OpenSees Basic Examples (2階建てフレームでの固有値解析) 解説
のコマンドのサマリは以下の通りです。
このコマンドを ファイル名 EigenAnal_twoStoreyShearFrame7.tcl として、テキストフォーマットで作成し、
OpenSeesの起動環境 で 起動しているOpenSees のコマンドラインに
OpenSees EigenAnal_twoStoreyShearFrame7.tcl <Enter>
と打ち込んで、実行します。
----- EigenAnal_twoStoreyShearFrame7.tcl 始まり ------
# Eigen analysis of a two-storey shear frame; Example 10.4 from "Dynamics of Structures" book by Anil Chopra - using equalDOF and very high Ib
# units: in, kips
wipe
#input
set m [expr 100.0/386.0]
set numModes 2
#material
set Ac 63.41
set Ic 320.0
set E 30000.0
set Ib 10e+12
set Ab 63.41
#geometry
set L 288.
set h 144.
# create data directory
file mkdir modes;
# define the model
#---------------------------------
#model builder
model BasicBuilder -ndm 2 -ndf 3
# nodal coordinates:
node 1 0. 0. ;
node 2 $L 0. ;
node 3 0. $h ;
node 4 $L $h ;
node 5 0. [expr 2*$h];
node 6 $L [expr 2*$h];
# Single point constraints -- Boundary Conditions
fix 1 1 1 1;
fix 2 1 1 1;
# MP constraints
equalDOF 3 4 2 3
equalDOF 5 6 2 3
# assign mass
mass 3 $m 0. 0. ;
mass 4 $m 0. 0. ;
mass 5 [expr $m/2.] 0. 0. ;
mass 6 [expr $m/2.] 0. 0. ;
# define geometric transformation:
set TransfTag 1;
geomTransf Linear $TransfTag ;
# define elements:
# columns
element elasticBeamColumn 1 1 3 $Ac $E [expr 2.*$Ic] $TransfTag;
element elasticBeamColumn 2 3 5 $Ac $E $Ic $TransfTag;
element elasticBeamColumn 3 2 4 $Ac $E [expr 2.*$Ic] $TransfTag;
element elasticBeamColumn 4 4 6 $Ac $E $Ic $TransfTag;
# beams
element elasticBeamColumn 5 3 4 $Ab $E $Ib $TransfTag;
element elasticBeamColumn 6 5 6 $Ab $E $Ib $TransfTag;
# record eigenvectors
#----------------------
for { set k 1 } { $k <= $numModes } { incr k } {
recorder Node -file [format "modes/mode%i.txt" $k] -nodeRange 1 6 -dof 1 2 3 "eigen $k"
}
# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"
# write the output file cosisting of periods
#--------------------------------------------
set period "modes/Periods.txt"
set Periods [open $period "w"]
foreach t $T {
puts $Periods " $t"
}
close $Periods
# create display for mode shapes
#---------------------------------
# $windowTitle $xLoc $yLoc $xPixels $yPixels
recorder display "Mode Shape 1" 10 10 500 500 -wipe
prp $h $h 1; # projection reference point (prp); defines the center of projection (viewer eye)
vup 0 1 0; # view-up vector (vup)
vpn 0 0 1; # view-plane normal (vpn)
viewWindow -200 200 -200 200; # coordiantes of the window relative to prp
display -1 5 20; # the 1st arg. is the tag for display mode (ex. -1 is for the first mode shape)
# the 2nd arg. is magnification factor for nodes, the 3rd arg. is magnif. factor of deformed shape
recorder display "Mode Shape 2" 10 510 500 500 -wipe
prp $h $h 1;
vup 0 1 0;
vpn 0 0 1;
viewWindow -200 200 -200 200
display -2 5 20
# Run a one step gravity load with no loading (to record eigenvectors)
#-----------------------------------------------------------------------
integrator LoadControl 0 1 0 0
# Convergence test
# tolerance maxIter displayCode
test EnergyIncr 1.0e-10 100 0
# Solution algorithm
algorithm Newton
# DOF numberer
numberer RCM
# Constraint handler
constraints Transformation
# System of equations solver
system ProfileSPD
analysis Static
set res [analyze 1]
if {$res < 0} {
puts "Modal analysis failed"
}
# get values of eigenvectors for translational DOFs
#---------------------------------------------------
set f11 [nodeEigenvector 3 1 1]
set f21 [nodeEigenvector 5 1 1]
set f12 [nodeEigenvector 3 2 1]
set f22 [nodeEigenvector 5 2 1]
puts "eigenvector 1: [list [expr {$f11/$f21}] [expr {$f21/$f21}] ]"
puts "eigenvector 2: [list [expr {$f12/$f22}] [expr {$f22/$f22}] ]"
after 10000
----- EigenAnal_twoStoreyShearFrame7.tcl 終わり ------
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