def modal_response(numEigen):
# calculate eigenvalues
eigenValues = op.eigen(
'-genBandArpack',
numEigen) #can be either of: {'-genBandArpack', '-fullGenLapack'}
return eigenValues
def eigen(self, struct, mode_count=1):
"""
Perform a modal analysis and get the vibration periods of the structure.
Parameters
----------
struct: Structure
The structure or system to analyze.
mode_count: int, optional
The number of vibration modes to evaluate. Default: 1.
Returns
-------
T_list: Series
A list of vibration periods corresponding to the requested number of
vibration modes.
"""
# initialize the analysis
self._initialize()
# define the structure - remove damping
struct = deepcopy(struct)
struct.xi = 0.
struct.create_FEM()
eigens = ops.eigen('-fullGenLapack', mode_count)
T_list = 2 * np.pi / np.sqrt(np.array(eigens))
return pd.Series(T_list, index=np.arange(1, mode_count + 1))
def test_ElasticFrame():
#
# some parameter
#
PI = 2.0 * asin(1.0)
g = 386.4
ft = 12.0
Load1 = 1185.0
Load2 = 1185.0
Load3 = 970.0
# floor masses
m1 = Load1 / (4 * g) # 4 nodes per floor
m2 = Load2 / (4 * g)
m3 = Load3 / (4 * g)
# floor distributed loads
w1 = Load1 / (90 * ft) # frame 90 ft long
w2 = Load2 / (90 * ft)
w3 = Load3 / (90 * ft)
# ------------------------------
# Start of model generation
# ------------------------------
# Remove existing model
ops.wipe()
# Create ModelBuilder (with two-dimensions and 2 DOF/node)
ops.model('BasicBuilder', '-ndm', 2, '-ndf', 3)
# Create nodes
# ------------
# Create nodes & add to Domain - command: node nodeId xCrd yCrd <-mass massX massY massRz>
# NOTE: mass in optional
ops.node(1, 0.0, 0.0)
ops.node(2, 360.0, 0.0)
ops.node(3, 720.0, 0.0)
ops.node(4, 1080.0, 0.0)
ops.node(5, 0.0, 162.0, '-mass', m1, m1, 0.0)
ops.node(6, 360.0, 162.0, '-mass', m1, m1, 0.0)
ops.node(7, 720.0, 162.0, '-mass', m1, m1, 0.0)
ops.node(8, 1080.0, 162.0, '-mass', m1, m1, 0.0)
ops.node(9, 0.0, 324.0, '-mass', m2, m2, 0.0)
ops.node(10, 360.0, 324.0, '-mass', m2, m2, 0.0)
ops.node(11, 720.0, 324.0, '-mass', m2, m2, 0.0)
ops.node(12, 1080.0, 324.0, '-mass', m2, m2, 0.0)
ops.node(13, 0.0, 486.0, '-mass', m3, m3, 0.0)
ops.node(14, 360.0, 486.0, '-mass', m3, m3, 0.0)
ops.node(15, 720.0, 486.0, '-mass', m3, m3, 0.0)
ops.node(16, 1080.0, 486.0, '-mass', m3, m3, 0.0)
# the boundary conditions - command: fix nodeID xResrnt? yRestrnt? rZRestrnt?
ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
ops.fix(3, 1, 1, 1)
ops.fix(4, 1, 1, 1)
# Define geometric transformations for beam-column elements
ops.geomTransf('Linear', 1) # beams
ops.geomTransf('PDelta', 2) # columns
# Define elements
# Create elastic beam-column - command: element elasticBeamColumn eleID node1 node2 A E Iz geomTransfTag
# Define the Columns
ops.element('elasticBeamColumn', 1, 1, 5, 75.6, 29000.0, 3400.0,
2) # W14X257
ops.element('elasticBeamColumn', 2, 5, 9, 75.6, 29000.0, 3400.0,
2) # W14X257
ops.element('elasticBeamColumn', 3, 9, 13, 75.6, 29000.0, 3400.0,
2) # W14X257
ops.element('elasticBeamColumn', 4, 2, 6, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 5, 6, 10, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 6, 10, 14, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 7, 3, 7, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 8, 7, 11, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 9, 11, 15, 91.4, 29000.0, 4330.0,
2) # W14X311
ops.element('elasticBeamColumn', 10, 4, 8, 75.6, 29000.0, 3400.0,
2) # W14X257
ops.element('elasticBeamColumn', 11, 8, 12, 75.6, 29000.0, 3400.0,
2) # W14X257
ops.element('elasticBeamColumn', 12, 12, 16, 75.6, 29000.0, 3400.0,
2) # W14X257
# Define the Beams
ops.element('elasticBeamColumn', 13, 5, 6, 34.7, 29000.0, 5900.0,
1) # W33X118
ops.element('elasticBeamColumn', 14, 6, 7, 34.7, 29000.0, 5900.0,
1) # W33X118
ops.element('elasticBeamColumn', 15, 7, 8, 34.7, 29000.0, 5900.0,
1) # W33X118
ops.element('elasticBeamColumn', 16, 9, 10, 34.2, 29000.0, 4930.0,
1) # W30X116
ops.element('elasticBeamColumn', 17, 10, 11, 34.2, 29000.0, 4930.0,
1) # W30X116
ops.element('elasticBeamColumn', 18, 11, 12, 34.2, 29000.0, 4930.0,
1) # W30X116
ops.element('elasticBeamColumn', 19, 13, 14, 20.1, 29000.0, 1830.0,
1) # W24X68
ops.element('elasticBeamColumn', 20, 14, 15, 20.1, 29000.0, 1830.0,
1) # W24X68
ops.element('elasticBeamColumn', 21, 15, 16, 20.1, 29000.0, 1830.0,
1) # W24X68
# Define loads for Gravity Analysis
# ---------------------------------
#create a Linear TimeSeries (load factor varies linearly with time): command timeSeries Linear tag
ops.timeSeries('Linear', 1)
# Create a Plain load pattern with a linear TimeSeries:
# command pattern Plain tag timeSeriesTag { loads }
ops.pattern('Plain', 1, 1)
