Maxwell Material: Difference between revisions

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{{CommandManualMenu}}
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This command is used to construct a Maxwell material (linear spring and nonlinear dashpot in series). The Maxwell material simulates the hysteretic response of viscous dampers.
This command is used to construct a ViscousDamper material, which represents the [http://en.wikipedia.org/wiki/Maxwell_material Maxwell Model] (linear spring and nonlinear dashpot in series). The ViscousDamper material simulates the hysteretic response of nonlinear viscous dampers. An adaptive iterative algorithm has been implemented and validated to solve numerically the constitutive equations within a nonlinear viscous damper with a high-precision accuracy.  


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''uniaxialMaterial Maxwell $matTag  $K $C $a $L'''
| style="background:lime; color:black; width:800px" | '''uniaxialMaterial ViscousDamper $matTag  $K $Cd $alpha <$LGap> < $NM $RelTol $AbsTol $MaxHalf> '''
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|  style="width:150px" | '''$matTag ''' || integer tag identifying material
|  style="width:150px" | '''$matTag ''' || integer tag identifying material
|-
|-
|  '''$K ''' || Elastic stiffness of linear spring (to model elastic stiffness of viscous damper)
|  '''$K ''' || Elastic stiffness of linear spring to model the axial flexibility of a viscous damper (e.g. combined stiffness of the supporting brace and internal damper portion)
|-
|-
|  '''$C ''' || Viscous parameter of damper
|  '''$Cd ''' || Damping coefficient
|-
|-
|  '''$a ''' || Viscous damper exponent
|  '''$alpha ''' || Velocity exponent
|-
|-
|  '''$L''' || Viscous damper length
|  '''$LGap ''' || Gap length to simulate the gap length due to the pin tolerance
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|-
|  '''$NM ''' || Employed adaptive numerical algorithm (default value NM = 1; 1 = Dormand-Prince54, 2=6th order Adams-Bashforth-Moulton, 3=modified Rosenbrock Triple)
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|  '''$RelTol ''' || Tolerance for absolute relative error control of the adaptive iterative algorithm (default value 10^-6)
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|  '''$AbsTol ''' ||  Tolerance for absolute error control of adaptive iterative algorithm (default value 10^-10)
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|  '''$MaxHalf ''' ||  Maximum number of sub-step iterations within an integration step (default value 15)
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| '''''1. Input parameters:'''''
| '''''1. Input parameters:'''''
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|-
| Assume a viscous damper with axial stiffness K=150.0kN/mm, viscous parameter C = 100.0kN(s/mm)<sup>0.3</sup>, an exponent a=0.3 and length equal to 5000mm.  
| Assume a viscous damper with axial stiffness K=300.0kN/mm, damping coefficient Cd=280.3kN(s/mm)<sup>0.3</sup>, and exponent a=0.30.  
|-
|-
| The input parameters for the material should be as follows:
| The input parameters for the material should be as follows:
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| uniaxialMaterial Maxwell           1  150.0     100.0      0.30     5000.0
| uniaxialMaterial ViscousDamper           1  300      280.3     0.30
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|-
|-
|-
| Using these properties a comparison between simulated responses from OpenSees and a MATLAB based program are shown in Figure 1.  
| Using these properties, Figure 1 shows the hysteretic response of this damper for sinusoidal displacement increments of 12, 24 and 36mm and a frequency f = 0.5Hz.  
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|-
|The sensitivity of the viscous damper with respect to its axial stiffness is shown in Figure 2 for the following set of parameters:  K=500.0kN/mm, C=100.0kN(s/mm)<sup>0.3</sup>, a=0.30.
|The sensitivity of the viscous damper with respect to its velocity exponent is shown in Figures 2 to 4 for the following set of parameters:   
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|-
| [[File:Fig1.png|425px|thumb|left|Figure 1. Viscous Damper with K=150.0kN/mm, C=100.0kN(s/mm)<sup>0.3</sup>, a=0.30]]  
| [[File:ViscousDamperFig.jpg|1000px|thumb|left| Viscous Damper with various input parameter variations]]  
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|-
| [[File:Fig2.png|425px|thumb|left|Figure 2. Viscous Damper with K=500.0kN/mm, C=100.0kN(s/mm)<sup>0.3</sup>, a=0.30]]
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|-
| '''''[http://opensees.berkeley.edu/wiki/index.php/Viscous_Damper_Material 2. Single story single bay frame with viscous damper]'''''
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|-
| '''''<a> href="http://opensees.berkeley.edu/wiki/index.php/Calibration_of_Maxwell_Material"> 2. Tcl input file for Viscous Damper Calibration.</a>'''''
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|-
| '''''3. OpenSees Example of 1-story steel moment frame with a viscous damper: (to be posted)'''''
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'''References''':
'''References''':
{|
{|
|  style="width:5px" | '''[1]''' || Olsson, A.K., and Austrell, P-E., (2001), "A fitting procedure for viscoelastic-elastoplastic material models," Proceedings of the Second European Conference on Constitutive Models for Rubber, Germany, 2001.
|  style="width:5px" | '''[1]''' || Akcelyan, S., Lignos, D. G., Hikino, T., and Nakashima, M. (2016). “Evaluation of simplified and state-of-the-art analysis procedures for steel frame buildings equipped with supplemental damping devices based on E-Defense full-scale shake table tests.” Journal of Structural Engineering, 142(6), 04016024. [http://ascelibrary.org/doi/ref/10.1061/%28ASCE%29ST.1943-541X.0001474]
|-
|  style="width:5px" | '''[2]''' || Oohara, K., and Kasai, K. (2002), “Time-History Analysis Models for Nonlinear Viscous Dampers”, Proc. Structural Engineers World Congress (SEWC), Yokohama, JAPAN, CD-ROM, T2-2-b-3 (in Japanese).
|-
|-
|'''[2]''' || Ottosen, N.S., and Ristinmaa, M., (1999). "The mechanics of constitutive modelling, (Numerical and thermodynamical topics)," Lund University,Division of Solid Mechanics, Sweden, 1999.
|'''[3]''' || Kasai K, Oohara K. “Algorithm and Computer Code To Simulate Response of Nonlinear Viscous Damper” Passively Controlled Structure Symposium 2001, Yokohama, Japan (in Japanese).  
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|-
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|}
Code Developed by : <span style="color:blue"> by Dr. Dimitrios G. Lignos, (McGill University) </span>
Code Developed and Implemented by : <span style="color:blue"> '''''[http://dimitrios-lignos.research.mcgill.ca/PAkcelyan.html Sarven Akcelyan]''''' & '''''[http://dimitrios-lignos.research.mcgill.ca/PLignos.html Prof. Dimitrios G. Lignos]''''', (McGill University) </span>

