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source/conf.py

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"""
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# Add any Sphinx extension module names here, as strings. They can be
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# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
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# ones.
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"user/index.rst",
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"user/manual/model/geomTransf/frame/index.rst",
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"user/manual/analysis/integrator/gimmeMCK.rst",
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"user/manual/analysis/modalProperties.rst",
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# "user/manual/analysis/modalProperties.rst",
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"user/manual/analysis/responseSpectrumAnalysis.rst",
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"user/manual/model/damping/elementalDamping.rst",
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"user/manual/model/eleLoad.rst",

source/user/guides/conventions.rst

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.. _conventions:
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Conventions
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^^^^^^^^^^^
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Degrees of Freedom
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------------------
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Several commands may accept an integer argument to specify a degree of freedom (DOF) in the model.
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This is always a 1-based index, meaning that the first DOF is 1, the second DOF is 2, and so on (as opposed to 0-based indexing, which is common in some programming languages).
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The DOFs are ordered as follows:
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.. csv-table::
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:header: "ndm", "ndf", "Order of components"
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:widths: 10, 10, 40
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1, 1, "u1"
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2, 2, "u1, u2"
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3, 3, "u1, u2, u3"
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2, 3, "u1, u2, r3"
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3, 6, "u1, u2, u3, r1, r2, r3"
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3, 6+n, "u1, u2, u3, r1, r2, r3, d4, d5, ..., d6+n"
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where:
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* ``u1, u2, u3`` are the translational displacements in the x, y, and z directions respectively,
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* ``r1, r2, r3`` are the rotational displacements about the x, y, and z axes respectively.
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source/user/guides/index.rst

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@@ -8,5 +8,6 @@ For a great guide to Tcl programming, see `this <https://antirez.com/articoli/tc
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:maxdepth: 1
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install
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conventions
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signatures
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references

source/user/manual/analysis/analysis.rst

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analysis
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^^^^^^^^
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This is the command issued to configure an analysis.
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.. tabs::
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.. tab:: Python

source/user/manual/analysis/codeExample/responseSpectrumAnalysisExample.py

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from opensees import *
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from opensees.openseespy import *
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from math import sqrt
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wipe()

