ForceBeamColumn3d::update()--could not invert flexibility

Jihoon · Post by **Jihoon** » Sun Jul 26, 2015 11:31 pm

I'm modeling Meloland Road Overpass(continuous 2 span, 1 single poer) now.

Pier : nonlinearBeamColumn (fiber section)
Deck : elasticBeamColumn
Pier & Deck connection : Ligid Link
Boundary : foundation Pile spring (Jian Zhang and Nicos Makris .2002)

It can not work when I use slcaled ground motion(amplitude : <min -0.3972g>/<max 0.3623>).
On the other hand It works when i use other ground motion(lower value of amplitude).

It shows just ' ForceBeamColumn3d::update()--could not invert flexibility' message.

I think this problem appear on the pier(fiber section).

How can I solve this problem?

Thanks~~!!!

Please refer the following code.

###########################################################################################
################################# section ###############################################
###########################################################################################
# MATERIAL parameters -------------------------------------------------------------------
set IDconcCore 1; # material ID tag -- confined core concrete
set IDconcCover 2; # material ID tag -- unconfined cover concrete
set IDreinf 3; # material ID tag -- reinforcement
# nominal concrete compressive strength
set fc [expr -27.6*$MPa]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 20000*$MPa]; # Concrete Elastic Modulus(Mpa)
# confined concrete
set fc1C [expr -34.474*$MPa]; # CONFINED concrete (mander model), maximum stress
set eps1C -0.004; # strain at maximum stress
set fc2C [expr -21.*$MPa]; # ultimate(crushing) stress
set eps2C -0.014; # strain at ultimate stress
# unconfined concrete
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U -0.002; # strain at maximum strength of unconfined concrete
set fc2U 0.; # ultimate stress
set eps2U -0.008; # strain at ultimate stress
# -----------
set Fy [expr 455.*$MPa]; # STEEL yield stress
set Es [expr 200000.*$MPa]; # modulus of steel
set epsP [expr $Fy/$Es]; # strain or deformation at which material reaches plastic state in tension
uniaxialMaterial Concrete01 $IDconcCore $fc1C $eps1C $fc2C $eps2C; # build core concrete (confined)
uniaxialMaterial Concrete01 $IDconcCover $fc1U $eps1U $fc2U $eps2U; # build cover concrete (unconfined)
uniaxialMaterial ElasticPP $IDreinf $Es $epsP; # build reinforcement material
#uniaxialMaterial Steel01 $IDreinf $Fy $Es 0;

# section GEOMETRY -------------------------------------------------------------
set DSec [expr 1.52*$m]; # Column Diameter
set coverSec [expr (1.52*$m/2.)*(2./11.)]; # Column cover to reinforcing steel NA.
set numBarsSec 18; # number of uniformly-distributed longitudinal-reinforcement bars
set barAreaSec [expr pow(0.057,2)*$PI*$m2/4]; # area of longitudinal-reinforcement bars
set SecTag 1; # set tag for symmetric section

# Generate a circular reinforced concrete section
# with one layer of steel evenly distributed around the perimeter and a confined core.
# confined core.
# by: Michael H. Scott, 2003
#
#
# Notes
# The center of the reinforcing bars are placed at the inner radius
# The core concrete ends at the inner radius (same as reinforcing bars)
# The reinforcing bars are all the same size
# The center of the section is at (0,0) in the local axis system
# Zero degrees is along section y-axis
#
set ri 0.0; # inner radius of the section, only for hollow sections
set ro [expr $DSec/2]; # overall (outer) radius of the section
set nfCoreR 9; # number of radial divisions in the core (number of "wedges") in the radial direction.
set nfCoreT 36; # number of theta divisions in the core (number of "rings") in the circumferential direction.
set nfCoverR 2; # number of radial divisions in the cover
set nfCoverT 36; # number of theta divisions in the cover

# Define the fiber section
section fiberSec $SecTag {
set rc [expr $ro-$coverSec]; # Core radius
patch circ $IDconcCore $nfCoreT $nfCoreR 0 0 $ri $rc 0 360; # Define the core patch
patch circ $IDconcCover $nfCoverT $nfCoverR 0 0 $rc $ro 0 360; # Define the cover patch
set theta [expr 360.0/$numBarsSec]; # Determine angle increment between bars
layer circ $IDreinf $numBarsSec $barAreaSec 0 0 $rc $theta 360; # Define the reinforcing layer
}

# assign torsional Stiffness for 3D Model
set SecTagTorsion 99; # ID tag for torsional section behavior
set SecTag3D 3; # ID tag for combined behavior for 3D model
uniaxialMaterial Elastic $SecTagTorsion $Ubig; # define elastic torsional stiffness(Ubig : real large number)
section Aggregator $SecTag3D $SecTagTorsion T -section $SecTag; # combine section properties

