Problem in convergence

[gopal]

Hi everybody

Please help me out. When the run following script it has convergence problem. I shall be greatful if someone find the solution and help me out of this problem.

I guess this is probably because of using zero length element.



# Basic SI unit system

set m 1.0; # Basic unit for length
set kg 1.0; # Basic unit for mass
set s 1.0; # Basic unit for time

# ---------------------------------------------------------------------------------- #

# Derived unit system

set mm [expr $m/1000]; # Unit of length in millimeter

set Mt [expr 1000.*$kg]; # Unit of mass in mteric tonne

set N [expr $kg*$m/pow($s,2)]; # Unit of force in Newton
set kN [expr 1000.*$N]; # Unit of force in kilo Newton

set Pa [expr $N/pow($m,2)]; # Unit of stress in Pascal
set MPa [expr 1000000.*$Pa]; # Unit of stress in Mega Pascal
set GPa [expr 1000.*$MPa]; # Unit of stress in Giga Pascal

puts "All units are defined"

# ---------------------------------------------------------------------------------- #

# Constants used in this module

set pi [expr 2.*asin(1.0)]; # constant PI

set g [expr 9.807*$m/pow($s,2)]; # Acceleration due to gravity in m/s2

set U 1.0e10; # Really large number
set u [expr 1./$U]; # Really small number

puts "All constants are defined"

# ---------------------------------------------------------------------------------- #

wipe

# Define model builder

model basic -ndm 3 -ndf 6; # 3D model with 6 DOFs at each node

# In order to capture proper variation of stiffness of deck and
# distribution of mass along the longitudinal bridge axis, the deck
# element is divided into smaller elastic beam elements
# Nodal coordinates of deck elements

node 1 0.0 20.0 0.0; # Abutment A1
node 2 10.0 20.0 0.0;
node 3 20.0 20.0 0.0;
node 4 30.0 20.0 0.0;
node 5 40.0 20.0 0.0; # Pier P1
node 6 50.0 20.0 0.0;
node 7 60.0 20.0 0.0;
node 8 70.0 20.0 0.0;
node 9 80.0 20.0 0.0;
node 10 90.0 20.0 0.0; # Pier P2
node 11 100.0 20.0 0.0;
node 12 110.0 20.0 0.0;
node 13 120.0 20.0 0.0;
node 14 130.0 20.0 0.0;
node 15 140.0 20.0 0.0; # Pier P3
node 16 150.0 20.0 0.0;
node 17 160.0 20.0 0.0;
node 18 170.0 20.0 0.0;
node 19 180.0 20.0 0.0; # Abutment A2

# Nodal coordinates of abutment and pier base

node 20 0.0 20.0 0.0;
node 21 40.0 10.0 0.0;
node 22 90.0 0.0 0.0;
node 23 140.0 10.0 0.0;
node 24 180.0 20.0 0.0;

# Zero length at pier-deck and pier-foundation connection

node 25 40.0 20.0 0.0;
node 26 90.0 20.0 0.0;
node 27 140.0 20.0 0.0;

node 28 40.0 10.0 0.0;
node 29 90.0 0.0 0.0;
node 30 140.0 10.0 0.0;

puts "Nodal coordinates are defined"

# ---------------------------------------------------------------------------------- #

# Calculaion of moving mass at different node

set m1 [expr 1000.*$kN/$g]; # mass at abutment node
set m2 [expr 2.*$m1]; # mass at intermediate node
set m3 [expr $m1]; # mass from pier
set m4 [expr $m3+$m2]; # mass at pier top

# Concentrated mass at nodal points associated with traslational
# DOFs. Inertial mass associated with rotational DOFs are ignored

