Bouc-Wen Type Hysteretic Plane Stress Element
Publication: Journal of Engineering Mechanics
Volume 138, Issue 3
Abstract
In this work, a plane-stress element is proposed for the elastoplastic dynamic analysis of two-dimensional structures exhibiting hysteretic behavior. The constant-strain triangular element formulation for the elastic case is modified by introducing the Bouc-Wen hysteretic model, properly defined in the 2D stress-strain space. Solutions are obtained by simultaneously solving two sets of governing equations, namely the global equilibrium equations and the local constitutive equations, using a predictor-corrector differential equation solver. In following the proposed method, the linearization of the constitutive relations usually performed in step-by-step solution approaches is avoided. The proposed element is capable of modeling cyclic induced phenomena such as stiffness degradation and strength deterioration. Furthermore, the solution method implemented improves the accuracy of the results without increasing the computational cost of the analysis. Examples are presented which demonstrate the efficiency of the proposed approach. The method can be extended to other types of finite elements by properly incorporating the nonlinear constitutive behavior into their stiffness matrices.
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References
Abaqus version 6.5 [Computer software]. Dassault Systmes Simulia, Providence, RI.
Baber, T. T., and Noori, M. N. (1985). “Random vibration of degrading, pinching systems.” J. Eng. Mech., 111(8), 1010–1026.
Baber, T. T., and Wen, Y.-K. (1980). “Seismic response of hysteretic degrading structures.” Publ. Turk. Natl. Comm. on Earthquake Eng., Vol. 7, Turkish National Committee on Earthquake Engineering, Istanbul, Turkey, 457–464.
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.
Bathe, K. J. (2007). Finite Element Procedures, Prentice Hall Engineering/Science/Mathematics, New York.
Bouc, R. (1967). “Forced vibration of mechanical systems with hysteresis.” Proceedings of the Fourth Conference on Non-linear oscillation, Institute of Radio Engineering and Electronics for the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.
Brasile, S., Casciaro, R., and Formica, G. (2009). “Finite element formulation for nonlinear analysis of masonry walls.” Comput. S, 88(3–4), 135–143.
Carpinteri, A., Corrado, M., Paggi, M., and Mancini, G. (2009). “New model for the analysis of size-scale effects on the ductility of reinforced concrete elements in bending.” J. Engrg. Mech. Div., 135(3), 221–229.
Casciati, F. (2006). “Stochastic dynamics of hysteretic media.” Probabilistic Methods in Applied Physics, Springer Berlin, Heidelberg, 270–283.
Chang, C., and Shi, Y. (2010). “Identification of time-varying hysteretic structures using wavelet multiresolution analysis.” Int. J. Non-linear Mech., 45(1), 21–34.
Charalampakis, A. E., and Koumousis, V. K. (2008). “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. (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.
Cherng, R. H., and Wen, Y. K. (1991). “Stochastic finite element analysis of non-linear plane trusses.” Journal of Non-Linear Mechanics, 26(6), 835–849.
Choi, S. B., and Lee, S. K. (2001). “A hysteresis model for the field dependent damping force of a magnetorheological damper.” J. Sound Vib., 245(2), 375–383.
Dede, T., and Ayvaz, Y. (2010). “Plasticity models for concrete material based on different criteria including Bresler-Pister.” Materials and Design, 31(1), 278–286.
Den Hartog, J. P. (1999). Strength of Materials, Dover, New York.
Erlicher, S., and Bursi, O. S. (2008). “Bouc—Wen-Type models with stiffness degradation: Thermodynamic analysis and applications.” J. Eng. Mech., 134(10), 843–855.
Foliente, G. C. (1995). “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng., 121(6), 1013–1022.
Gerolymos, N., and Gazetas, G. (2007). “A model for grain-crushing-induced landslides—Application to Nikawa, Kobe 1995.” Soil Dyn. Earthquake Eng., 27(9), 803–819.
Guggenberger, J., and Grundmann, H. (2005). “Stochastic response of large FEM models with hysteretic behavior in beam elements.” Comp. Methods Appl. Mech. Engrg., 194(12–16), 1739–1756.
Hill, R. (1998). The Mathematical Theory of Plasticity, Oxford Univ. Press, Oxford.
Hinchberger, S. D. (2009). “Simple single-surface failure criterion for concrete.” J. Eng. Mech., 135(7), 729–732.
Hjelle, O., and Daehlen, M. (2006). Triangulations and Applications, Springer, Berlin.
Kachanov, L. M. (2004). Fundamentals of the theory of plasticity, Dover, New York.
Kwan, A. K. H., and He, X. G. (2001). “Finite element analysis of effect of concrete confinement on behavior of shear walls.” Comput. S, 79(19), 1799–1810.
Lubliner, J. (2008). Plasticity Theory, Dover, New York.
MATLAB version 6.5/release 13 [Computer software]. Mathworks, Natick, MA.
Munoz, J. J., Bonet, J., Huerta, A., and Peraire, J. (2009). “Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading.” Int. J. Numer. Meth. Engng, 77(4), 471–501.
Neto de Souza, E. A., Peric, D., and Owen, D. R. J. (2008). Computational Methods for Plasticity Theory and Applications, Willey, West Sussex, UK.
Pires, J. A. (1996). “Stochastic seismic response analysis of soft soil sites.” Nucl. Eng. Des., 160(3), 363–377.
Radhakrishnan, K., and Hindmarsh, A. C. (1993). “Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations.” LLNL report UCRL-ID-113855, U.S. Dept. of Energy, Oak Ridge, TN.
Simo, J. C., and Taylor, R. L. (1986). “A return mapping algorithm for plane stress elastoplasticity.” Int. J. Numer. Methods Eng., 22(3), 649–670.
Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Hysteretic models for deteriorating inelastic structures.” J. Eng. Mech., 126(6), 633–640.
Sivaselvan, M. V., and Reinhorn, A. M. (2003). “Nonlinear analysis towards collapse simulation—A dynamic systems approach.” MCEER Technical Report, University at Buffalo, NY.
Symeonov, V. K., Sivaselvan, M. V., and Reinhorn, A. M. (2000). “Nonlinear analysis of structural frame systems by the state space approach.” Computer Aided Civil and Infrastructure Engineering, 15(2), 76–89.
Taherizadeh, A., Green, D. E., Ghaei, A., and Yoon, J. W. (2010). “A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming.” Int. J. Plast., 26(2), 288–309.
Valanis, K. C. (1971). “A theory of viscoplasticity without a yield surface.” Arch. Mech. Stossowanej, 23(4), 517–551.
Valoroso, N., and Rosati, L. (2009). “Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity Part I: Theoretical Formulation”. International Journal of Solids and Structures, 46(1), 74–91.
Washizu, K. (1982). Variational Methods in Elasticity and Plasticity, Pergamon Pr, 1982.
Wen, Y. (1976). “Method of random vibration of hysteretic systems.” Journal of Engineering Mechanics Division, 102(2), 249–263.
Zhang, H., and Kuang, J. S. (2008). “Eight-node membrane element with drilling degrees of freedom for analysis of in-plane stiffness of thick floor plates.” Int. J. Numer. Meth. Engng, 76(13), 2117–2136.
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Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 3 • March 2012
Pages: 235 - 246
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Mar 23, 2010
Accepted: Aug 25, 2011
Published online: Aug 27, 2011
Published in print: Mar 1, 2012
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