Hi,
I have been trying so hard to get the load-displacement relationship of the Lee's frame example in the paper: Response Gradients for Nonlinear Beam-Column Elements under Large Displacements,2007. Lee's Frame is an L shape with L=120 cm, rectangular section with b=1.0 cm and d=3.0 cm, E=720 MPa. An applied force of 2.7 Kn is applied at distance 24 cm from the right end of the beam. I have used elastic section, Corotaional transformation, and ten force Based elements as it said in the paper with dLambda=0.005 KN. My results are different than those obtained in the paper. So I will appreciate if anyone can help me with that.
Thanks.
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Load-displacement response of Lee's frame
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Re: Load-displacement response of Lee's frame
i would normally tell you to email the papers authors to ask for help, but as i know the 2 and what the response would be, post it here and maybe someone else can help.
Re: Load-displacement response of Lee's frame
Hi,
I have been trying so hard to get the load-displacement relationship of the Lee's frame example in the paper: Response Gradients for Nonlinear Beam-Column Elements under Large Displacements,2007. Lee's Frame is an L shape with L=120 cm, rectangular section with b=1.0 cm and d=3.0 cm, E=720 MPa. An applied force of 2.7 Kn is applied at distance 24 cm from the right end of the beam. I have used elastic section, Corotaional transformation, and ten force Based elements as it said in the paper with dLambda=0.005 KN. My results are different than those obtained in the paper. So I will appreciate if anyone can help me with that.
Thanks.
I have been trying so hard to get the load-displacement relationship of the Lee's frame example in the paper: Response Gradients for Nonlinear Beam-Column Elements under Large Displacements,2007. Lee's Frame is an L shape with L=120 cm, rectangular section with b=1.0 cm and d=3.0 cm, E=720 MPa. An applied force of 2.7 Kn is applied at distance 24 cm from the right end of the beam. I have used elastic section, Corotaional transformation, and ten force Based elements as it said in the paper with dLambda=0.005 KN. My results are different than those obtained in the paper. So I will appreciate if anyone can help me with that.
Thanks.
Re: Load-displacement response of Lee's frame
i meant post the script not the description over again!
Re: Load-displacement response of Lee's frame
Dear Dr.McKenna,
Thanks for your reply, I have posted my question again in a hope to get an answer.
Thanks for your reply, I have posted my question again in a hope to get an answer.
Re: Load-displacement response of Lee's frame
Sorry, Here is the script
wipe
# example 1
# units are N,mm
set L 120.0
set N 10
set Np 3
set h [expr $L/$N]
set E 720.0;
#set fy 10.4;
set b 1.0;
set d 3.0;
set A [expr $b*$d];
set I [expr $b*$d*$d*$d/12.0];
model basic -ndm 2 -ndf 3
# create nodes
# tag X Y
node 0 0.0 0.0
# Define the column nodes
for {set i 1} {$i <= $N} {incr i} {
node $i 0.0 [expr $i*$h]
}
# define beam nodes
for {set i [expr $N+1]} {$i <=[expr 2*$N]} {incr i} {
node $i [expr ($i-$N)*$h] $L
}
set Z [expr 2*$N]
# Define Boundary conditions
# Tag dof1 dof2 dof3
fix 0 1 1 0
fix $Z 1 1 0
geomTransf Corotational 1
#uniaxialMaterial Elastic $matTag $E <$eta> <$Eneg>
#uniaxialMaterial Elastic 1 $E
# sect Elastic secTag E A I
section Elastic 5 $E $A $I
#uniaxialMaterial Hardening 1 $E $fy 0 [expr $alpha/(1-$alpha)*$E]
#section WFSection2d $secTag $matTag $d $tw $bf $tf $Nfw $Nff
#section WFSection2d 5 1 $d $b $b 0 25 0
# Define Column elements
# Define Column and Beam elements
for {set i 1} {$i<=$Z} {incr i} {