mass 1 $m1 $m1 $m1 0.0 0.0 0.0; # Abutment top A1
mass 2 $m2 $m2 $m2 0.0 0.0 0.0;
mass 3 $m2 $m2 $m2 0.0 0.0 0.0;
mass 4 $m2 $m2 $m2 0.0 0.0 0.0;
mass 5 $m4 $m4 $m4 0.0 0.0 0.0; # Pier top P1
mass 6 $m2 $m2 $m2 0.0 0.0 0.0;
mass 7 $m2 $m2 $m2 0.0 0.0 0.0;
mass 8 $m2 $m2 $m2 0.0 0.0 0.0;
mass 9 $m2 $m2 $m2 0.0 0.0 0.0;
mass 10 $m4 $m4 $m4 0.0 0.0 0.0; # Pier top P2
mass 11 $m2 $m2 $m2 0.0 0.0 0.0;
mass 12 $m2 $m2 $m2 0.0 0.0 0.0;
mass 13 $m2 $m2 $m2 0.0 0.0 0.0;
mass 14 $m2 $m2 $m2 0.0 0.0 0.0;
mass 15 $m4 $m4 $m4 0.0 0.0 0.0; # Pier top P3
mass 16 $m2 $m2 $m2 0.0 0.0 0.0;
mass 17 $m2 $m2 $m2 0.0 0.0 0.0;
mass 18 $m2 $m2 $m2 0.0 0.0 0.0;
mass 19 $m1 $m1 $m1 0.0 0.0 0.0; # Abutment top A2

puts "Nodal masses are defined"

# ---------------------------------------------------------------------------------- #

# Boundary conditions : single point constraint

# Abutment and piers are fixed at base
fix 20 1 1 1 1 1 1;
fix 21 1 1 1 1 1 1;
fix 22 1 1 1 1 1 1;
fix 23 1 1 1 1 1 1;
fix 24 1 1 1 1 1 1;

# Nodal points of deck are free to translate and rorate
fix 1 0 0 0 0 0 0;
fix 2 0 0 0 0 0 0;
fix 3 0 0 0 0 0 0;
fix 4 0 0 0 0 0 0;
fix 5 0 0 0 0 0 0;
fix 6 0 0 0 0 0 0;
fix 7 0 0 0 0 0 0;
fix 8 0 0 0 0 0 0;
fix 9 0 0 0 0 0 0;
fix 10 0 0 0 0 0 0;
fix 11 0 0 0 0 0 0;
fix 12 0 0 0 0 0 0;
fix 13 0 0 0 0 0 0;
fix 14 0 0 0 0 0 0;
fix 15 0 0 0 0 0 0;
fix 16 0 0 0 0 0 0;
fix 17 0 0 0 0 0 0;
fix 18 0 0 0 0 0 0;
fix 19 0 0 0 0 0 0;
fix 25 0 0 0 0 0 0;
fix 26 0 0 0 0 0 0;
fix 27 0 0 0 0 0 0;
fix 28 0 0 0 0 0 0;
fix 29 0 0 0 0 0 0;
fix 30 0 0 0 0 0 0;

puts "Boundary conditions are defined"

# ---------------------------------------------------------------------------------- #

# Basic material parameters for reinforcing steel
# ReinforingSteel type material is used [Grade 400] as per CALTRAN SDC 1.3

set fy [expr 475.*$MPa]; # Yield stress of steel
set fu [expr 655.*$MPa]; # Ultimate stress of steel
set Es [expr 200.*$GPa]; # Elastic tangent modulus
set Esh [expr 670.*$MPa]; # Strain hardening modulus
set esh 0.0115; # Strain at commencement of strain hardening
set eult 0.09; # Strain at ultimate strain
set efac 0.2; # Fracture strain

# ---------------------------------------------------------------------------------- #

# Basic material parameters for concrete as per CALTRAN SDC 1.3

set fc [expr -40*$MPa]; # Grade of concrete
set Ec [expr 4700.*sqrt(-$fc/$MPa)]; # Initial tangent modulus
set Gc [expr 0.4*$Ec]; # Shear modulus

# Details of confining reinforcement

set rhos 0.007; # Volumetric ratio of confining steel
set Ke 0.95; # For circular section
set fL [expr 0.5*$Ke*$rhos*$fy]; # Average confining stress

set const [expr 2.254*sqrt(1+7.94*$fL/(-$fc)) - 2*$fL/(-$fc) - 1.254];

# Core concrete (Mander model) : Confined

set fc1C [expr $const*$fc]; # Maximum stress
set e1C [expr -0.002*(1+5*($fc1C/$fc-1))]; # Strain at max stress
set e2C [expr -0.004+1.4*$rhos*$fy*$efac/$fc1C];# Strain at ult stress
set Esec [expr $fc1C/$e1C]; # Secant modulus
set xu [expr $e2C/$e1C];
set r [expr $Ec/($Ec-$Esec)];
set fc2C [expr $fc1C*$xu*$r/($r-1+pow($xu,$r))]; # Ultimate stress