ops.eleLoad('-ele', 13, 14, 15, '-type', '-beamUniform', -w1)
ops.eleLoad('-ele', 16, 17, 18, '-type', '-beamUniform', -w2)
ops.eleLoad('-ele', 19, 20, 21, '-type', '-beamUniform', -w3)
# ---------------------------------
# Create Analysis for Gravity Loads
# ---------------------------------
# Create the system of equation, a SPD using a band storage scheme
ops.system('BandSPD')
# Create the DOF numberer, the reverse Cuthill-McKee algorithm
ops.numberer('RCM')
# Create the constraint handler, a Plain handler is used as h**o constraints
ops.constraints('Plain')
# Create the integration scheme, the LoadControl scheme using steps of 1.0
ops.integrator('LoadControl', 1.0)
# Create the solution algorithm, a Linear algorithm is created
ops.test('NormDispIncr', 1.0e-10, 6)
ops.algorithm('Newton')
# create the analysis object
ops.analysis('Static')
# ---------------------------------
# Perform Gravity Analysis
# ---------------------------------
ops.analyze(1)
# print "node 5: nodeDisp 5"
# print "node 6: nodeDisp 6"
# print "node 7: nodeDisp 7"
# print "node 8: nodeDisp 8"
# print "node 9: nodeDisp 9"
# print "node 10: nodeDisp 10"
# ---------------------------------
# Check Equilibrium
# ---------------------------------
# invoke command to determine nodal reactions
ops.reactions()
node1Rxn = ops.nodeReaction(
1
) # nodeReaction command returns nodal reactions for specified node in a list
node2Rxn = ops.nodeReaction(2)
node3Rxn = ops.nodeReaction(3)
node4Rxn = ops.nodeReaction(4)
inputedFy = -Load1 - Load2 - Load3 # loads added negative Fy diren to ele
computedFx = node1Rxn[0] + node2Rxn[0] + node3Rxn[0] + node4Rxn[0]
computedFy = node1Rxn[1] + node2Rxn[1] + node3Rxn[1] + node4Rxn[1]
print("\nEqilibrium Check After Gravity:")
print("SumX: Inputed: 0.0 + Computed:", computedFx, " = ",
0.0 + computedFx)
print("SumY: Inputed: ", inputedFy, " + Computed: ", computedFy, " = ",
inputedFy + computedFy)
# ---------------------------------
# Lateral Load
# ---------------------------------
# gravity loads constant and time in domain to e 0.0
ops.loadConst('-time', 0.0)
ops.timeSeries('Linear', 2)
ops.pattern('Plain', 2, 2)
ops.load(13, 220.0, 0.0, 0.0)
ops.load(9, 180.0, 0.0, 0.0)
ops.load(5, 90.0, 0.0, 0.0)
# ---------------------------------
# Create Recorder
# ---------------------------------
#recorder Element -file EleForces.out -ele 1 4 7 10 forces
# ---------------------------------
# Perform Lateral Analysis
# ---------------------------------
ops.analyze(1)
# print "node 5: nodeDisp 5"
# print "node 6: nodeDisp 6"
# print "node 7: nodeDisp 7"
# print "node 8: nodeDisp 8"
# print "node 9: nodeDisp 9"
# print "node 10: nodeDisp 10"
# ---------------------------------
# Check Equilibrium
# ---------------------------------
ops.reactions()
node1Rxn = ops.nodeReaction(
1
) # =nodeReaction( command returns nodal reactions for specified node in a list
node2Rxn = ops.nodeReaction(2)
node3Rxn = ops.nodeReaction(3)
node4Rxn = ops.nodeReaction(4)
inputedFx = 220.0 + 180.0 + 90.0
computedFx = node1Rxn[0] + node2Rxn[0] + node3Rxn[0] + node4Rxn[0]
computedFy = node1Rxn[1] + node2Rxn[1] + node3Rxn[1] + node4Rxn[1]
print("\nEqilibrium Check After Lateral Loads:")
print("SumX: Inputed: ", inputedFx, " + Computed: ", computedFx, " = ",
inputedFx + computedFx)
print("SumY: Inputed: ", inputedFy, " + Computed: ", computedFy, " = ",
inputedFy + computedFy)
# print ele information for columns at base
#print ele 1 4 7 10
# ---------------------------------
# Check Eigenvalues
# ---------------------------------
eigenValues = ops.eigen(5)
print("\nEigenvalues:")
eigenValue = eigenValues[0]
T1 = 2 * PI / sqrt(eigenValue)
print("T1 = ", T1)
eigenValue = eigenValues[1]
T2 = 2 * PI / sqrt(eigenValue)
print("T2 = ", T2)
eigenValue = eigenValues[2]
T3 = 2 * PI / sqrt(eigenValue)
print("T3 = ", T3)
eigenValue = eigenValues[3]
T4 = 2 * PI / sqrt(eigenValue)
print("T4 = ", T4)
eigenValue = eigenValues[4]
T5 = 2 * PI / sqrt(eigenValue)
print("T5 = ", T5)
assert abs(T1 - 1.0401120938612862) < 1e-12 and abs(
T2 - 0.3526488583606463
) < 1e-12 and abs(T3 - 0.1930409642350476) < 1e-12 and abs(
T4 - 0.15628823050715784) < 1e-12 and abs(T5 -
0.13080166151268388) < 1e-12
#recorder Node -file eigenvector.out -nodeRange 5 16 -dof 1 2 3 eigen 0
#record
print("==========================")
# --------------------------------------------------------------------------------------------------
# OpenSees (Tcl) code by: Silvia Mazzoni & Frank McKenna, 2006
##########################################################################################################################################################################
