Hello eveyone,
I modeled a single degree of freedom column with the Bouc- Wen model for nonlinear time history analysis for EL Centro 1940 earthquake. The result I got it. It is not totally different from the paper .I would appreciate to let me know where is the problem.
THE SCRIPT OF PROGRAM
wipe; # clear memory of all past model definitions
file mkdir Data; # create data directory
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
# define GEOMETRY -------------------------------------------------------------
set LCol 1.0; # column length
set Weight 1.0; # superstructure weight
# define section geometry
set HCol 0.10; # Column Depth
set BCol 0.10; # Column Width
# calculated parameters
set PCol 1e-9; # nodal dead-load weight per column
set g 1.0; # g.
set Mass [expr $PCol/$g]; # nodal mass
# calculated geometry parameters
set ACol [expr 1e-9]; # cross-sectional area, make stiff
set IzCol [expr 0.133333333]; # Column moment of inertia
# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol
# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ
# nodal masses:
mass 2 $Mass 1e-9 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColMatTagFlex 2; # assign a tag number to the column flexural behavior
set ColMatTagAxial 3; # assign a tag number to the column axial behavior
set ColSecTag 1; # assign a tag number to the column section tag
set BeamSecTag 2; # assign a tag number to the beam section tag
# MATERIAL parameters
set fc -4.0; # CONCRETE Compressive Strength (+Tension, -Compression)
set Ec [expr 10.0]; # Concrete Elastic Modulus (the term in sqr root needs to be in psi
# COLUMN section
# calculated stiffness parameters
set EICol [expr $Ec*$IzCol]; # EI, for moment-curvature relationship
set EACol [expr $Ec*$ACol]; # EA, for axial-force-strain relationship
set MyCol 320; # yield moment
set PhiYCol 20; # yield curvature
set EIColCrack [expr $MyCol/$PhiYCol]; # cracked section inertia
set b 0.01 ;
# strain-hardening ratio (ratio between post-yield tangent and initial elastic tangent)
set alfa 0.05 ;
set k0 16.0 ;
set n 1.0 ;
set gamma 0.5;
set beta 0.5;
set A0 1.0 ;
set deltaA 1e-9 ;
set deltaNu 1e-9 ;
set deltaEta 1e-9;
set numModes 1;
uniaxialMaterial BoucWen $ColMatTagFlex $alfa $k0 $n $gamma $beta $A0 $deltaA $deltaNu $deltaEta ;
uniaxialMaterial Elastic $ColMatTagAxial $EACol; # this is not used as a material, this is an axial-force-strain response
section Aggregator $ColSecTag $ColMatTagAxial P $ColMatTagFlex Mz; # combine axial and flexural behavior into one section (no P-M interaction here)
# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the
global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
geomTransf Linear $ColTransfTag ;
# element connectivity:
set numIntgrPts 10; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag;
# Define RECORDERS -------------------------------------------------------------
recorder Node -file Data/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file Data/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file Data/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
recorder Drift -file Data/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file Data/FCol.out -time -ele 2 globalForce; # element forces -- column
recorder Element -file Data/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file Data/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file Data/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file Data/DefoColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts deformation; # section deformations, axial and curvature,
node j
# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"
puts "Model Built"
# DYNAMIC EQ ANALYSIS --------------------------------------------------------
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfile "BM68elc.acc" ; # ground-motion filenames
set GMfact 1.; # ground-motion scaling factor
# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.01]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 53.48]; # maximum duration of ground-motion analysis -- should be 50*$sec
# DYNAMIC ANALYSIS PARAMETERS
# CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis
(http://opensees.berkeley.edu/OpenSees/m ... al/617.htm)
# Plain Constraints -- Removes constrained degrees of freedom from the system of equations
# Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints
# Penalty Method -- Uses penalty numbers to enforce constraints
# Transformation Method -- Performs a condensation of constrained degrees of freedom
constraints Transformation ;
# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/m ... al/366.htm)