# Cover concrete (Parabolic model) : Unconfined

set fc1U $fc; # Maximum stress
set e1U -0.002; # Strain at maximum stress
set fc2U 0.; # Ultimate stress at spalling
set e2U -0.005; # Strain at ultimate stress

# ---------------------------------------------------------------------------------- #

# The following parameters are used to model Strain Penetration
# behaviour of fully anchored steel reinforcing Bars

set db [expr 42.*$mm]; # Rebar diameter
set alpha 0.4; # As per CEB FIP MC 90
set Sy [expr 0.1*pow(0.45*$db*$fy/sqrt(-$fc),2.5)+0.013];
set Su [expr 30.*$Sy];
set b 0.3;
set R 0.5;

# ---------------------------------------------------------------------------------- #

# The folowing parameters are used to model bilinear abutment

set Ka1 [expr 7500000.*$kN/$m]; # Stiffness in vert dir
set Ka2 [expr 250000.*$kN/$m]; # Stiffness in long dir
set Ka3 [expr 750000.*$kN/$m]; # Stiffness in tran dir

set Ca1 [expr 3.2*sqrt($Ka1)*$Mt/$s]; # Damping coeff in vert dir
set Ca2 [expr 3.2*sqrt($Ka2)*$Mt/$s]; # Damping coeff in long dir
set Ca3 [expr 3.2*sqrt($Ka3)*$Mt/$s]; # Damping coeff in tran dir

set a 1. ; # constant used for damping

set Gap2 [expr 100.*$mm] ; # Gap in the long dir

set eyld1 [expr 10000.*$kN/$Ka1] ; # Yield force in vert dir
set Fyld2 [expr 10000.*$kN] ; # Yield force in long dir
set eyld3 [expr 10000.*$kN/$Ka3] ; # Yield force in tran dir

puts "All material parameters are defined"

# ---------------------------------------------------------------------------------- #

# Elastic properties of deck element

set deckA 10.0; # cross sectional area m2
set deckJ 6.5; # torsional inertia m4
set deckIy 20.0; # moment of inertia about major axis m4
set deckIz 5.0; # moment of inertia about minor axis m4

# Inelastic properties of circular pier element in flexure

# Parameters to generate column section

set colD [expr 2.5*$m]; # Diameter of column
set cover [expr 50.*$mm]; # Clear cover to any reinf

set AreaCol [expr 0.25*$pi*pow($colD,2)]; # Area of column

set rhoL 0.0125; # Long reinf ratio
set NbCol 20; # Number of long reinf

set AsCol [expr $rhoL*$AreaCol]; # Total long reinf area
set AbCol [expr $AsCol/$NbCol]; # Each reinf area

set roCol [expr $colD/2.0]; # outer radius of column
set riCol 0.0; # inner radius of column

set nfCoreR 8; # number of radial fibres in core
set nfCoreT 16; # number of tangential fibres in core
set nfCoverR 2; # number of radial fibres in cover
set nfCoverT 16; # number of tangential fibres in cover

# Parameters to generate Force based nolinear beam element

set numInt 6; # Number of integration points

# ID tag for different sections used in this model

set SecPierID 11; # ID tag for intermediate location
set SecBondID 12; # ID tag for joint

set Flex1ID 21; # ID tag for intermediate (flexure)
set Flex2ID 22; # ID tag for joint (flexure)

# ID tag for different materials used in this model

set coreID 31; # ID tag for core concrete
set coverID 32; # ID tag for cover concrete
set steelID 33; # ID tag for reinforcing steel
set shearID 34; # ID tag for concrete in shear
set slipID 35; # ID tag for rebar with bond slip
set torID 36; # ID tag for concrete in torsion

set Stif1ID 37; # ID tag for abut stiff in local x-dir
set Stif2ID 38; # ID tag for abut stiff in local y-dir
set Stif3ID 39; # ID tag for abut stiff in local z-dir

set Damp1ID 40; # ID tag for abut damping in local x-dir
set Damp2ID 41; # ID tag for abut damping in local y-dir
set Damp3ID 42; # ID tag for abut damping in local z-dir

set Abut1ID 43; # ID tag for combined stiff & damping in local x-dir
set Abut2ID 44; # ID tag for combined stiff & damping in local y-dir
set Abut3ID 45; # ID tag for combined stiff & damping in local z-dir


