Hi everyone!
I did a 2D portal nonlinear time history analysis. Comparing to the results of the SAP2000, I found that it just has the elastic behavior. After I enhance the groundmotion input, and it can not converge.
Can anyone tell me how I can get the plastic behavior of the model?
Is there anything wrong with my scripe?
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# --------------------------------------------------------------------------------------------------
# nonlinearBeamColumn element, inelastic fiber section
#
#
# ^Y
# |
# 3_________(3)________4 __
# | | |
# | | |
# | | |
# (1) (2) LCol
# | | |
# | | |
# | | |
# =1= =2= _|_ -------->X
# |----------LBeam------------|
#
# SET UP ----------------------------------------------------------------------------
wipe; # clear memory of all past model definitions
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
set dataDir Data;
# define GEOMETRY -------------------------------------------------------------
set LCol 4000; # column length
set LBeam 4000; # beam length
set Weight 20000; # superstructure weight
# define section geometry
set HCol 400; # Column Depth
set BCol 400; # Column Width
set HBeam 600.; # Beam Depth
set BBeam 400.; # Beam Width
# calculated parameters
set PCol [expr $Weight/2]; # nodal dead-load weight per column
set Mass [expr $PCol/10000]; # nodal mass
set MCol [expr 1./12.*($Weight/$LBeam)*pow($LBeam,2)]; # beam-end moment due to distributed load.
# calculated geometry parameters
set ACol [expr $BCol*$HCol]; # cross-sectional area
set ABeam [expr $BBeam*$HBeam];
set IzCol [expr 1./12.*$BCol*pow($HCol,3)]; # Column moment of inertia
set IzBeam [expr 1./12.*$BBeam*pow($HBeam,3)]; # Beam moment of inertia
# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 $LBeam 0;
node 3 0 $LCol ;
node 4 $LBeam $LCol ;
# Single point constraints -- Boundary Conditions
fix 1 1 1 0; # node DX DY RZ
fix 2 1 1 0; # node DX DY RZ
fix 3 0 0 0;
fix 4 0 0 0;
# nodal masses:
mass 3 $Mass 0. 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
mass 4 $Mass 0. 0.;
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section
set BeamSecTag 2; # assign a tag number to the beam section
# define section geometry
set coverCol 30.; # Column cover to reinforcing steel NA.
set numBarsCol 5; # number of longitudinal-reinforcement bars in each side of column section. (symmetric top & bot)
set barAreaCol 314.; # area of longitudinal-reinforcement bars
# MATERIAL parameters -------------------------------------------------------------------
set IDconcU 1; # material ID tag -- unconfined cover concrete
set IDreinf 2; # material ID tag -- reinforcement
# nominal concrete compressive strength
set fc -20.; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set eps1U -0.003; # strain at maximum strength of unconfined concrete
set Ec [expr 2*$fc/$eps1U];
# unconfined concrete
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set fc2U [expr 0.2*$fc1U]; # ultimate stress
set eps2U -0.05; # strain at ultimate stress
set lambda 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# tensile-strength properties
set ftU [expr -0.14*$fc1U]; # tensile strength +tension
set Ets [expr $ftU/0.002]; # tension softening stiffness
# steel
set Fy 360.; # STEEL yield stress
set Es 200000.; # modulus of steel
set Bs 0.01; # strain-hardening ratio
set R0 18; # control the transition from elastic to plastic branches
set cR1 0.925; # control the transition from elastic to plastic branches
set cR2 0.15; # control the transition from elastic to plastic branches
uniaxialMaterial Concrete02 $IDconcU $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets; # build cover concrete (unconfined)
uniaxialMaterial Steel02 $IDreinf $Fy $Es $Bs $R0 $cR1 $cR2; # build reinforcement material
# FIBER SECTION properties -------------------------------------------------------------
# symmetric section
# y
# ^
# |
# --------------------- -- --
# | o o o | | -- cover
# | | |
# | | |
# z <--- | + | H
# | | |
# | | |
# | o o o | | -- cover
# --------------------- -- --
# |-------- B --------|
#
# RC section:
set coverY [expr $HCol/2.0]; # The distance from the section z-axis to the edge of the cover concrete -- outer edge of cover concrete
set coverZ [expr $BCol/2.0]; # The distance from the section y-axis to the edge of the cover concrete -- outer edge of cover concrete
set coreY [expr $coverY-$coverCol];
set coreZ [expr $coverZ-$coverCol];
set nfY 16; # number of fibers for concrete in y-direction
set nfZ 4; # number of fibers for concrete in z-direction
section fiberSec $ColSecTag {; # Define the fiber section
patch quadr $IDconcU $nfZ $nfY -$coverY $coverZ -$coverY -$coverZ $coverY -$coverZ $coverY $coverZ; # Define the concrete patch
layer straight $IDreinf $numBarsCol $barAreaCol -$coreY $coreZ -$coreY -$coreZ; # top layer reinfocement
layer straight $IDreinf $numBarsCol $barAreaCol $coreY $coreZ $coreY -$coreZ; # bottom layer reinforcement
}; # end of fibersection definition
# BEAM section:
section Elastic $BeamSecTag $Ec $ABeam $IzBeam; # elastic beam section
# 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
set BeamTransfTag 2; # associate a tag to beam transformation (good practice to keep col and beam separate)
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ; # only columns can have PDelta effects (gravity effects)
geomTransf Linear $BeamTransfTag ;
# element connectivity:
set numIntgrPts 10; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 3 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables
element nonlinearBeamColumn 2 2 4 $numIntgrPts $ColSecTag $ColTransfTag;
element nonlinearBeamColumn 3 3 4 $numIntgrPts $BeamSecTag $BeamTransfTag;
# Define RECORDERS -------------------------------------------------------------
recorder Node -file $dataDir/DFree.out -time -node 3 4 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file $dataDir/DBase.out -time -node 1 2 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBase.out -time -node 1 2 -dof 1 2 3 reaction; # support reaction
recorder Drift -file $dataDir/Drift.out -time -iNode 1 2 -jNode 3 4 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file $dataDir/FCol.out -time -ele 1 2 globalForce; # element forces -- column
recorder Element -file $dataDir/FBeam.out -time -ele 3 globalForce; # element forces -- beam
recorder Element -file $dataDir/ForceColSec1.out -time -ele 1 2 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file $dataDir/DefoColSec1.out -time -ele 1 2 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceColSec$numIntgrPts.out -time -ele 1 2 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoColSec$numIntgrPts.out -time -ele 1 2 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
recorder Element -file $dataDir/ForceBeamSec1.out -time -ele 3 section 1 force; # Beam section forces, axial and moment, node i
recorder Element -file $dataDir/DefoBeamSec1.out -time -ele 3 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceBeamSec$numIntgrPts.out -time -ele 3 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoBeamSec$numIntgrPts.out -time -ele 3 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
# define GRAVITY -------------------------------------------------------------
set WzBeam [expr $Weight/$LBeam];
pattern Plain 1 Linear {
eleLoad -ele 3 -type -beamUniform -$WzBeam ; # distributed superstructure-weight on beam
}
# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer Plain; # renumber dof's to minimize band-width (optimization), if you want to
system BandGeneral; # how to store and solve the system of equations in the analysis
test NormDispIncr $Tol 8 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$NstepGravity]; # first load increment;
integrator LoadControl $DGravity; # determine the next time step for an analysis
analysis Static; # define type of analysis static or transient
analyze $NstepGravity; # apply gravity
# ------------------------------------------------- maintain constant gravity loads and reset time to zero
loadConst -time 0.0
puts "Model Built"
# define DAMPING--------------------------------------------------------------------------------------
# apply Rayleigh DAMPING from $xDamp
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
set xDamp 0.02; # 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
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
# --------------------------------- perform Dynamic Ground-Motion Analysis
# the following commands are unique to the Uniform Earthquake excitation
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfile "atkk.txt" ; # ground-motion filenames
set GMfact 1; # ground-motion scaling factor
set dt 0.02;
# set up ground-motion-analysis parameters
set DtAnalysis 0.02; # time-step Dt for lateral analysis
set TmaxAnalysis 30.; # maximum duration of ground-motion analysis -- should be 50*$sec
set IDloadTag 400; # for uniformSupport excitation
set g 10000;
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 up 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 RCM
# 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
# try UmfPack for large problems
system BandGeneral
# 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 --
variable TolDynamic 1.e-8; # Convergence Test: tolerance
variable maxNumIterDynamic 10; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
variable printFlagDynamic 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
variable testTypeDynamic NormDispIncr; # Convergence-test type
test $testTypeDynamic $TolDynamic $maxNumIterDynamic $printFlagDynamic;
# for improved-convergence procedure:
variable maxNumIterConvergeDynamic 2000;
variable printFlagConvergeDynamic 0;
# 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 --
algorithm ModifiedNewton ;
# 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
variable NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
variable NewmarkBeta 0.25; # Newmark-integrator beta parameter
variable integratorTypeDynamic Newmark;
integrator $integratorTypeDynamic $NewmarkGamma $NewmarkBeta
# ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/m ... al/324.htm)
# Static Analysis -- solves the KU=R problem, without the mass or damping matrices.
# Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant.
# variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when
# there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable.
analysis Transient
set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)];
set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful
if {$ok != 0} { ; # 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 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 $testTypeDynamic $TolDynamic $maxNumIterDynamic 0
algorithm $algorithmTypeDynamic
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmTypeDynamic
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmTypeDynamic
}
}
}; # end if ok !0
puts "Ground Motion Done. End Time: [getTime]"
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Thank you very much!
About the nonlinear time history
Moderators: silvia, selimgunay, Moderators