# determines the mapping between equation numbers and degrees-of-freedom
# Plain -- Uses the numbering provided by the user
# RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm
numberer Plain
# SYSTEM (http://opensees.berkeley.edu/OpenSees/m ... al/371.htm)
# Linear Equation Solvers (how to store and solve the system of equations in the analysis)
# -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology.
# ProfileSPD -- Direct profile solver for symmetric positive definite matrices
# BandGeneral -- Direct solver for banded unsymmetric matrices
# BandSPD -- Direct solver for banded symmetric positive definite matrices
# SparseGeneral -- Direct solver for unsymmetric sparse matrices (-piv option)
# SparseSPD -- Direct solver for symmetric sparse matrices
# UmfPack -- Direct UmfPack solver for unsymmetric matrices
system SparseGeneral -piv
# TEST: # convergence test to
# Convergence TEST (http://opensees.berkeley.edu/OpenSees/m ... al/360.htm)
# -- Accept the current state of the domain as being on the converged solution path
# -- determine if convergence has been achieved at the end of an iteration step
# NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration
# NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration
# EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration
# RelativeNormUnbalance --
# RelativeNormDispIncr --
# RelativeEnergyIncr --
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 10; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
set TestType EnergyIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;
# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/m ... al/682.htm)
# Linear -- Uses the solution at the first iteration and continues
# Newton -- Uses the tangent at the current iteration to iterate to convergence
# ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence
# NewtonLineSearch --
# KrylovNewton --
# BFGS --
# Broyden --
set algorithmType ModifiedNewton
algorithm $algorithmType;
# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/m ... al/689.htm)
# LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain
# DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain
# Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized
# Arc Length -- Specifies the incremental arc-length of the load-displacement path
# Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects
# Newmark -- The two parameter time-stepping method developed by Newmark
# HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method
# Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
integrator Newmark $NewmarkGamma $NewmarkBeta
# ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/m ... al/324.htm)
# Static Analysis -- solves the KU=R problem, without the mass or damping matrices.
# Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also
constant.
# variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method
is used when
# there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the
output is also variable.
analysis Transient
# define DAMPING--------------------------------------------------------------------------------------
# apply Rayleigh DAMPING from $xDamp
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
set xDamp 0.05; # 2% damping ratio
set lambda [eigen 1]; # eigenvalue mode 1
set omega [expr pow($lambda,0.5)];
set alphaM 0.; # M-prop. damping; D = alphaM*M
set betaKcurr 0.; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr 2.*$xDamp/($omega)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit 0.; # initial-stiffness proportional damping +beatKinit*Kini
# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
# --------------------------------- perform Dynamic Ground-Motion Analysis
# Uniform EXCITATION: acceleration input
set IDloadTag 400; # load tag
set dt 0.01; # time step for input ground motion
set GMfatt [expr $g*$GMfact]; # data in input file is in g Unifts -- ACCELERATION TH
set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfatt"; # time series information
pattern UniformExcitation $IDloadTag $GMdirection -accel $AccelSeries ; # create Unifform excitation
set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)];
set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful
if {$ok != 0} { ; # if analysis was not successful.
# change some analysis parameters to achieve convergence
# performance is slower inside this loop
# Time-controlled analysis
set ok 0;
set controlTime [getTime];
while {$controlTime < $TmaxAnalysis && $ok == 0} {
set ok [analyze 1 $DtAnalysis]
set controlTime [getTime]
set ok [analyze 1 $DtAnalysis]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 1000 0
algorithm Newton -initial
set ok [analyze 1 $DtAnalysis]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
}
}; # end if ok !0
puts "Ground Motion Done. End Time: [getTime]"
Bouc wen Model
Moderators: silvia, selimgunay, Moderators
Re: Bouc wen Model
I'm not sure what is your question.
Re: Bouc wen Model
Hi
Thank you so much for your reply
I modeled a column by BOUC-Wen Model which is a smooth hysteresis model . My ground motion is ELcentro1940 and my coulm specification is: damping ratio=0.02 , mass=1.0 stiffness=16.0 and with the hysteresis parameter of bouc wen mode alfa=0.03 and beta=gamma=1.0.
I satatrted to generate the result for my column but I didnot obtain the same result which is given in the published paper with the folllowing title:
Wang, C. H., & Chang, S. Y. (2006). “Efficient computation for dynamic analysis of inelastic structures with smooth hysteresis”. 4the Int. Conf. on Earthquake Engineering(4ICEE), Taipei, Taiwan, October 2006.
so I posted the script based on the generated results. I would appreciate if you let me know where I am making mistake.
Thank you so much for your reply
I modeled a column by BOUC-Wen Model which is a smooth hysteresis model . My ground motion is ELcentro1940 and my coulm specification is: damping ratio=0.02 , mass=1.0 stiffness=16.0 and with the hysteresis parameter of bouc wen mode alfa=0.03 and beta=gamma=1.0.