# ID tag for coordinate transformation

set IDpierTrans 51; # ID tag for pier
set IDdeckTrans 52; # ID tag for deck

puts "All element parameters are defined"

# ---------------------------------------------------------------------------------- #

# Definition of concrete material in flexure

uniaxialMaterial Concrete04 $coreID $fc1C $e1C $fc2C $e2C; # Core conc
uniaxialMaterial Concrete04 $coverID $fc1U $e1U $fc2U $e2U; # Cover conc

# Defintion of concrete material in shear and torsion

uniaxialMaterial Elastic $shearID $Gc ;

uniaxialMaterial Elastic $torID $Gc ;


# Definition of reinforcement steel model

uniaxialMaterial ReinforcingSteel $steelID $fy $fu $Es $Esh $esh $eult;

# Definition of anchorage slip model of rebars

uniaxialMaterial Bond_SP01 $slipID $fy $Sy $fu $Su $b $R

# Definition of abutment spring

uniaxialMaterial ElasticPP $Stif1ID $Ka1 $eyld1 ;
uniaxialMaterial ElasticPPGap $Stif2ID $Ka2 -$Fyld2 -$Gap2 ;
uniaxialMaterial ElasticPP $Stif3ID $Ka3 $eyld3 ;

uniaxialMaterial Viscous $Damp1ID $Ca1 $a ;
uniaxialMaterial Viscous $Damp2ID $Ca2 $a ;
uniaxialMaterial Viscous $Damp3ID $Ca3 $a ;

uniaxialMaterial Parallel $Abut1ID $Stif1ID $Damp1ID ;
uniaxialMaterial Parallel $Abut2ID $Stif2ID $Damp2ID ;
uniaxialMaterial Parallel $Abut3ID $Stif3ID $Damp3ID ;

puts "All materials are defined" ;

# ---------------------------------------------------------------------------------- #

# Generation of circular section for intermediate pier section

section fiberSec $Flex1ID {
set rc [expr $roCol-$cover]; # core radius
patch circ $coreID $nfCoreT $nfCoreR 0 0 $riCol $rc 0 360;
patch circ $coverID $nfCoverT $nfCoverR 0 0 $rc $roCol 0 360;

set theta [expr 360.0/$NbCol]; # Angle between bars
layer circ $steelID $NbCol $AbCol 0 0 $rc $theta 360;

}

# Generation of circular section for end pier section in flexure

section fiberSec $Flex2ID {
set rc [expr $roCol-$cover]; # core radius
patch circ $coreID $nfCoreT $nfCoreR 0 0 $riCol $rc 0 360;
patch circ $coverID $nfCoverT $nfCoverR 0 0 $rc $roCol 0 360;

set theta [expr 360.0/$NbCol]; # Angle between bars
layer circ $slipID $NbCol $AbCol 0 0 $rc $theta 360;

}

# Intermediate pier section

section Aggregator $SecPierID $shearID Vy $shearID Vz $torID T -section $Flex1ID

#section Aggregator $SecPierID $shearID Vy $shearID Vy -section $Flex1ID

# End pier section

section Aggregator $SecBondID $shearID Vy $shearID Vz $torID T -section $Flex2ID

puts "All sections are defined"

# ---------------------------------------------------------------------------------- #

# Definition of elements

# Deck

geomTransf Linear $IDdeckTrans 0 -1 0;

element elasticBeamColumn 101 1 2 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 102 2 3 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 103 3 4 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 104 4 5 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 105 5 6 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 106 6 7 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 107 7 8 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 108 8 9 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 109 9 10 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 110 10 11 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 111 11 12 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 112 12 13 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 113 13 14 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 114 14 15 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 115 15 16 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 116 16 17 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 117 17 18 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;
element elasticBeamColumn 118 18 19 $deckA $Ec $Gc $deckJ $deckJ $deckJ $IDdeckTrans;

# Intermediate pier column

geomTransf Linear $IDpierTrans 0 0 1;

element nonlinearBeamColumn 201 25 28 $numInt $SecPierID $IDpierTrans;
element nonlinearBeamColumn 202 26 29 $numInt $SecPierID $IDpierTrans;
element nonlinearBeamColumn 203 27 30 $numInt $SecPierID $IDpierTrans;

