maple 13 [Computer software]. Maplesoft, New York.
Mathematica [Computer software]. Wolfram Research, Champaign, IL. 〈http://reference.wolfram.com/mathematica/guide/Mathematica.html〉 (Dec. 4, 2008).
McKenna, F., Fenves, G. L., and Scott, M. H. (2000). “Open system for earthquake engineering simulation.” Univ. of California, Berkeley, CA. 〈http://OpenSees.berkeley.edu〉 (Sept. 7, 2009).
Mercan, O., and Ricles, J. M. (2007). “Stability and accuracy analysis of outer loop dynamics in real-time pseudodynamic testing of SDOF systems.” Earthquake Eng. Struct. Dyn., 36(11), 1523–1543.
Neuenhofer, A., and Filippou, F. C. (1998). “Geometrically nonlinear flexibility-based frame finite element.” J. Struct. Eng., 124(6), 704–711.
Papachristidis, A., Fragiadakis, M., and Papadrakakis, M. (2010). “A 3D fibre beam-column element with shear modelling for the inelastic analysis of steel structures.” Comput. Mech., 45(6), 553–572.
Papakonstantinou, K. G., Dimizas, P. C., and Koumousis, V. K. (2008). “An inelastic beam element with hysteretic damping.” Shock Vib., 15(3–4), 273–290.
Patnaik, S. N., Coroneos, R. M., and Hopkins, D. A. (1998). “Recent advances in the method of forces: Integrated force method of structural analysis.” Adv. Eng. Softw., 29(3–6), 463–474.
Piyawat, K., and Pei, J. S. (2009). “Linking nonlinear system identification with nonlinear dynamic simulation under OpenSees: Some justifications and implementations.” J. Eng. Mech., 135(11), 1213–1226.
Radhakrishnan, K., and Hindmarsh, A. C. (1993). “Description and use of LSODE, the Livermore solver for ordinary differential equations.” LLNL Rep. UCRL-ID-113855Lawrence Livermore National Laboratory, Livermore, CA.
Roh, H., and Reinhorn, A. M. (2010). “Nonlinear static analysis of structures with rocking columns.” J. Struct. Eng.. 136(5), 532–542.
Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Hysteretic models for deteriorating inelastic structures.” J. Eng. Mech., 126(6), 633–640.
Skelton, R. P., Maier, H. J., and Christ, H.-J. (1997). “The Bauschinger effect, Masing model and the Ramberg-Osgood relation for cyclic deformation in metals.” Mater. Sci. Eng. A, 238(2), 377–390.
Spacone, E., Ciampi, V., and Filippou, F. C. (1996). “Mixed formulation of nonlinear beam finite element.” Comput. Struct. 58(1), 71–83.
Symeonov, V. K., Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Nonlinear analysis of structural frame systems by the state space approach.” Comput. Aided Civ. Infrastruct. Eng., 15(2), 76–89.
Thyagarajan, R. S. (1989). “Modeling and analysis of hysteretic structural behavior.” Technical Rep.: EERL:1989.EERL-89-03, California Institute of Technology, Pasadena, CA.
Thyagarajan, R. S., and Iwan, W. D. (1990). “Performance characteristics of a widely used hysteretic model in structural dynamics.” Proc., 4th U.S. Natl. Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Palm Springs.
Valanis, K. C., and Lee, C. F. (1984). “Endochronic theory of cyclic plasticity with applications.” J. Appl. Mech., 51(2), 367–374.
Valles, R. E., Reinhorn, A. M., Kunnath, S. K., Madan, A., and Li, C. (1996). “IDARC2D version 4.0: A computer program for the inelastic damage analysis of buildings.” Technical Rep. NCEER-96-0010, National Center for Earthquake Engineering Research, State University of New York at Buffalo, NY.
Visintin, A. (2003). Differential models of hysterisis, Springer, New York.
Wen, Y. K. (1976). “Method for random vibration of hysteretic systems.” J. Eng. Mech. Div., 102(2), 249–263.
Wong, C. W., Ni, Y. Q., and Ko, J. M. (1994). “Steady-state oscillations of hysteretic differential model. II: performance analysis.” J. Eng. Mech., 120(11), 2299–2325.
Wong, K., and Yang, Ron (1999). “Inelastic dynamic response of structures using force analogy method.” J. Eng. Mech., 125(10), 1190.
Xu, J., and Dolan, J. D. (2009). “Development of a nailed wood joint element in ABAQUS.” J. Struct. Eng., 135(8), 968–976.
Zhang, C., and Liu, X. (1997). “A large increment method for material nonlinearity problems.” Adv. Struct. Eng., 1(2), 99–109.
Zienkiewicz, O. C., and Taylor, R. L. (2005). The finite element method, Elsevier Butterworth-Heinemann, Oxford.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 1 • January 2012
Pages: 36 - 49
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Nov 12, 2009
Accepted: Jul 27, 2011
Published online: Jul 29, 2011
Published in print: Jan 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.