source/user/manual/analysis/codeExample/responseSpectrumAnalysisExample.tcl

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@@ -5,27 +5,27 @@ model basic -ndm 3 -ndf 6
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# the response spectrum function
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set Tn {0.0 0.06 0.1 0.12 0.18 0.24 0.3 0.36 0.4 0.42 \
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0.48 0.54 0.6 0.66 0.72 0.78 0.84 0.9 0.96 1.02 \
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1.08 1.14 1.2 1.26 1.32 1.38 1.44 1.5 1.56 1.62 \
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1.68 1.74 1.8 1.86 1.92 1.98 2.04 2.1 2.16 2.22 \
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2.28 2.34 2.4 2.46 2.52 2.58 2.64 2.7 2.76 2.82 \
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2.88 2.94 3.0 3.06 3.12 3.18 3.24 3.3 3.36 3.42 \
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3.48 3.54 3.6 3.66 3.72 3.78 3.84 3.9 3.96 4.02 \
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4.08 4.14 4.2 4.26 4.32 4.38 4.44 4.5 4.56 4.62 \
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4.68 4.74 4.8 4.86 4.92 4.98 5.04 5.1 5.16 5.22 \
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5.28 5.34 5.4 5.46 5.52 5.58 5.64 5.7 5.76 5.82 \
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5.88 5.94 6.0}
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0.48 0.54 0.6 0.66 0.72 0.78 0.84 0.9 0.96 1.02 \
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1.08 1.14 1.2 1.26 1.32 1.38 1.44 1.5 1.56 1.62 \
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1.68 1.74 1.8 1.86 1.92 1.98 2.04 2.1 2.16 2.22 \
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2.28 2.34 2.4 2.46 2.52 2.58 2.64 2.7 2.76 2.82 \
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2.88 2.94 3.0 3.06 3.12 3.18 3.24 3.3 3.36 3.42 \
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3.48 3.54 3.6 3.66 3.72 3.78 3.84 3.9 3.96 4.02 \
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4.08 4.14 4.2 4.26 4.32 4.38 4.44 4.5 4.56 4.62 \
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4.68 4.74 4.8 4.86 4.92 4.98 5.04 5.1 5.16 5.22 \
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5.28 5.34 5.4 5.46 5.52 5.58 5.64 5.7 5.76 5.82 \
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5.88 5.94 6.0}
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set Sa {1.9612 3.72628 4.903 4.903 4.903 4.903 4.903 4.903 4.903 4.6696172 \
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4.0861602 3.6321424 3.2683398 2.971218 2.7241068 2.5142584 2.3348086 2.1788932 2.0425898 1.9229566 \
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1.8160712 1.7199724 1.6346602 1.5562122 1.485609 1.4208894 1.3620534 1.3071398 1.2571292 1.211041 \
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1.166914 1.1267094 1.0894466 1.054145 1.0217852 0.990406 0.960988 0.9335312 0.9080356 0.8835206 \
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0.8599862 0.838413 0.8168398 0.7972278 0.7785964 0.759965 0.7432948 0.7266246 0.710935 0.6952454 \
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0.6805364 0.666808 0.6540602 0.6285646 0.6040496 0.5814958 0.5609032 0.5403106 0.5206986 0.5030478 \
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0.485397 0.4697074 0.4540178 0.4393088 0.4255804 0.411852 0.3991042 0.3863564 0.3755698 0.3638026 \
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0.353016 0.34321 0.333404 0.3245786 0.3157532 0.3069278 0.2981024 0.2902576 0.2833934 0.2755486 \
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0.2686844 0.2618202 0.254956 0.2490724 0.2431888 0.2373052 0.2314216 0.2265186 0.220635 0.215732 \
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0.210829 0.205926 0.2020036 0.1971006 0.1931782 0.1892558 0.1853334 0.181411 0.1774886 0.1735662 \
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0.1706244 0.166702 0.1637602}
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4.0861602 3.6321424 3.2683398 2.971218 2.7241068 2.5142584 2.3348086 2.1788932 2.0425898 1.9229566 \
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1.8160712 1.7199724 1.6346602 1.5562122 1.485609 1.4208894 1.3620534 1.3071398 1.2571292 1.211041 \
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1.166914 1.1267094 1.0894466 1.054145 1.0217852 0.990406 0.960988 0.9335312 0.9080356 0.8835206 \
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0.8599862 0.838413 0.8168398 0.7972278 0.7785964 0.759965 0.7432948 0.7266246 0.710935 0.6952454 \
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0.6805364 0.666808 0.6540602 0.6285646 0.6040496 0.5814958 0.5609032 0.5403106 0.5206986 0.5030478 \
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0.485397 0.4697074 0.4540178 0.4393088 0.4255804 0.411852 0.3991042 0.3863564 0.3755698 0.3638026 \
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0.353016 0.34321 0.333404 0.3245786 0.3157532 0.3069278 0.2981024 0.2902576 0.2833934 0.2755486 \
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0.2686844 0.2618202 0.254956 0.2490724 0.2431888 0.2373052 0.2314216 0.2265186 0.220635 0.215732 \
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0.210829 0.205926 0.2020036 0.1971006 0.1931782 0.1892558 0.1853334 0.181411 0.1774886 0.1735662 \
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0.1706244 0.166702 0.1637602}
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timeSeries Path 1 -time $Tn -values $Sa
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# a uniaxial material for transverse shear
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set scalf [lrepeat [llength $eigs] 1.0]
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# CQC function
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proc CQC {mu lambdas dmp scalf} {
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set u 0.0
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set ne [llength $lambdas]
149-
for {set i 0} {$i < $ne} {incr i} {
150-
for {set j 0} {$j < $ne} {incr j} {
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set di [lindex $dmp $i]
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set dj [lindex $dmp $j]
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set bij [expr [lindex $lambdas $i]/[lindex $lambdas $j]]
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set rho [expr \
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((8.0*sqrt($di*$dj)*($di+$bij*$dj)*($bij**(3.0/2.0))) / \
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(pow(1.0-$bij**2.0,2.0) + 4.0*$di*$dj*$bij*(1.0+pow($bij,2.0)) + \
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4.0*(pow($di,2.0) + pow($dj,2.0))*pow($bij,2.0)))]
158-
set u [expr $u + [lindex $scalf $i]*[lindex $mu $i] * [lindex $scalf $j]*[lindex $mu $j] * $rho]
159-
}
160-
}
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return [expr sqrt($u)]
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set u 0.0
148+
set ne [llength $lambdas]
149+
for {set i 0} {$i < $ne} {incr i} {
150+
for {set j 0} {$j < $ne} {incr j} {
151+
set di [lindex $dmp $i]
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set dj [lindex $dmp $j]
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set bij [expr [lindex $lambdas $i]/[lindex $lambdas $j]]
154+
set rho [expr \
155+
((8.0*sqrt($di*$dj)*($di+$bij*$dj)*($bij**(3.0/2.0))) / \
156+
(pow(1.0-$bij**2.0,2.0) + 4.0*$di*$dj*$bij*(1.0+pow($bij,2.0)) + \
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4.0*(pow($di,2.0) + pow($dj,2.0))*pow($bij,2.0)))]
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set u [expr $u + [lindex $scalf $i]*[lindex $mu $i] * [lindex $scalf $j]*[lindex $mu $j] * $rho]
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}
160+
}
161+
return [expr sqrt($u)]
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}
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# ========================================================================
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set f [open $filename "r"]
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set lines [split [read $f] "\n"]
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foreach line $lines {
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if {[llength $line] > 0} {
179-
set tokens [split $line " "]
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lappend My [lindex $tokens 2]
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}
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if {[llength $line] > 0} {
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set tokens [split $line " "]
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lappend My [lindex $tokens 2]
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}
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}
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close $f
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puts "Use Tn and Sa lists.\n"
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puts [format "%10s %15s" "Mode" "My"]
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for {set i 0} {$i < [llength $eigs]} {incr i} {
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puts [format "%10g %15f" [expr $i+1] [lindex $My $i]]
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puts [format "%10g %15f" [expr $i+1] [lindex $My $i]]
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}
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puts [format "%10s %15f" "CQC" $MyCQC]
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set f [open $filename "r"]
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set lines [split [read $f] "\n"]
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foreach line $lines {
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if {[llength $line] > 0} {
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set tokens [split $line " "]
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lappend My [lindex $tokens 2]
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}
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if {[llength $line] > 0} {
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set tokens [split $line " "]
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lappend My [lindex $tokens 2]
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}
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close $f
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puts [format "%10s %15s" "Mode" "My"]
225225
for {set i 0} {$i < [llength $eigs]} {incr i} {
226-
puts [format "%10g %15f" [expr $i+1] [lindex $My $i]]
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puts [format "%10g %15f" [expr $i+1] [lindex $My $i]]
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}
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puts [format "%10s %15f" "CQC" $MyCQC]
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remove recorder 0
237237
set My {}
238238
for {set i 0} {$i < [llength $eigs]} {incr i} {
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responseSpectrumAnalysis $direction -Tn $Tn -Sa $Sa -mode [expr $i+1]
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set force [eleResponse 1 section 1 force]
241-
lappend My [lindex $force 2]
239+
responseSpectrumAnalysis $direction -Tn $Tn -Sa $Sa -mode [expr $i+1]
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set force [eleResponse 1 section 1 force]
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lappend My [lindex $force 2]
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# post process the results doing the CQC modal combination for the My response (3rd column in section forces)
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puts "Grab results during the loop and do CQC combination with them.\n"
248248
puts [format "%10s %15s" "Mode" "My"]
249249
for {set i 0} {$i < [llength $eigs]} {incr i} {
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250+
puts [format "%10g %15f" [expr $i+1] [lindex $My $i]]
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source/user/manual/analysis/index.rst