# Zero length section of pier end

element zeroLengthSection 210 5 25 $SecBondID;
element zeroLengthSection 211 10 26 $SecBondID;
element zeroLengthSection 212 15 27 $SecBondID;
element zeroLengthSection 213 28 21 $SecBondID;
element zeroLengthSection 214 29 22 $SecBondID;
element zeroLengthSection 215 30 23 $SecBondID;

# Zero length element of abutment

element zeroLength 301 20 1 -mat $Abut1ID $Abut2ID $Abut3ID -dir 1 2 3;
element zeroLength 302 24 19 -mat $Abut1ID $Abut2ID $Abut3ID -dir 1 2 3;

puts "All elements are defined"

# ---------------------------------------------------------------------------------- #

# Definition of weights at nodal points

set w1 [expr 100.*$kN]; # weight at abutment node
set w2 [expr 2.*$w1]; # weight at intermediate node
set w3 [expr $w1+10.*$kN]; # weight from pier
set w4 [expr $w3+$w2]; # weight at pier top

# define LoadPattern 1. impose load in a linear manner

pattern Plain 1 Linear { ;

load 1 0.0 -$w1 0.0 0.0 0.0 0.0; # Abutment top A1
load 2 0.0 -$w2 0.0 0.0 0.0 0.0;
load 3 0.0 -$w2 0.0 0.0 0.0 0.0;
load 4 0.0 -$w2 0.0 0.0 0.0 0.0;
load 5 0.0 -$w4 0.0 0.0 0.0 0.0; # Pier top P1
load 6 0.0 -$w2 0.0 0.0 0.0 0.0;
load 7 0.0 -$w2 0.0 0.0 0.0 0.0;
load 8 0.0 -$w2 0.0 0.0 0.0 0.0;
load 9 0.0 -$w2 0.0 0.0 0.0 0.0;
load 10 0.0 -$w4 0.0 0.0 0.0 0.0; # Pier top P2
load 11 0.0 -$w2 0.0 0.0 0.0 0.0;
load 12 0.0 -$w2 0.0 0.0 0.0 0.0;
load 13 0.0 -$w2 0.0 0.0 0.0 0.0;
load 14 0.0 -$w2 0.0 0.0 0.0 0.0;
load 15 0.0 -$w4 0.0 0.0 0.0 0.0; # Pier top P3
load 16 0.0 -$w2 0.0 0.0 0.0 0.0;
load 17 0.0 -$w2 0.0 0.0 0.0 0.0;
load 18 0.0 -$w2 0.0 0.0 0.0 0.0;
load 19 0.0 -$w1 0.0 0.0 0.0 0.0; # Abutment top A2

}

puts "Gravity loads are defined" ;

# ---------------------------------------------------------------------------------- #

# Define solution procedure

system UmfPack ; # To store & solve the system of equation


constraints Plain; # To enforce homogeneous SP constraint

test NormDispIncr 1.0e-5 10 1; # convergence criteria

algorithm Newton ; # Determines the sequence of steps

numberer RCM ; # Renumbering the of DOF to reduce bandwidth

integrator LoadControl 0.01; # Define load stepping

analysis Static; # Type of analysis

analyze 20 ;

#loadConst -time 0.0;

puts "Static analysis is completed"

nodeDisp 1 1 2 3 4 5 6;

[José Melo]

[quote="gopal"]Hi everybody

Please help me out. When the run following script it has convergence problem. I shall be greatful if someone find the solution and help me out of this problem.

I guess this is probably because of using zero length element.



Hi,

I do not know if helps, but the translational degree-of-freedom of the nodes zero length element should be constrained to the node to prevent sliding of the beam-column element under lateral loads because the shear resistance is not included in the zero-length section element.
You use this command: equalDOF in the nodes of zero length element.

[silvia]

why not try the scripts from the examples manual.
put in
set ok [analyze 20]
if {$ok!=.....

from examples 5 and on...


however, if you are not getting convergence on the first step, check your model -- start with somethign simpler, make sure it works and build up. you might want to put in an [eigen] command, to make sure you have a properly-constrained model.

[feergoortens]

SOVANE, South Africa — South Africa, trying to overcome years of denial and delay in confronting its monumental AIDS crisis, is now in the midst of a feverish buildup of testing, treatment and prevention that United Nations officials say is the largest and fastest expansion of AIDS services ever attempted by any nation.