# #################################################
# Deck
# #################################################
set Gs $Ubig; # Shear Modulus(set large)
set J $Ubig; # torsional moment of inertia of cross section(set large)
set SecTagAb 4;
set SecTagPi 5;
#set SecTag3DAb 6;
#set SecTag3DPi 7;
# SecTag E A Iz Iy G J
section Elastic $SecTagAb $Ec [expr 17.33*$m2] [expr 2.5336*$m4] [expr 134.8273*$m4] $Gs $J; #four vertical webs
section Elastic $SecTagPi $Ec [expr 17.33*$m2] [expr 4.3372*$m4] [expr 144.4167*$m4] $Gs $J; #filled with concrete

###########################################################################################
################################# bridge nod ############################################
###########################################################################################
#Pier
node 101 32. 0. 0.;
node 102 32. 0.5 0.;
node 103 32. 1. 0.;
node 104 32. 1.5 0.;
node 105 32. 2. 0.;
node 106 32. 2.5 0.;
node 107 32. 3. 0.;
node 108 32. 3.5 0.;
node 109 32. 4. 0.;
node 110 32. 4.5 0.;
node 111 32. 5. 0.;

#Pier Foundation(B=4.5m, H=4.5m)
node 301 32. 0. [expr 4.5/2.];
node 302 32. 0. 0.;
node 303 32. 0. [expr -4.5/2.];

#Deck
for {set i 1} {$i <= 65} {incr i} {
node [expr $i+200] [expr $i-1.] 5. 0.
};

# Abutment
# Left(x=0m)
node 401 0. 5. 5.;
node 402 0. 5. 0.;
node 403 0. 5. -5.;
# Right(x=64m)
node 501 64. 5. 5.;
node 502 64. 5. 0.;
node 503 64. 5. -5.;

# spring nodes

for {set i 1} {$i <= 18} {incr i} {
# spring nodes of 301 node
if {$i <= 3} {
# fixed spring nodes
node $i 32. 0. [expr 4.5/2.]
}
# spring nodes of 303 node
if {3 < $i && $i <= 6} {
# fixed spring nodes
node $i 32. 0. [expr -4.5/2.]
}
# spring nodes of 401 node
if {6 < $i && $i <= 9} {
# fixed spring nodes
node $i 0. 5. 5.
}
# spring nodes of 403 node
if {9 < $i && $i <= 12} {
# fixed spring nodes
node $i 0. 5. -5.
}
# spring nodes of 501 node
if {12 < $i && $i <= 15} {
# fixed spring nodes
node $i 64. 5. 5.
}
# spring nodes of 503 node
if {15 < $i && $i <= 18} {
# fixed spring nodes
node $i 64. 5. -5.
}
}

# spring node fixities
# fixed spring nodes
for {set i 1} {$i <= 18} {incr i} {
fix [expr $i] 1 1 1 1 1 1
}

# determine support nodes where ground motions are input, for multiple-support excitation
set iSupportNode "1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18"

#Pier Mass
mass 101 [expr 4.4458*$t] 0. [expr 4.4458*$t] 0. 0. 0.;
mass 111 [expr 4.4458*$t] 0. [expr 4.4458*$t] 0. 0. 0.;
for {set i 1} {$i <= 9} {incr i} {
mass [expr $i+101] [expr 8.8915*$t] 0. [expr 8.8915*$t] 0. 0. 0.;
}

# Deck mass
mass 201 [expr 6.2064*$t] 0. [expr 6.2064*$t] 0. 0. 0.;
for {set i 1} {$i <= 30} {incr i} {
mass [expr $i+200] [expr 12.4127*$t] 0. [expr 12.4127*$t] 0. 0. 0.;
}
mass 232 [expr 21.4119*$t] 0. [expr 21.4119*$t] 0. 0. 0.;
mass 233 [expr (30.4111 + 4.4458)*$t] 0. [expr (30.4111 + 4.4458)*$t] 0. 0. 0.;
mass 234 [expr 21.4119*$t] 0. [expr 21.4119*$t] 0. 0. 0.;
for {set i 1} {$i <= 30} {incr i} {
mass [expr $i+234] [expr 12.4127*$t] 0. [expr 12.4127*$t] 0. 0. 0.;
}
mass 265 [expr 6.2064*$t] 0. [expr 6.2064*$t] 0. 0. 0.;

###########################################################################################
################################# bridge element ########################################
###########################################################################################
# set up geometric transformations of element
# separate columns and beams, in case of P-Delta analysis for columns
# in 3D model, assign vector vecxz
set IDColTransf 4; # all columns(parallel to Y axis)
set IDBeamTransf 5; # all beams(parallel to X axis)
set IDGirdTransf 6; # all girders(parallel to Z axis)
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $IDColTransf 0 0 1 ; # only columns can have PDelta effects (gravity effects)
geomTransf Linear $IDBeamTransf 0 0 1;
geomTransf Linear $IDGirdTransf 1 0 0;