import openseespy.opensees as op
#import the os module
#import os
import math
op.wipe()
#########################################################################################################################################################################
import InelasticFiberSection
#applying Dynamic Ground motion analysis
Tol = 1e-8
GMdirection = 1
GMfile = 'BM68elc.acc'
GMfact = 1.0
Lambda = op.eigen('-fullGenLapack', 1) # eigenvalue mode 1
Omega = math.pow(Lambda, 0.5)
betaKcomm = 2 * (0.02 / Omega)
xDamp = 0.02 # 2% damping ratio
alphaM = 0.0 # M-prop. damping; D = alphaM*M
betaKcurr = 0.0 # K-proportional damping; +beatKcurr*KCurrent
betaKinit = 0.0 # initial-stiffness proportional damping +beatKinit*Kini
op.rayleigh(alphaM, betaKcurr, betaKinit, betaKcomm) # RAYLEIGH damping
# Uniform EXCITATION: acceleration input
IDloadTag = 400 # load tag
dt = 0.01 # time step for input ground motion
GMfatt = 1.0 # data in input file is in g Unifts -- ACCELERATION TH
maxNumIter = 10
# Create the solution algorithm, a Newton-Raphson algorithm
ops.algorithm('Newton')
# Create the DOF numberer, the reverse Cuthill-McKee algorithm
ops.numberer('RCM')
# Create the integration scheme, the Newmark with alpha =0.5 and beta =.25
ops.integrator('Newmark', 0.5, 0.25)
# Create the analysis object
ops.analysis('Transient')
# Perform an eigenvalue analysis
numEigen = 2
eigenValues = ops.eigen(numEigen)
print("eigen values at start of transient:", eigenValues)
# set some variables
tFinal = nPts * dt
tCurrent = ops.getTime()
ok = 0
time = [tCurrent]
u3 = [0.0]
# Perform the transient analysis
while ok == 0 and tCurrent < tFinal:
ok = ops.analyze(1, .01)
def test_PortalFrame2d():
# set some properties
print("================================================")
print("PortalFrame2d.py: Verification 2d Elastic Frame")
print(" - eigenvalue and static pushover analysis")
ops.wipe()
ops.model('Basic', '-ndm', 2)
# properties
# units kip, ft
numBay = 2
numFloor = 7
bayWidth = 360.0
storyHeights = [162.0, 162.0, 156.0, 156.0, 156.0, 156.0, 156.0]
E = 29500.0
massX = 0.49
M = 0.
coordTransf = "Linear" # Linear, PDelta, Corotational
massType = "-lMass" # -lMass, -cMass
beams = [
'W24X160', 'W24X160', 'W24X130', 'W24X130', 'W24X110', 'W24X110',
'W24X110'
]
eColumn = [
'W14X246', 'W14X246', 'W14X246', 'W14X211', 'W14X211', 'W14X176',
'W14X176'
]
iColumn = [
'W14X287', 'W14X287', 'W14X287', 'W14X246', 'W14X246', 'W14X211',
'W14X211'
]
columns = [eColumn, iColumn, eColumn]
WSection = {
'W14X176': [51.7, 2150.],
'W14X211': [62.1, 2670.],
'W14X246': [72.3, 3230.],
'W14X287': [84.4, 3910.],
'W24X110': [32.5, 3330.],
'W24X130': [38.3, 4020.],
'W24X160': [47.1, 5120.]
}
nodeTag = 1
# procedure to read
def ElasticBeamColumn(eleTag, iNode, jNode, sectType, E, transfTag, M,
massType):
found = 0
prop = WSection[sectType]
A = prop[0]
I = prop[1]
ops.element('elasticBeamColumn', eleTag, iNode, jNode, A, E, I,
transfTag, '-mass', M, massType)
# add the nodes
# - floor at a time
yLoc = 0.
for j in range(0, numFloor + 1):
xLoc = 0.
for i in range(0, numBay + 1):
ops.node(nodeTag, xLoc, yLoc)
xLoc += bayWidth
nodeTag += 1
if j < numFloor:
storyHeight = storyHeights[j]
yLoc += storyHeight
# fix first floor
ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
ops.fix(3, 1, 1, 1)
#rigid floor constraint & masses
nodeTagR = 5
nodeTag = 4
for j in range(1, numFloor + 1):
for i in range(0, numBay + 1):
if nodeTag != nodeTagR:
ops.equalDOF(nodeTagR, nodeTag, 1)
else:
ops.mass(nodeTagR, massX, 1.0e-10, 1.0e-10)
nodeTag += 1
nodeTagR += numBay + 1
# add the columns
# add column element
ops.geomTransf(coordTransf, 1)
eleTag = 1
for j in range(0, numBay + 1):
end1 = j + 1
end2 = end1 + numBay + 1
thisColumn = columns[j]
for i in range(0, numFloor):
secType = thisColumn[i]
ElasticBeamColumn(eleTag, end1, end2, secType, E, 1, M, massType)
end1 = end2
end2 += numBay + 1
eleTag += 1
# add beam elements
for j in range(1, numFloor + 1):
end1 = (numBay + 1) * j + 1
end2 = end1 + 1
secType = beams[j - 1]
for i in range(0, numBay):
ElasticBeamColumn(eleTag, end1, end2, secType, E, 1, M, massType)
end1 = end2
end2 = end1 + 1
eleTag += 1
# calculate eigenvalues & print results
numEigen = 7
eigenValues = ops.eigen(numEigen)
PI = 2 * asin(1.0)
#
# apply loads for static analysis & perform analysis
#
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(22, 20.0, 0., 0.)
ops.load(19, 15.0, 0., 0.)
ops.load(16, 12.5, 0., 0.)
ops.load(13, 10.0, 0., 0.)
ops.load(10, 7.5, 0., 0.)
ops.load(7, 5.0, 0., 0.)
ops.load(4, 2.5, 0., 0.)