I satatrted to generate the result for my column but I didnot obtain the same result which is given in the published paper with the folllowing title:
Wang, C. H., & Chang, S. Y. (2006). “Efficient computation for dynamic analysis of inelastic structures with smooth hysteresis”. 4the Int. Conf. on Earthquake Engineering(4ICEE), Taipei, Taiwan, October 2006.
so I posted the script based on the generated results. I would appreciate if you let me know where I am making mistake.
Re: Bouc wen Model
Hi
Thank you so much for your reply
I modeled a column by BOUC-Wen Model which is a smooth hysteresis model . My ground motion is ELcentro1940 and my coulm specification is: damping ratio=0.02 , mass=1.0 stiffness=16.0 and with the hysteresis parameter of bouc wen mode alfa=0.03 and beta=gamma=1.0.
I satatrted to generate the result for my column but I didnot obtain the same result which is given in the published paper with the folllowing title:
Wang, C. H., & Chang, S. Y. (2006). “Efficient computation for dynamic analysis of inelastic structures with smooth hysteresis”. 4the Int. Conf. on Earthquake Engineering(4ICEE), Taipei, Taiwan, October 2006.
so I posted the script based on the generated results. I would appreciate if you let me know where I am making mistake.
# SET UP ----------------------------------------------------------------------------
# units: KN, m, sec
wipe; # clear memory of all past model definitions
file mkdir Data; # create data directory
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
# define GEOMETRY -------------------------------------------------------------
set LCol 1.0; # column length
set Weight 1.0; # superstructure weight
# define section geometry
set HCol 0.10; # Column Depth
set BCol 0.10; # Column Width
# calculated parameters
set PCol $Weight; # nodal dead-load weight per column
set g 1.0; # g.
set Mass [expr $PCol/$g]; # nodal mass
# calculated geometry parameters
set ACol [expr 1e-9]; # cross-sectional area, make stiff
set IzCol [expr 0.133333333]; # Column moment of inertia
# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol
# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ
# nodal masses:
mass 2 $Mass 1e-9 1e-9; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColMatTagFlex 2; # assign a tag number to the column flexural behavior
set ColMatTagAxial 3; # assign a tag number to the column axial behavior
set ColSecTag 1; # assign a tag number to the column section tag
set BeamSecTag 2; # assign a tag number to the beam section tag
# MATERIAL parameters
set fc -4.0; # CONCRETE Compressive Strength (+Tension, -Compression)
set Ec 10.0; # Concrete Elastic Modulus (the term in sqr root needs to be in psi
# COLUMN section
# calculated stiffness parameters
set EICol [expr $Ec*$IzCol]; # EI, for moment-curvature relationship
set EACol [expr $Ec*$ACol]; # EA, for axial-force-strain relationship
set MyCol 320; # yield moment
set PhiYCol 20; # yield curvature
set EIColCrack [expr $MyCol/$PhiYCol]; # cracked section inertia
set b 0.01 ;
# strain-hardening ratio (ratio between post-yield tangent and initial elastic tangent)
set alfa 0.05 ;
set k0 16.0 ;
set n 1.0 ;
set gamma 0.5;
set beta 0.5;
set A0 1.0 ;
set deltaA 1e-9 ;
set deltaNu 1e-9 ;
set deltaEta 1e-9;
set numModes 1;
uniaxialMaterial BoucWen $ColMatTagFlex $alfa $k0 $n $gamma $beta $A0 $deltaA $deltaNu $deltaEta ;
uniaxialMaterial Elastic $ColMatTagAxial $EACol; # this is not used as a material, this is an axial-force-strain response
section Aggregator $ColSecTag $ColMatTagAxial P $ColMatTagFlex Mz; # combine axial and flexural behavior into one section (no P-M interaction here)
# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
geomTransf Linear $ColTransfTag ;
# element connectivity:
set numIntgrPts 10; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag;
# Define RECORDERS -------------------------------------------------------------
recorder Node -file Data/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file Data/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file Data/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
recorder Drift -file Data/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file Data/FCol.out -time -ele 2 globalForce; # element forces -- column
recorder Element -file Data/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file Data/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file Data/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file Data/DefoColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"
puts "Model Built"
# DYNAMIC EQ ANALYSIS --------------------------------------------------------
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfile "BM68elc.acc" ; # ground-motion filenames
set GMfact -1.; # ground-motion scaling factor
# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.01]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 53.48]; # maximum duration of ground-motion analysis -- should be 50*$sec
# DYNAMIC ANALYSIS PARAMETERS
constraints Transformation ;
# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/m ... al/366.htm)
numberer Plain
# SYSTEM (http://opensees.berkeley.edu/OpenSees/m ... al/371.htm)
system SparseGeneral -piv
# TEST: # convergence test to
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 10; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
