Damping

husseinokail · Post by **husseinokail** » Mon Nov 17, 2008 6:35 pm

Follows is a model of just one disp baed beam element under earthquake motion. and I plot the moment curature at the integration point (1).

when i use damping based on the initial stiffness i get a moment curvature which is totaly different than the one based on the last committed stiffness. which doesn't make sense provided that the moment curvature is a property of the section. the one with initial stiffness looks totally wrong

Any thoughts on this???????????????????????????
Thanks alot

# 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; # set up name for data directory
file mkdir $dataDir/; # create data directory
# define UNITS ----------------------------------------------------------------------------
set in 1.; # define basic units -- output units
set kip 1.; # define basic units -- output units
set sec 1.; # define basic units -- output units
set LunitTXT "inch"; # define basic-unit text for output
set FunitTXT "kip"; # define basic-unit text for output
set TunitTXT "sec"; # define basic-unit text for output
set ft [expr 12.*$in]; # define engineering units
set ksi [expr $kip/pow($in,2)];
set psi [expr $ksi/1000.];
set lbf [expr $psi*$in*$in]; # pounds force
set pcf [expr $lbf/pow($ft,3)]; # pounds per cubic foot
set in2 [expr $in*$in]; # inch^2
set in4 [expr $in*$in*$in*$in]; # inch^4
set cm [expr $in/2.54]; # centimeter, needed for displacement input in MultipleSupport excitation
set PI [expr 2*asin(1.0)]; # define constants
set g [expr 32.2*$ft/pow($sec,2)]; # gravitational acceleration
set Ubig 1.e10; # a really large number
set Usmall [expr 1/$Ubig]; # a really small number
# define GEOMETRY -------------------------------------------------------------
set Weight [expr .1837*$kip]; # superstructure weight
set HCol [expr 3.625*$in]; # Column Depth
set BCol [expr 4.*$ft]; # Column Width
# calculated parameters
set PCol [expr $Weight]; # nodal dead-load weight per column
set Mass [expr 5*$Weight/$g]; # nodal mass
# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 16;
# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ
# nodal masses:
mass 2 $Mass 1e-9 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section
# MATERIAL parameters -------------------------------------------------------------------
set IDconcU 1; # material ID tag -- unconfined cover concrete
# nominal concrete compressive strength
set fc [expr -.7*$ksi]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus
# unconfined concrete
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U -0.003; # strain at maximum strength of unconfined concrete
set fc2U [expr 0.2*$fc1U]; # ultimate stress
set eps2U -0.01; # strain at ultimate stress
set lambda 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# tensile-strength properties
set ftU [expr -0.05*$fc1U]; # tensile strength +tension
set Ets [expr $ftU/0.002]; # tension softening stiffness
uniaxialMaterial Concrete02 $IDconcU $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets; # build cover concrete (unconfined)
# 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 nfY 16; # number of fibers for concrete in y-direction
set nfZ 1; # number of fibers for concrete in z-direction
section fiberSec $ColSecTag {; # Define the fiber section
patch quad $IDconcU $nfZ $nfY -$coverY $coverZ -$coverY -$coverZ $coverY -$coverZ $coverY $coverZ; # Define the concrete patch
}; # end of fibersection definition
# 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 ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ;
# element connectivity:
set numIntgrPts 5; # number of integration points for force-based element
element dispBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables
# Define RECORDERS -------------------------------------------------------------
recorder Element -file $dataDir/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file $dataDir/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
load 2 0 -$PCol 0
}
# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for testconstraints Plain;
# how it handles boundary conditions
constraints Plain
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 $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$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 $NstepGravity; # apply gravity
loadConst -time 0.0
puts "Model Built"
set GMdirection 1; # ground-motion direction
set GMfile "sylmar100.txt" ; # ground-motion filenames
# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.005*$sec]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 20. *$sec]; # maximum duration of ground-motion analysis -- should be 50*$sec
constraints Transformation ;
numberer Plain
system BandGeneral
set Tol 1.e-12; # Convergence Test: tolerance
set maxNumIter 100; # 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 NormDispIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;
set algorithmType Newton
algorithm $algorithmType;
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
integrator Newmark $NewmarkGamma $NewmarkBeta
analysis Transient
set xDamp 0.05; # 2% damping ratio
set lambda [eigen 1]; # eigenvalue mode 1
set omega [expr pow($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
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
set IDloadTag 400; # load tag
set dt [expr 1./1024.]; # time step for input ground motion
set GMfatt [expr 1.*$g]; # 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]"