ops.integrator('LoadControl', 1.0)
ops.algorithm('Linear')
ops.analysis('Static')
ops.analyze(1)
# determine PASS/FAILURE of test
ok = 0
#
# print pretty output of comparsions
#
# SAP2000 SeismoStruct
comparisonResults = [[
1.2732, 0.4313, 0.2420, 0.1602, 0.1190, 0.0951, 0.0795
], [1.2732, 0.4313, 0.2420, 0.1602, 0.1190, 0.0951, 0.0795]]
print("\n\nPeriod Comparisons:")
print('{:>10}{:>15}{:>15}{:>15}'.format('Period', 'OpenSees', 'SAP2000',
'SeismoStruct'))
#formatString {%10s%15.5f%15.4f%15.4f}
for i in range(0, numEigen):
lamb = eigenValues[i]
period = 2 * PI / sqrt(lamb)
print('{:>10}{:>15.5f}{:>15.4f}{:>15.4f}'.format(
i + 1, period, comparisonResults[0][i], comparisonResults[1][i]))
resultOther = comparisonResults[0][i]
if abs(period - resultOther) > 9.99e-5:
ok = -1
# print table of camparsion
# Parameter SAP2000 SeismoStruct
comparisonResults = [[
"Disp Top", "Axial Force Bottom Left", "Moment Bottom Left"
], [1.45076, 69.99, 2324.68], [1.451, 70.01, 2324.71]]
tolerances = [9.99e-6, 9.99e-3, 9.99e-3]
print("\n\nSatic Analysis Result Comparisons:")
print('{:>30}{:>15}{:>15}{:>15}'.format('Parameter', 'OpenSees', 'SAP2000',
'SeismoStruct'))
for i in range(3):
response = ops.eleResponse(1, 'forces')
if i == 0:
result = ops.nodeDisp(22, 1)
elif i == 1:
result = abs(response[1])
else:
result = response[2]
print('{:>30}{:>15.3f}{:>15.2f}{:>15.2f}'.format(
comparisonResults[0][i], result, comparisonResults[1][i],
comparisonResults[2][i]))
resultOther = comparisonResults[1][i]
tol = tolerances[i]
if abs(result - resultOther) > tol:
ok = -1
print("failed-> ", i, abs(result - resultOther), tol)
assert ok == 0
def test_Ex1aCanti2DEQmodif():
# SET UP ----------------------------------------------------------------------------
ops.wipe() # clear opensees model
ops.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
# file mkdir data # create data directory
# define GEOMETRY -------------------------------------------------------------
# nodal coordinates:
ops.node(1, 0., 0.) # node#, X Y
ops.node(2, 0., 432.)
# Single point constraints -- Boundary Conditions
ops.fix(1, 1, 1, 1) # node DX DY RZ
# nodal masses:
ops.mass(2, 5.18, 0., 0.) # node#, Mx My Mz, Mass=Weight/g.
# Define ELEMENTS -------------------------------------------------------------
# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
ops.geomTransf('Linear', 1) # associate a tag to transformation
# connectivity:
ops.element('elasticBeamColumn', 1, 1, 2, 3600.0, 3225.0, 1080000.0, 1)
# define GRAVITY -------------------------------------------------------------
ops.timeSeries('Linear', 1)
ops.pattern(
'Plain',
1,
1,
)
ops.load(2, 0., -2000., 0.) # node#, FX FY MZ -- superstructure-weight
ops.constraints('Plain') # how it handles boundary conditions
ops.numberer(
'Plain'
) # renumber dof's to minimize band-width (optimization), if you want to
ops.system(
'BandGeneral'
) # how to store and solve the system of equations in the analysis
ops.algorithm('Linear') # use Linear algorithm for linear analysis
ops.integrator(
'LoadControl', 0.1
) # determine the next time step for an analysis, # apply gravity in 10 steps
ops.analysis('Static') # define type of analysis static or transient
ops.analyze(10) # perform gravity analysis
ops.loadConst('-time', 0.0) # hold gravity constant and restart time
# DYNAMIC ground-motion analysis -------------------------------------------------------------
# create load pattern
G = 386.0
ops.timeSeries(
'Path', 2, '-dt', 0.005, '-filePath', 'A10000.dat', '-factor', G
) # define acceleration vector from file (dt=0.005 is associated with the input file gm)
ops.pattern(
'UniformExcitation', 2, 1, '-accel',
2) # define where and how (pattern tag, dof) acceleration is applied
# set damping based on first eigen mode
evals = ops.eigen('-fullGenLapack', 1)
freq = evals[0]**0.5
dampRatio = 0.02
ops.rayleigh(0., 0., 0., 2 * dampRatio / freq)
# display displacement shape of the column
# recorder display "Displaced shape" 10 10 500 500 -wipe
# prp 200. 50. 1
# vup 0 1 0
# vpn 0 0 1
# display 1 5 40
# create the analysis
ops.wipeAnalysis() # clear previously-define analysis parameters
ops.constraints('Plain') # how it handles boundary conditions
ops.numberer(
'Plain'
) # renumber dof's to minimize band-width (optimization), if you want to
ops.system(
'BandGeneral'
) # how to store and solve the system of equations in the analysis
ops.algorithm('Linear') # use Linear algorithm for linear analysis
ops.integrator('Newmark', 0.5,
0.25) # determine the next time step for an analysis
ops.analysis('Transient') # define type of analysis: time-dependent
ops.analyze(3995, 0.01) # apply 3995 0.01-sec time steps in analysis
u2 = ops.nodeDisp(2, 2)
print("u2 = ", u2)
assert abs(u2 + 0.07441860465116277579) < 1e-12
ops.wipe()
print("=========================================")
def ModalAnalysis3D(numEigen):
"""
|-----------------------------------------------------------------------|
| |
| Modal Analysis of 3D systems |
| |
| Author: Volkan Ozsarac |
| Affiliation: University School for Advanced Studies IUSS Pavia |
| Earthquake Engineering PhD Candidate |
| |
|-----------------------------------------------------------------------|
"""
import numpy as np
import openseespy.opensees as op
import time
import sys
print('Extracting the mass matrix, ignore the following warnings...\n')
op.wipeAnalysis()
op.system('FullGeneral')
op.analysis('Transient')
# Extract the Mass Matrix
op.integrator('GimmeMCK',1.0,0.0,0.0)
op.analyze(1,0.0)
time.sleep(0.5)
# Number of equations in the model
N = op.systemSize() # Has to be done after analyze
Mmatrix = op.printA('-ret') # Or use op.printA('-file','M.out')
Mmatrix = np.array(Mmatrix) # Convert the list to an array
Mmatrix.shape = (N,N) # Make the array an NxN matrix
print('\nExtracted the mass matrix, ignore the previous warnings...')