set TestType EnergyIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;
# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/m ... al/682.htm)
set algorithmType ModifiedNewton
algorithm $algorithmType;
# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/m ... al/689.htm)
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
integrator Newmark $NewmarkGamma $NewmarkBeta
# ANALYSIS -- defines what type of analysis is to be performed
analysis Transient
# define DAMPING--------------------------------------------------------------------------------------
# apply Rayleigh DAMPING from $xDamp
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
set xDamp 0.05; # 2% damping ratio
set lambda [eigen 1]; # eigenvalue mode 1
set omega [expr pow($lambda,0.5)];
set alphaM 0.; # M-prop. damping; D = alphaM*M
set betaKcurr 0.; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr 2.*$xDamp/($omega)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit 0.; # initial-stiffness proportional damping +beatKinit*Kini
# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
# --------------------------------- perform Dynamic Ground-Motion Analysis
# Uniform EXCITATION: acceleration input
set IDloadTag 400; # load tag
set dt 0.01; # time step for input ground motion
set GMfatt [expr $g*$GMfact]; # data in input file is in g Unifts -- ACCELERATION TH
set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfatt"; # time series information
pattern UniformExcitation $IDloadTag $GMdirection -accel $AccelSeries ; # create Unifform excitation
set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)];
set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful
if {$ok != 0} { ; # if analysis was not successful.
# change some analysis parameters to achieve convergence
# performance is slower inside this loop
# Time-controlled analysis
set ok 0;
set controlTime [getTime];
while {$controlTime < $TmaxAnalysis && $ok == 0} {
set ok [analyze 1 $DtAnalysis]
set controlTime [getTime]
set ok [analyze 1 $DtAnalysis]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 1000 0
algorithm Newton -initial
set ok [analyze 1 $DtAnalysis]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
}
}; # end if ok !0
puts "Ground Motion Done. End Time: [getTime]"
Thank you so much for your reply
I modeled a column by BOUC-Wen Model which is a smooth hysteresis model . My ground motion is ELcentro1940 and my coulm specification is: damping ratio=0.02 , mass=1.0 stiffness=16.0 and with the hysteresis parameter of bouc wen mode alfa=0.03 and beta=gamma=1.0.
I satatrted to generate the result for my column but I didnot obtain the same result which is given in the published paper with the folllowing title:
Wang, C. H., & Chang, S. Y. (2006). “Efficient computation for dynamic analysis of inelastic structures with smooth hysteresis”. 4the Int. Conf. on Earthquake Engineering(4ICEE), Taipei, Taiwan, October 2006.
so I posted the script based on the generated results. I would appreciate if you let me know where I am making mistake.
# SET UP ----------------------------------------------------------------------------
# units: KN, m, sec
wipe; # clear memory of all past model definitions
file mkdir Data; # create data directory
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
# define GEOMETRY -------------------------------------------------------------
set LCol 1.0; # column length
set Weight 1.0; # superstructure weight
# define section geometry
set HCol 0.10; # Column Depth
set BCol 0.10; # Column Width
# calculated parameters
set PCol $Weight; # nodal dead-load weight per column
set g 1.0; # g.
set Mass [expr $PCol/$g]; # nodal mass
# calculated geometry parameters
set ACol [expr 1e-9]; # cross-sectional area, make stiff
set IzCol [expr 0.133333333]; # Column moment of inertia
# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol
# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ
# nodal masses:
mass 2 $Mass 1e-9 1e-9; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColMatTagFlex 2; # assign a tag number to the column flexural behavior
set ColMatTagAxial 3; # assign a tag number to the column axial behavior
set ColSecTag 1; # assign a tag number to the column section tag
set BeamSecTag 2; # assign a tag number to the beam section tag
# MATERIAL parameters
set fc -4.0; # CONCRETE Compressive Strength (+Tension, -Compression)
set Ec 10.0; # Concrete Elastic Modulus (the term in sqr root needs to be in psi
# COLUMN section
# calculated stiffness parameters
set EICol [expr $Ec*$IzCol]; # EI, for moment-curvature relationship
set EACol [expr $Ec*$ACol]; # EA, for axial-force-strain relationship
set MyCol 320; # yield moment
set PhiYCol 20; # yield curvature
set EIColCrack [expr $MyCol/$PhiYCol]; # cracked section inertia
set b 0.01 ;
# strain-hardening ratio (ratio between post-yield tangent and initial elastic tangent)
set alfa 0.05 ;
set k0 16.0 ;
set n 1.0 ;
set gamma 0.5;
set beta 0.5;
set A0 1.0 ;
set deltaA 1e-9 ;
set deltaNu 1e-9 ;
set deltaEta 1e-9;
set numModes 1;
uniaxialMaterial BoucWen $ColMatTagFlex $alfa $k0 $n $gamma $beta $A0 $deltaA $deltaNu $deltaEta ;
uniaxialMaterial Elastic $ColMatTagAxial $EACol; # this is not used as a material, this is an axial-force-strain response