# ###########################
# Define Pier/Deck Elements #
# ###########################
set np 10; # number of Gauss integration points for nonlinear curvature distribution
set Gs $Ubig; # Shear Modulus(set large)
set J $Ubig; # torsional moment of inertia of cross section(set large)

# Pier--------------------------------------------------------------------
# columns
for {set i 1} {$i <= 10} {incr i} {
element nonlinearBeamColumn [expr $i+1100] [expr $i+100] [expr $i+101] $np $SecTag3D $IDColTransf;
}
rigidLink beam 111 233;

# Pier Foundation--------------------------------------------------------------------
# girder
element elasticBeamColumn 99999 301 302 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;
element elasticBeamColumn 99998 302 303 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;
# # Pier & Pier Foundation Connection
rigidLink beam 302 101;

# Deck------------------------------------------------------------------
# beams
#four vertical webs section
for {set i 1} {$i <= 31} {incr i} {
element nonlinearBeamColumn [expr $i+1200] [expr $i+200] [expr $i+201] $np $SecTagAb $IDBeamTransf;
}
for {set i 34} {$i <= 64} {incr i} {
element nonlinearBeamColumn [expr $i+1200] [expr $i+200] [expr $i+201] $np $SecTagAb $IDBeamTransf;
}
#filled with concrete section
element nonlinearBeamColumn 1232 232 233 $np $SecTagPi $IDBeamTransf;
element nonlinearBeamColumn 1233 233 234 $np $SecTagPi $IDBeamTransf;

# Abutment------------------------------------------------------------------
#Left(x=0m)
#girder
element elasticBeamColumn 99997 401 402 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;
element elasticBeamColumn 99996 402 403 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;

#Right(x=64m)
#girder
element elasticBeamColumn 99995 501 502 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;
element elasticBeamColumn 99994 502 503 1.e5 10.e10 50. $Ubig 1.e7 1.e7 $IDGirdTransf;

# Abutment & Deck Connection
#beam
rigidLink beam 402 201;
rigidLink beam 502 265;

# #########################
# Spring Elements---------#
# #########################
# Pier(node 301)---------------------------------
# beams
uniaxialMaterial Elastic 4 [expr 260*$MN]; #longitudinal
uniaxialMaterial Elastic 5 [expr 409*$MN]; #rotation
element zeroLength 1001 1 301 -mat 4 5 -dir 1 4;
# column
uniaxialMaterial Elastic 6 [expr 887*$MN]; #longitudinal
uniaxialMaterial Elastic 7 [expr 7611*$MN]; #rotation
element zeroLength 1002 2 301 -mat 6 7 -dir 2 5;
# girder
uniaxialMaterial Elastic 8 [expr 260*$MN]; #longitudinal
uniaxialMaterial Elastic 9 [expr -409*$MN]; #rotation
element zeroLength 1003 3 301 -mat 8 9 -dir 3 6;

# Pier(node 303)---------------------------------
# beams
element zeroLength 1004 4 303 -mat 4 5 -dir 1 4;
# column
element zeroLength 1005 5 303 -mat 6 7 -dir 2 5;
# girder
element zeroLength 1006 6 303 -mat 8 9 -dir 3 6;

# Abutment Left(node 401)----------------------------
# beams
uniaxialMaterial Elastic 10 [expr 77*$MN]; #longitudinal
element zeroLength 1007 7 401 -mat 10 -dir 1;
# column
uniaxialMaterial Elastic 11 [expr 434*$MN]; #longitudinal
element zeroLength 1008 8 401 -mat 11 -dir 2;
# girder
uniaxialMaterial Elastic 12 [expr 77*$MN]; #longitudinal
element zeroLength 1009 9 401 -mat 12 -dir 3;

# Abutment Left(node 403)----------------------------
# beams
element zeroLength 1010 10 403 -mat 10 -dir 1;
# column
element zeroLength 1011 11 403 -mat 11 -dir 2;
# girder
element zeroLength 1012 12 403 -mat 12 -dir 3;

# Abutment Right(node 501)-----------------------------
# beams
uniaxialMaterial Elastic 13 [expr 77*$MN]; #longitudinal
element zeroLength 1013 13 501 -mat 13 -dir 1;
# column
uniaxialMaterial Elastic 14 [expr 434*$MN]; #longitudinal
element zeroLength 1014 14 501 -mat 14 -dir 2;
# girder
uniaxialMaterial Elastic 15 [expr 77*$MN]; #longitudinal
element zeroLength 1015 15 501 -mat 15 -dir 3;

# Abutment Right(node 503)-----------------------------
# beams
element zeroLength 1016 16 503 -mat 13 -dir 1;
# column
element zeroLength 1017 17 503 -mat 14 -dir 2;
# girder
element zeroLength 1018 18 503 -mat 15 -dir 3;