# Rerrange the mass matrix in accordance with nodelist order from getNodeTags()
DOFs = [] # These are the idx of all the DOFs used in the extract mass matrix, order is rearranged
used = {} # Save here the nodes and their associated dofs used in global mass matrix
lx = np.zeros([N,1]) # influence vector (x)
ly = np.zeros([N,1]) # influence vector (y)
lz = np.zeros([N,1]) # influence vector (z)
lrx = np.zeros([N,1]) # influence vector (rx)
lry = np.zeros([N,1]) # influence vector (ry)
lrz = np.zeros([N,1]) # influence vector (rz)
idx = 0 # index
NDF = 6 # NDF is number of DOFs/node
for node in op.getNodeTags():
used[node] = []
for j in range(NDF):
temp = op.nodeDOFs(node)[j]
if temp not in DOFs and temp >=0:
DOFs.append(op.nodeDOFs(node)[j])
used[node].append(j+1)
if j == 0: lx[idx,0] = 1
if j == 1: ly[idx,0] = 1
if j == 2: lz[idx,0] = 1
if j == 3: lrx[idx,0] = 1
if j == 4: lry[idx,0] = 1
if j == 5: lrz[idx,0] = 1
idx += 1
Mmatrix = Mmatrix[DOFs,:][:,DOFs]
op.wipeAnalysis()
listSolvers = ['-genBandArpack','-fullGenLapack','-symmBandLapack']
ok = 1
for s in listSolvers:
print("Using %s as solver..." % s[1:])
try:
eigenValues = op.eigen(s,numEigen)
catchOK = 0
ok = 0
except:
catchOK = 1
if catchOK==0:
for i in range(numEigen):
if eigenValues[i] < 0: ok = 1
if ok==0:
print('Eigenvalue analysis is completed.')
break
if ok!=0:
print("Error on Modal Analysis...")
sys.exit()
else:
Lamda = np.asarray(eigenValues)
Omega = Lamda**0.5
T = 2*np.pi/Omega
f = 1/T
print('Modal properties for the first %d modes:' % numEigen)
Mx = []; My = []; Mz = []; Mrx = []; Mry = []; Mrz = []
dofs = ['x','y','z','rx','ry','rz']
print('Mode| T [sec] | f [Hz] | \u03C9 [rad/sec] | Mx [%] | My [%] | Mz [%] | \u2211Mx [%] | \u2211My [%] | \u2211Mz [%]')
for mode in range(1,numEigen+1): # Although Mrx, Mry and Mrz are calculated, I am not printing these
idx = 0
phi = np.zeros([N,1])
for node in used:
for dof in used[node]:
phi[idx,0]=op.nodeEigenvector(node,mode,dof)
idx += 1
for dof in dofs:
l = eval('l'+dof)
Mtot = l.T@Mmatrix@l # Total mass in specified global dof
Mn = phi.T@Mmatrix@phi # Modal mass in specified global dof
Ln = phi.T@Mmatrix@l # Effective modal mass in specified global dof
Mnstar = Ln**2/Mn/Mtot*100 # Normalised effective modal mass participating [%], in specified global dof
eval('M'+dof).append(Mnstar[0,0]) # Save the modal mass for the specified dof
print('%3s |%7s |%6s |%9s |%6s |%6s |%6s |%7s |%7s |%7s' \
% ("{:.0f}".format(mode), "{:.3f}".format(T[mode-1]), "{:.3f}".format(f[mode-1]), "{:.2f}".format(Omega[mode-1]), \
"{:.2f}".format(Mx[mode-1]), "{:.2f}".format(My[mode-1]), "{:.2f}".format(Mz[mode-1]), \
"{:.2f}".format(sum(Mx)), "{:.2f}".format(sum(My)), "{:.2f}".format(sum(Mz))))
Mtot = lx.T@Mmatrix@lx; Mtot = Mtot[0,0]
def __init__(self):
# AIが取れるアクションの設定
self.action = np.array([
0, 0.02, 0.03, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1
])
self.naction = len(self.action)
self.beta = 1 / 4
# 1質点系モデル
self.T0 = 4
self.h = self.action[0]
self.hs = [self.h]
self.m = 100
self.k = 4 * np.pi**2 * self.m / self.T0**2
# 入力地震動
self.dt = 0.02
to_meter = 0.01 # cmをmに変換する値
self.wave_url = 'https://github.com/kakemotokeita/dqn-seismic-control/blob/master/wave/sample.csv'
with urllib.request.urlopen(self.wave_url) as wave_file:
self.wave_data = np.loadtxt(
wave_file, usecols=(0, ), delimiter=',', skiprows=3) * to_meter
# OpenSees設定
op.wipe()
op.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
# 節点
self.bot_node = 1
self.top_node = 2
op.node(self.bot_node, 0., 0.)
op.node(self.top_node, 0., 0.)
# 境界条件
op.fix(self.top_node, FREE, FIXED, FIXED)
op.fix(self.bot_node, FIXED, FIXED, FIXED)
op.equalDOF(1, 2, *[Y, ROTZ])
# 質量
op.mass(self.top_node, self.m, 0., 0.)