# element dispBeamColumn $tag ndI ndJ Np secTag secTransfTag
#element dispBeamColumnNL $i [expr $i-1] $i $Np 5 1
element forceBeamColumn $i [expr $i-1] $i 1 Lobatto 5 $Np
}
recorder display "Deflection" 10 10 600 600 -wipe
vup 0 1 0
prp 10 10 1000
display 10 10 1
# Define Load
pattern Plain 1 Linear {
# create member loads at distance 24 cm from node 4
# nd Fx Fy FZ
load 12 0.0 -1.0 0.0
}
test NormDispIncr 1.0e-6 100 1
#test NormUnbalance 1.0e-6 100 1
algorithm Newton
set dLambda 0.005
# Type dLambda
#integrator LoadControl $dLambda
integrator DisplacementControl 12 2 -1
#integrator MinUnbalDispNorm $dLambda
system UmfPack ;# Symmetric, negative definite equation solver
numberer RCM ;# Use Reverse Cuthill-McKee to assign equation numbers
constraints Plain ; # Handle constraints by simply imposing b.c.s
analysis Static
# end of analysis genyration
if {$N==4} {
set outFile [open four.out w]
}
if {$N==10} {
set outFile [open ten.out w]
}
if {$N==16} {
set outFile [open sixteen.out w]
}
set Nstep 100
for {set i 1} {$i <= $Nstep} {incr i} {
set ok [analyze 1]
if {$ok < 0} {
break
} else {
puts $outFile " [eleForce 12 2] [nodeDisp 12 2]"
}
}
close $outFile
wipe
# example 1
# units are N,mm
set L 120.0
set N 10
set Np 3
set h [expr $L/$N]
set E 720.0;
#set fy 10.4;
set b 1.0;
set d 3.0;
set A [expr $b*$d];
set I [expr $b*$d*$d*$d/12.0];
model basic -ndm 2 -ndf 3
# create nodes
# tag X Y
node 0 0.0 0.0
# Define the column nodes
for {set i 1} {$i <= $N} {incr i} {
node $i 0.0 [expr $i*$h]
}
# define beam nodes
for {set i [expr $N+1]} {$i <=[expr 2*$N]} {incr i} {
node $i [expr ($i-$N)*$h] $L
}
set Z [expr 2*$N]
# Define Boundary conditions
# Tag dof1 dof2 dof3
fix 0 1 1 0
fix $Z 1 1 0
geomTransf Corotational 1
#uniaxialMaterial Elastic $matTag $E <$eta> <$Eneg>
#uniaxialMaterial Elastic 1 $E
# sect Elastic secTag E A I
section Elastic 5 $E $A $I
#uniaxialMaterial Hardening 1 $E $fy 0 [expr $alpha/(1-$alpha)*$E]
#section WFSection2d $secTag $matTag $d $tw $bf $tf $Nfw $Nff
#section WFSection2d 5 1 $d $b $b 0 25 0
# Define Column elements
# Define Column and Beam elements
for {set i 1} {$i<=$Z} {incr i} {
# element dispBeamColumn $tag ndI ndJ Np secTag secTransfTag
#element dispBeamColumnNL $i [expr $i-1] $i $Np 5 1
element forceBeamColumn $i [expr $i-1] $i 1 Lobatto 5 $Np
}
recorder display "Deflection" 10 10 600 600 -wipe
vup 0 1 0
prp 10 10 1000
display 10 10 1
# Define Load
pattern Plain 1 Linear {
# create member loads at distance 24 cm from node 4
# nd Fx Fy FZ
load 12 0.0 -1.0 0.0
}
test NormDispIncr 1.0e-6 100 1
#test NormUnbalance 1.0e-6 100 1
algorithm Newton
set dLambda 0.005
# Type dLambda
#integrator LoadControl $dLambda
integrator DisplacementControl 12 2 -1
#integrator MinUnbalDispNorm $dLambda
system UmfPack ;# Symmetric, negative definite equation solver
numberer RCM ;# Use Reverse Cuthill-McKee to assign equation numbers
constraints Plain ; # Handle constraints by simply imposing b.c.s
analysis Static
# end of analysis genyration
if {$N==4} {
set outFile [open four.out w]
}
if {$N==10} {
set outFile [open ten.out w]
}
if {$N==16} {
set outFile [open sixteen.out w]
}
set Nstep 100
for {set i 1} {$i <= $Nstep} {incr i} {
set ok [analyze 1]
if {$ok < 0} {
break
} else {
puts $outFile " [eleForce 12 2] [nodeDisp 12 2]"
}
}
close $outFile
Re: Load-displacement response of Lee's frame
After looking at the main reference of this example (Geometrically non-Linear and Elastoplastic Three-Dimensional Shear Flexible Beam Element Of Von-Mises-Type Hardening Material), I noticed that the given numbers are unit-less, so after many trails, I found that ignoring units gives me the closest results.