Difference between revisions of "BoucWen Material"
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NOTES: | NOTES: | ||
| − | # | + | #Parameter <math>\gamma</math> is usually in the range from -1 to 1 and parameter <math>\beta</math> is usually in the range from 0 to 1. Depending on the values of <math>\gamma</math> and <math>\beta</math> softening, hardening or quasi-linearity can be simulated. The hysteresis loop will exhibit '''softening''' for the following cases: (a) <math>\beta</math> + <math>\gamma</math> > 0 and <math>\beta</math> - <math>\gamma</math> > 0, (b) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> <0, and (c) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> = 0. The hysteresis loop will exhibit '''hardening''' if <math>\beta</math>+<math>\gamma</math> < 0 and <math>\beta</math>-<math>\gamma</math> > 0, and '''quasi-linearity''' if <math>\beta</math>+<math>\gamma</math> = 0 and <math>\beta</math>-<math>\gamma</math> > 0. |
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REFERENCES: | REFERENCES: | ||
| − | Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." | + | Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." PEER report, PEER-2003/14 [http://peer.berkeley.edu/publications/peer_reports/reports_2003/0314.pdf]. |
Baber, T. T. and Noori, M. N. (1985). "Random vibration of degrading, pinching systems." Journal | Baber, T. T. and Noori, M. N. (1985). "Random vibration of degrading, pinching systems." Journal | ||
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pp16-25, Marseille, France. | pp16-25, Marseille, France. | ||
| − | Wen, Y.-K. (1976). | + | Wen, Y.-K. (1976). "Method for random vibration of hysteretic systems." Journal of Engineering |
Mechanics Division, 102(EM2), 249-263. | Mechanics Division, 102(EM2), 249-263. | ||
Latest revision as of 12:15, 11 September 2023
This command is used to construct a uniaxial Bouc-Wen smooth hysteretic material object. This material model is an extension of the original Bouc-Wen model that includes stiffness and strength degradation (Baber and Noori (1985)).
| uniaxialMaterial BoucWen $matTag $alpha $ko $n $gamma $beta $Ao $deltaA $deltaNu $deltaEta |
| $matTag | integer tag identifying material |
| $alpha | ratio of post-yield stiffness to the initial elastic stiffenss (0< <math>\alpha</math> <1) |
| $ko | initial elastic stiffness |
| $n | parameter that controls transition from linear to nonlinear range (as n increases the transition becomes sharper; n is usually grater or equal to 1) |
| $gamma $beta | parameters that control shape of hysteresis loop; depending on the values of <math>\gamma</math> and <math>\beta</math> softening, hardening or quasi-linearity can be simulated (look at the NOTES) |
| $Ao $deltaA | parameters that control tangent stiffness |
| $deltaNu $deltaEta | parameters that control material degradation |
NOTES:
- Parameter <math>\gamma</math> is usually in the range from -1 to 1 and parameter <math>\beta</math> is usually in the range from 0 to 1. Depending on the values of <math>\gamma</math> and <math>\beta</math> softening, hardening or quasi-linearity can be simulated. The hysteresis loop will exhibit softening for the following cases: (a) <math>\beta</math> + <math>\gamma</math> > 0 and <math>\beta</math> - <math>\gamma</math> > 0, (b) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> <0, and (c) <math>\beta</math>+<math>\gamma</math> >0 and <math>\beta</math>-<math>\gamma</math> = 0. The hysteresis loop will exhibit hardening if <math>\beta</math>+<math>\gamma</math> < 0 and <math>\beta</math>-<math>\gamma</math> > 0, and quasi-linearity if <math>\beta</math>+<math>\gamma</math> = 0 and <math>\beta</math>-<math>\gamma</math> > 0.
REFERENCES:
Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." PEER report, PEER-2003/14 [1].
Baber, T. T. and Noori, M. N. (1985). "Random vibration of degrading, pinching systems." Journal of Engineering Mechanics, 111(8), 1010-1026.
Bouc, R. (1971). "Mathematical model for hysteresis." Report to the Centre de Recherches Physiques, pp16-25, Marseille, France.
Wen, Y.-K. (1976). "Method for random vibration of hysteretic systems." Journal of Engineering Mechanics Division, 102(EM2), 249-263.