# 弾性剛性
elastic_mat_tag = 1
Fy = 1e10
E0 = self.k
b = 1.0
op.uniaxialMaterial('Steel01', elastic_mat_tag, Fy, E0, b)
# Assign zero length element
beam_tag = 1
op.element('zeroLength', beam_tag, self.bot_node, self.top_node,
"-mat", elastic_mat_tag, "-dir", 1, '-doRayleigh', 1)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
self.values = list(-1 * self.wave_data) # should be negative
op.timeSeries('Path', load_tag_dynamic, '-dt', self.dt, '-values',
*self.values)
op.pattern('UniformExcitation', pattern_tag_dynamic, X, '-accel',
load_tag_dynamic)
# 減衰の設定
self.w0 = op.eigen('-fullGenLapack', 1)[0]**0.5
self.alpha_m = 0.0
self.beta_k = 2 * self.h / self.w0
self.beta_k_init = 0.0
self.beta_k_comm = 0.0
op.rayleigh(self.alpha_m, self.beta_k, self.beta_k_init,
self.beta_k_comm)
# Run the dynamic analysis
op.wipeAnalysis()
op.algorithm('Newton')
op.system('SparseGeneral')
op.numberer('RCM')
op.constraints('Transformation')
op.integrator('Newmark', 0.5, 0.25)
op.analysis('Transient')
tol = 1.0e-10
iterations = 10
op.test('EnergyIncr', tol, iterations, 0, 2)
self.i_pre = 0
self.i = 0
self.i_next = 0
self.time = 0
self.analysis_time = (len(self.values) - 1) * self.dt
self.dis = 0
self.vel = 0
self.acc = 0
self.a_acc = 0
self.force = 0
self.resp = {
"time": [],
"dis": [],
"acc": [],
"a_acc": [],
"vel": [],
"force": [],
}
self.done = False
def build_model(model_params):
"""
Generates OpenSeesPy model of an elastic cantilever and runs gravity analysis.
Assumes that length is measured in inches and acceleration in in/s2
Parameters
----------
NumberOfStories: int
Number of stories
StructureType: string
Type of structural system - expects one of the HAZUS structure classes
PlanArea: float
Area of the structure's footprint
"""
# Assumptions
h_story = 12 # Story height [ft]
w_story = 200 # Story weight [psf]
# constants for unit conversion
ft = 1.0
inch = 12.0
m = 3.28084
ft2 = 1.0
inch2 = inch**2.
m2 = m**2.
psf = 1.0
Nsm = 4.88242 # N per square meter
stories = model_params["NumberOfStories"]
node_tags = list(range(stories + 1))
# The fundamental period is approximated as per ASCE 7-16 12.8.2.1
h_n = stories * h_story # [ft]
if model_params['StructureType'] in [
'S1',
]:
# steel moment-resisting frames
C_t = 0.028
x = 0.8
elif model_params['StructureType'] in [
'C1',
]:
# concrete moment-resisting frames
C_t = 0.016
x = 0.9
elif model_params['StructureType'] in ['BRBF', 'ECBF']:
# steel eccentrically braced frames or
# steel buckling-restrained braced frame
C_t = 0.03
x = 0.75
else:
C_t = 0.02
x = 0.75
T1 = C_t * h_n**x # Eq 12.8-7 in ASCE 7-16
# check the units
units = model_params["units"]
if 'length' in units.keys():
if units['length'] == 'm':
G = 9.81
h_story = h_story * m
w_story = w_story * Nsm
elif units['length'] == 'ft':
G = 32.174
h_story = h_story * ft
w_story = w_story / ft2
else: # elif units['length'] == 'in':
G = 386.1
h_story = h_story * inch
w_story = w_story / inch2
# The weight at each story is assumed to be identical
W = model_params["PlanArea"] * w_story
m = W / G
# We calculate stiffness assuming half of the mass vibrates at the top
K = ((m * stories) / 2.) / (T1 / (2 * pi))**2.
# set model dimensions and degrees of freedom
ops.model('basic', '-ndm', 3, '-ndf', 6)
# define an elastic and a rigid material
elastic_tag = 100
rigid_tag = 110
ops.uniaxialMaterial('Elastic', elastic_tag, K)
ops.uniaxialMaterial('Elastic', rigid_tag, 1.e9)
# define pattern for gravity loads
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 101, 1)
for story in range(0, stories + 1):
# define nodes
ops.node(node_tags[story], 0., 0., story * h_story)
# define fixities
if story == 0:
ops.fix(node_tags[0], 1, 1, 1, 1, 1, 1)
else:
ops.fix(node_tags[story], 0, 0, 0, 1, 1, 1)
# define elements
if story > 0:
element_tag = 1000 + story - 1
ops.element('twoNodeLink', element_tag, node_tags[story - 1],
node_tags[story], '-mat', rigid_tag, elastic_tag,
elastic_tag, '-dir', 1, 2, 3, '-orient', 0., 0., 1.,
0., 1., 0., '-doRayleigh')
# define masses
ops.mass(node_tags[story], m, m, m, 0., 0., 0.)
# define loads
ops.load(node_tags[story], 0., 0., -W, 0., 0., 0.)
# define damping based on first eigenmode
damp_ratio = 0.05
angular_freq = ops.eigen(1)[0]**0.5
beta_k = 2 * damp_ratio / angular_freq
ops.rayleigh(0., beta_k, 0., 0.)