section Aggregator $ColSecTag $ColMatTagAxial P $ColMatTagFlex Mz; # combine axial and flexural behavior into one section (no P-M interaction here)
# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
geomTransf Linear $ColTransfTag ;
# element connectivity:
set numIntgrPts 10; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag;
# Define RECORDERS -------------------------------------------------------------
recorder Node -file Data/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file Data/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file Data/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
recorder Drift -file Data/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file Data/FCol.out -time -ele 2 globalForce; # element forces -- column
recorder Element -file Data/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file Data/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file Data/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file Data/DefoColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"
puts "Model Built"
# DYNAMIC EQ ANALYSIS --------------------------------------------------------
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfile "BM68elc.acc" ; # ground-motion filenames
set GMfact -1.; # ground-motion scaling factor
# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.01]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 53.48]; # maximum duration of ground-motion analysis -- should be 50*$sec
# DYNAMIC ANALYSIS PARAMETERS
constraints Transformation ;
# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/m ... al/366.htm)
numberer Plain
# SYSTEM (http://opensees.berkeley.edu/OpenSees/m ... al/371.htm)
system SparseGeneral -piv
# TEST: # convergence test to
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 10; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
set TestType EnergyIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;
# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/m ... al/682.htm)
set algorithmType ModifiedNewton
algorithm $algorithmType;
# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/m ... al/689.htm)
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
integrator Newmark $NewmarkGamma $NewmarkBeta
# ANALYSIS -- defines what type of analysis is to be performed
analysis Transient
# define DAMPING--------------------------------------------------------------------------------------
# apply Rayleigh DAMPING from $xDamp
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
set xDamp 0.05; # 2% damping ratio
set lambda [eigen 1]; # eigenvalue mode 1
set omega [expr pow($lambda,0.5)];
set alphaM 0.; # M-prop. damping; D = alphaM*M
set betaKcurr 0.; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr 2.*$xDamp/($omega)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit 0.; # initial-stiffness proportional damping +beatKinit*Kini
# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
# --------------------------------- perform Dynamic Ground-Motion Analysis
# Uniform EXCITATION: acceleration input
set IDloadTag 400; # load tag
set dt 0.01; # time step for input ground motion
set GMfatt [expr $g*$GMfact]; # data in input file is in g Unifts -- ACCELERATION TH
set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfatt"; # time series information
pattern UniformExcitation $IDloadTag $GMdirection -accel $AccelSeries ; # create Unifform excitation
set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)];
set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful
if {$ok != 0} { ; # if analysis was not successful.
# change some analysis parameters to achieve convergence
# performance is slower inside this loop
# Time-controlled analysis
set ok 0;
set controlTime [getTime];
while {$controlTime < $TmaxAnalysis && $ok == 0} {
set ok [analyze 1 $DtAnalysis]
set controlTime [getTime]
set ok [analyze 1 $DtAnalysis]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 1000 0
algorithm Newton -initial
set ok [analyze 1 $DtAnalysis]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
}
}; # end if ok !0
puts "Ground Motion Done. End Time: [getTime]"
Re: Bouc wen Model
Make sure that the parameters used in the paper are equivalent to the ones you used in the model. The references for Bouc-Wen material in OpenSees are given here: http://opensees.berkeley.edu/wiki/index ... n_Material. There are several BoucWen models with parameters defined somewhat differently.
Re: Bouc wen Model
Dear Vesna,
Than you for your email but I am sure I defined the right parameter. I would appreciate if you looked at the script and let me know if I am making any mistake in the program.
This is just a single degree of freedom column.
Thanks
Than you for your email but I am sure I defined the right parameter. I would appreciate if you looked at the script and let me know if I am making any mistake in the program.
This is just a single degree of freedom column.
Thanks
Re: Bouc wen Model
I looked at your model and what I saw is that you used BoucWen material to define moment-curvature relationship. However, this material is written in stress-strain form and can not be used for moment-curvature (if you read reference 1. under Buck-Wen material you will see this). What you have to do is to define fiber section and to assign BoucWen materail to each fiber of the section.