BoucWen Material: Difference between revisions
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NOTES: | NOTES: | ||
#Parameters <math>\gamma</math> and <math>\beta</math> are 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+\gamma > 0 and \beta-\gamma > 0</math>, (b) <math>\beta+\gamma >0 and \beta-\gamma <0</math>, and (c) <math>\beta+\gamma >0 and \beta-\gamma = 0</math>. The hysteresis loop will exhibit hardening if <math>\beta+\gamma < 0 and \beta-\gamma > 0</math>, and quasi-linearity if <math>\beta+\gamma = 0 and \beta-\gamma > 0</math>. | #Parameters <math>\gamma</math> and <math>\beta</math> are 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 + \gamma > 0 and \beta - \gamma > 0</math>, (b) <math>\beta+\gamma >0 and \beta-\gamma <0</math>, and (c) <math>\beta+\gamma >0 and \beta-\gamma = 0</math>. The hysteresis loop will exhibit hardening if <math>\beta+\gamma < 0 and \beta-\gamma > 0</math>, and quasi-linearity if <math>\beta+\gamma = 0 and \beta-\gamma > 0</math>. | ||
REFERENCES: | REFERENCES: | ||
Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." REER report, PEER-2003/14 . | Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." REER report, PEER-2003/14. | ||
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 | ||
of Engineering Mechanics, 111(8), 1010-1026. | of Engineering Mechanics, 111(8), 1010-1026. | ||
Bouc, R. (1971). "Mathematical model for hysteresis." Report to the Centre de Recherches Physiques, | Bouc, R. (1971). "Mathematical model for hysteresis." Report to the Centre de Recherches Physiques, | ||
pp16-25, Marseille, France. | pp16-25, Marseille, France. | ||
Wen, Y.-K. (1976). \Method for random vibration of hysteretic systems." Journal of Engineering | 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. | ||
Revision as of 20:36, 18 November 2010
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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 (parameter $deltaEta also controls yielding strain) |
NOTES:
- Parameters <math>\gamma</math> and <math>\beta</math> are 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 + \gamma > 0 and \beta - \gamma > 0</math>, (b) <math>\beta+\gamma >0 and \beta-\gamma <0</math>, and (c) <math>\beta+\gamma >0 and \beta-\gamma = 0</math>. The hysteresis loop will exhibit hardening if <math>\beta+\gamma < 0 and \beta-\gamma > 0</math>, and quasi-linearity if <math>\beta+\gamma = 0 and \beta-\gamma > 0</math>.
REFERENCES:
Haukaas, T. and Der Kiureghian, A. (2003). "Finite element reliability and sensitivity methods for performance-based earthquake engineering." REER report, PEER-2003/14.
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.