# run gravity analysis
tol = 1e-8 # convergence tolerance for test
iter = 100 # max number of iterations
nstep = 100 # apply gravity loads in 10 steps
incr = 1. / nstep # first load increment
# analysis settings
ops.constraints(
'Transformation'
) # enforce boundary conditions using transformation constraint handler
ops.numberer(
'RCM') # renumbers dof's to minimize band-width (optimization)
ops.system(
'BandGeneral'
) # stores system of equations as 1D array of size bandwidth x number of unknowns
ops.test(
'EnergyIncr', tol, iter, 0
) # tests for convergence using dot product of solution vector and norm of right-hand side of matrix equation
ops.algorithm(
'Newton'
) # use Newton's solution algorithm: updates tangent stiffness at every iteration
ops.integrator(
'LoadControl', incr
) # determine the next time step for an analysis # apply gravity in 10 steps
ops.analysis('Static') # define type of analysis, static or transient
ops.analyze(nstep) # perform gravity analysis
# after gravity analysis, change time and tolerance for the dynamic analysis
ops.loadConst('-time', 0.0)
def get_inelastic_response(mass,
k_spring,
f_yield,
motion,
dt,
xi=0.05,
r_post=0.0):
"""
Run seismic analysis of a nonlinear SDOF
:param mass: SDOF mass
:param k_spring: spring stiffness
:param f_yield: yield strength
:param motion: list, acceleration values
:param dt: float, time step of acceleration values
:param xi: damping ratio
:param r_post: post-yield stiffness
:return:
"""
osi = o3.OpenSeesInstance(ndm=2)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
opy.fix(top_node.tag, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
opy.fix(bot_node.tag, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
opy.equalDOF(top_node.tag, bot_node.tag, *[o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
opy.mass(top_node.tag, mass, 0., 0.)
# Define material
bilinear_mat = o3.uniaxial_material.Steel01(osi,
fy=f_yield,
e0=k_spring,
b=r_post)
# Assign zero length element, # Note: pass actual node and material objects into element
o3.element.ZeroLength(osi, [bot_node, top_node],
mats=[bilinear_mat],
dirs=[o3.cc.DOF2D_X],
r_flag=1)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * motion) # should be negative
opy.timeSeries('Path', load_tag_dynamic, '-dt', dt, '-values', *values)
opy.pattern('UniformExcitation', pattern_tag_dynamic, o3.cc.X, '-accel',
load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = opy.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2**0.5
beta_k = 2 * xi / angular_freq
o3.rayleigh.Rayleigh(osi,
alpha_m=0.0,
beta_k=beta_k,
beta_k_init=0.0,
beta_k_comm=0.0)
# Run the dynamic analysis
opy.wipeAnalysis()
newmark_gamma = 0.5
newmark_beta = 0.25
o3.algorithm.Newton(osi)
o3.constraints.Transformation(osi)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.SparseGeneral(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = (len(values) - 1) * dt
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while opy.getTime() < analysis_time:
curr_time = opy.getTime()
opy.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(opy.nodeDisp(top_node.tag, o3.cc.X))
outputs["rel_vel"].append(opy.nodeVel(top_node.tag, o3.cc.X))
outputs["rel_accel"].append(opy.nodeAccel(top_node.tag, o3.cc.X))
opy.reactions()
outputs["force"].append(-opy.nodeReaction(
bot_node.tag, o3.cc.X)) # Negative since diff node
opy.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def createOutputDatabase(self, Nmodes=0, deltaT=0.0, recorders=[]):
"""
This function creates a directory to save all the output data.
Command: createODB("ModelName",<"LoadCase Name">, <Nmodes=Nmodes(int)>, <recorders=*recorder(list)>)
ModelName : (string) Name of the model. The main output folder will be named "ModelName_ODB" in the current directory.
LoadCase Name: (string), Optional. Name of the load case forder to be created inside the ModelName_ODB folder. If not provided,
no load case data will be read.
Nmodes : (int) Optional key argument to save modeshape data. Default is 0, no modeshape data is saved.
deltaT : (float) Optional time interval for recording. will record when next step is deltaT greater than last recorder step.
(default: records at every time step)
recorders : (string) A list of additional quantities a users would like to record in the output database.
The arguments for these additional inputs match the standard OpenSees arguments to avoid any confusion.
'localForce','basicDeformation', 'plasticDeformation','stresses','strains'
The recorders for node displacement and reactions are saved by default to help plot the deformed shape.
Example: createODB(TwoSpanBridge, Pushover, Nmodes=3, recorders=['stresses', 'strains'])
Future: The integrationPoints output works only for nonlinear beam column elements. If a model has a combination
of elastic and nonlienar elements, we need to create a method distinguish.
"""
ODBdir = self.ODBdir # ODB Dir name
if not os.path.exists(ODBdir):
os.makedirs(ODBdir)
nodeList = op.getNodeTags()
eleList = op.getEleTags()
dofList = [int(ii + 1) for ii in range(len(op.nodeCoord(nodeList[0])))]
# Save node and element data in the main Output folder
self.saveNodesandElements()
#########################
## Create mode shape dir
#########################
if Nmodes > 0:
ModeShapeDir = os.path.join(ODBdir, "ModeShapes")
if not os.path.exists(ModeShapeDir):
os.makedirs(ModeShapeDir)
## Run eigen analysis internally and get information to print
Tarray = np.zeros([1,
Nmodes]) # To save all the periods of vibration