Latest revision as of 02:22, 30 September 2016



This command is used to construct a ViscousDamper material, which represents the Maxwell Model (linear spring and nonlinear dashpot in series). The ViscousDamper material simulates the hysteretic response of nonlinear viscous dampers. An adaptive iterative algorithm has been implemented and validated to solve numerically the constitutive equations within a nonlinear viscous damper with a high-precision accuracy.

uniaxialMaterial ViscousDamper $matTag $K $Cd $alpha <$LGap> < $NM $RelTol $AbsTol $MaxHalf>
$matTag integer tag identifying material
$K Elastic stiffness of linear spring to model the axial flexibility of a viscous damper (e.g. combined stiffness of the supporting brace and internal damper portion)
$Cd Damping coefficient
$alpha Velocity exponent
$LGap Gap length to simulate the gap length due to the pin tolerance
$NM Employed adaptive numerical algorithm (default value NM = 1; 1 = Dormand-Prince54, 2=6th order Adams-Bashforth-Moulton, 3=modified Rosenbrock Triple)
$RelTol Tolerance for absolute relative error control of the adaptive iterative algorithm (default value 10^-6)
$AbsTol Tolerance for absolute error control of adaptive iterative algorithm (default value 10^-10)
$MaxHalf Maximum number of sub-step iterations within an integration step (default value 15)

Examples:

1. Input parameters:
Assume a viscous damper with axial stiffness K=300.0kN/mm, damping coefficient Cd=280.3kN(s/mm)0.3, and exponent a=0.30.
The input parameters for the material should be as follows:
uniaxialMaterial ViscousDamper 1 300 280.3 0.30
Using these properties, Figure 1 shows the hysteretic response of this damper for sinusoidal displacement increments of 12, 24 and 36mm and a frequency f = 0.5Hz.
The sensitivity of the viscous damper with respect to its velocity exponent is shown in Figures 2 to 4 for the following set of parameters:
Viscous Damper with various input parameter variations
2. Single story single bay frame with viscous damper

References:

[1] Akcelyan, S., Lignos, D. G., Hikino, T., and Nakashima, M. (2016). “Evaluation of simplified and state-of-the-art analysis procedures for steel frame buildings equipped with supplemental damping devices based on E-Defense full-scale shake table tests.” Journal of Structural Engineering, 142(6), 04016024. [1]
[2] Oohara, K., and Kasai, K. (2002), “Time-History Analysis Models for Nonlinear Viscous Dampers”, Proc. Structural Engineers World Congress (SEWC), Yokohama, JAPAN, CD-ROM, T2-2-b-3 (in Japanese).
[3] Kasai K, Oohara K. “Algorithm and Computer Code To Simulate Response of Nonlinear Viscous Damper” Passively Controlled Structure Symposium 2001, Yokohama, Japan (in Japanese).

Code Developed and Implemented by : Sarven Akcelyan & Prof. Dimitrios G. Lignos, (McGill University)

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