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algorithm
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analyze
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constraints
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numberer
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system
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test
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eigen
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..
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analysis/modalProperties
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analysis/responseSpectrumAnalysis
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modalProperties
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responseSpectrumAnalysis
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..
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numberer
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source/user/manual/analysis/integrator.rst

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:caption: Transient Integrators
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:maxdepth: 1
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integrator/CentralDifference
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integrator/Newmark
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integrator/HHT
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integrator/GeneralizedAlpha
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integrator/TRBDF2
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integrator/ExplicitDifference
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..
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integrator/CentralDifference
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integrator/HHT
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integrator/ExplicitDifference
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References
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----------

source/user/manual/analysis/integrator/GeneralizedAlpha.rst

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.. _GeneralizedAlphaMethod:
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Generalized Alpha Method
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^^^^^^^^^^^^^^^^^^^^^^^^
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Generalized Alpha
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^^^^^^^^^^^^^^^^^
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.. function:: integrator GeneralizedAlpha $alphaM $alphaF <$gamma $beta>
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source/user/manual/analysis/modalProperties.rst

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.. _modalProperties:
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modalProperties
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***************
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^^^^^^^^^^^^^^^
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This command is used to compute the modal properties of a model after an :ref:`eigen`.
77
This command computes the following modal properties:
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1313
* :math:`MPF` : The modal participation factors.
1414
* :math:`MPM` : The modal participation masses.
1515
* :math:`MPMc` : The cumulative modal participation masses.
16-
* :math:`MPM\left(\%\right)` : The modal participation masse ratios.
16+
* :math:`MPM\left(\%\right)` : The modal participation masse ratios.
1717
* :math:`MPMc\left(\%\right)` : The cumulative modal participation masse ratios.
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1919
.. function:: modalProperties <-print> <-return> <-file $reportFileName> <-unorm>
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181181
* Only the values in :math:`gm` and :math:`MPF` depend on the normalization of the eigenvectors. This normalization depends on the solver used in the :ref:`eigen`. The default -genBandArpack uses a mass-normalization, so that the :math:`gm` is the identity. On the contrary, the -fullGenLapack uses a displacement-normalization, so that the largest component of the eigenvector is 1. If you use the -genBandArpack, but want a displacement-normalization of the eigenvectors, use the **-unorm** option.
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183183
Theory
184-
^^^^^^
184+
======
185185
The eigenvalues :math:`\lambda` and the eigenvectors :math:`\Phi` can be obtained after solving the *generalized eigenvalue problem* for two symmetric matrices :math:`K` (stiffness) and :math:`M` (mass) given by:
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.. math::

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