Explicit Nemark or Central Difference

[husseinokail]

Follows is a script for a SDOF it works with nemark but once i change the intergrator to explicit schemes like central diffference or explicit newmark it fails at the first step Any Suggestions??? Thanks

# 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 dir Sylmar100;
set GMfile "sylmar100.txt" ;
file mkdir $dir;
source LibUnits.tcl
# nodal coordinates:
node 1 0. 0.;
node 2 0. 25.;

# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ

set ColTransfTag 1; # associate a tag to column transformation
geomTransf Linear $ColTransfTag

# MATERIAL parameters -------------------------------------------------------------------
set AW [expr 48*3.625]
set IW [expr 48*3.625*3.625*3.625/12]
set RW [expr 114*$pcf/$g]
set EW 2000
element elasticBeamColumn 1 1 2 $AW $EW $IW $ColTransfTag;

recorder Node -file $dir/node2.txt -time -node 2 -dof 1 2 disp;

mass 2 [expr $AW*16*$RW] 0 0;

set IDloadTag 400;
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfact [expr $g]; # data in input file is in g Unifts -- ACCELERATION TH

# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.001*$sec]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 20.*$sec]; # duration of ground-motion analysis

# DYNAMIC ANALYSIS PARAMETERS
constraints Plain
numberer Plain
set Tol 1.e-6; # Convergence Test: tolerance
test NormDispIncr $Tol 900000 0;
algorithm Linear;
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
#integrator Newmark $NewmarkGamma $NewmarkBeta
integrator CentralDifference
#integrator NewmarkExplicit 0.5
system BandGeneral
analysis Transient



## define DAMPING--------------------------------------------------------------------------------------
## apply Rayleigh DAMPING from $xDamp
## D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
#set damping 0.05; # 5% damping ratio
#set eigenvalues [eigen 2]; # eigenvalue mode 1
#set w1 [expr sqrt([lindex $eigenvalues 0])]
#set w2 [expr sqrt([lindex $eigenvalues 1])]
#set am [expr $damping*2.0*$w1*$w2/($w1+$w2)]
#set bkinit [expr $damping*2.0/($w1+$w2)];
#set bk 0.0;
#set bklast 0.0;
#rayleigh $am $bk $bkinit $bklast
#
# --------------------------------- perform Dynamic Ground-Motion Analysis
# Uniform EXCITATION: acceleration input
# load tag
set dt 0.0009765625; # time step for input ground motion
set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfact"; # 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
puts "Ground Motion Done. End Time: [getTime]"

[fmk]

you need to provide a full mass matrix to get the explicit integration schemes to work .. have a look at the theory to see why.