op.wipeAnalysis()
eigenVal = op.eigen(Nmodes + 1)
for mm in range(1, Nmodes + 1):
Tarray[0, mm - 1] = 4 * asin(1.0) / (eigenVal[mm - 1])**0.5
modeTFile = os.path.join(ModeShapeDir, "ModalPeriods.out")
np.savetxt(modeTFile, Tarray, delimiter=self.delim, fmt=self.fmt)
### Save mode shape data
for ii in range(1, Nmodes + 1):
self.saveModeShapeData(ii)
op.wipeAnalysis()
LoadCaseDir = self.LoadCaseDir
if not os.path.exists(LoadCaseDir):
os.makedirs(LoadCaseDir)
NodeDispFile = os.path.join(LoadCaseDir, "NodeDisp_All.out")
EleForceFile = os.path.join(LoadCaseDir, "EleForce_All.out")
ReactionFile = os.path.join(LoadCaseDir, "Reaction_All.out")
EleStressFile = os.path.join(LoadCaseDir, "EleStress_All.out")
EleStrainFile = os.path.join(LoadCaseDir, "EleStrain_All.out")
EleBasicDefFile = os.path.join(LoadCaseDir, "EleBasicDef_All.out")
ElePlasticDefFile = os.path.join(LoadCaseDir, "ElePlasticDef_All.out")
# EleIntPointsFile = os.path.join(LoadCaseDir,"EleIntPoints_All.out")
# Save recorders in the ODB folder
op.recorder('Node', '-file', NodeDispFile, '-time', '-dT', deltaT,
'-node', *nodeList, '-dof', *dofList, 'disp')
op.recorder('Node', '-file', ReactionFile, '-time', '-dT', deltaT,
'-node', *nodeList, '-dof', *dofList, 'reaction')
if 'localForce' in recorders:
op.recorder('Element', '-file', EleForceFile, '-time', '-dT',
deltaT, '-ele', *eleList, '-dof', *dofList,
'localForce')
if 'basicDeformation' in recorders:
op.recorder('Element', '-file', EleBasicDefFile, '-time', '-dT',
deltaT, '-ele', *eleList, '-dof', *dofList,
'basicDeformation')
if 'plasticDeformation' in recorders:
op.recorder('Element', '-file', ElePlasticDefFile, '-time', '-dT',
deltaT, '-ele', *eleList, '-dof', *dofList,
'plasticDeformation')
if 'stresses' in recorders:
op.recorder('Element', '-file', EleStressFile, '-time', '-dT',
deltaT, '-ele', *eleList, 'stresses')
if 'strains' in recorders:
op.recorder('Element', '-file', EleStrainFile, '-time', '-dT',
deltaT, '-ele', *eleList, 'strains')
def test_EigenFrame():
ops.wipe()
ops.model('Basic', '-ndm', 2)
# units kip, ft
# properties
bayWidth = 20.0
storyHeight = 10.0
numBay = 10
numFloor = 9
A = 3.0 #area = 3ft^2
E = 432000.0 #youngs mod = 432000 k/ft^2
I = 1.0 #second moment of area I=1ft^4
M = 3.0 #mas/length = 4 kip sec^2/ft^2
coordTransf = "Linear" # Linear, PDelta, Corotational
massType = "-lMass" # -lMass, -cMass
# add the nodes
# - floor at a time
nodeTag = 1
yLoc = 0.
for j in range(0, numFloor + 1):
xLoc = 0.
for i in range(0, numBay + 1):
ops.node(nodeTag, xLoc, yLoc)
xLoc += bayWidth
nodeTag += 1
yLoc += storyHeight
# fix base nodes
for i in range(1, numBay + 2):
ops.fix(i, 1, 1, 1)
# add column element
ops.geomTransf(coordTransf, 1)
eleTag = 1
for i in range(0, numBay + 1):
end1 = i + 1
end2 = end1 + numBay + 1
for j in range(0, numFloor):
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E, I, 1,
'-mass', M, massType)
end1 = end2
end2 = end1 + numBay + 1
eleTag += 1
# add beam elements
for j in range(1, numFloor + 1):
end1 = (numBay + 1) * j + 1
end2 = end1 + 1
for i in range(0, numBay):
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E, I, 1,
'-mass', M, massType)
end1 = end2
end2 = end1 + 1
eleTag += 1
# calculate eigenvalues
numEigen = 3
eigenValues = ops.eigen(numEigen)
PI = 2 * asin(1.0)
#recorder('PVD','EigenFrame','eigen',numEigen)
#record()
# determine PASS/FAILURE of test
testOK = 0
# print table of camparsion
# Bathe & Wilson Peterson SAP2000 SeismoStruct
comparisonResults = [[0.589541, 5.52695, 16.5878],
[0.589541, 5.52696, 16.5879],
[0.589541, 5.52696, 16.5879],
[0.58955, 5.527, 16.588]]
print("\n\nEigenvalue Comparisons:")
tolerances = [9.99e-6, 9.99e-6,
9.99e-5] # tolerances prescribed by documented precision
formatString = '{:>15}{:>15}{:>15}{:>15}{:>15}'
print(
formatString.format('OpenSees', 'Bathe&Wilson', 'Peterson', 'SAP2000',
'SeismoStruct'))
formatString = '{:>15.5f}{:>15.4f}{:>15.4f}{:>15.4f}{:>15.3f}'
for i in range(0, numEigen):
lamb = eigenValues[i]
print(
formatString.format(lamb, comparisonResults[0][i],
comparisonResults[1][i],
comparisonResults[2][i],
comparisonResults[3][i]))
resultOther = comparisonResults[2][i]
tol = tolerances[i]
if abs(lamb - resultOther) > tol:
testOK = -1
print("failed->", abs(lamb - resultOther), tol)
assert testOK == 0
def test_DynAnal_BeamWithQuadElements():
ops.wipe() # clear opensees model
# create data directory
# file mkdir Data
#-----------------------------
# Define the model
# ----------------------------
# Create ModelBuilder with 2 dimensions and 2 DOF/node
ops.model('BasicBuilder', '-ndm', 2, '-ndf', 2)
# create the material
ops.nDMaterial('ElasticIsotropic', 1, 1000.0, 0.25, 3.0)
# set type of quadrilateral element (uncomment one of the three options)
Quad = 'quad'
#set Quad bbarQuad
#set Quad enhancedQuad
# set up the arguments for the three considered elements
if Quad == "enhancedQuad":
eleArgs = "PlaneStress2D 1"
if Quad == "quad":
eleArgs = "1 PlaneStress2D 1"
if Quad == "bbarQuad":
eleArgs = "1"
# set up the number of elements in x (nx) and y (ny) direction
nx = 16 # NOTE: nx MUST BE EVEN FOR THIS EXAMPLE
ny = 4
# define numbering of node at the left support (bn), and the two nodes at load application (l1, l2)
bn = nx + 1
l1 = int(nx / 2 + 1)
l2 = int(l1 + ny * (nx + 1))
# create the nodes and elements using the block2D command
ops.block2D(nx, ny, 1, 1, Quad, 1., 'PlaneStress2D', 1, 1, 0., 0., 2, 40.,
0., 3, 40., 10., 4, 0., 10.)
# define boundary conditions
ops.fix(1, 1, 1)
ops.fix(bn, 0, 1)
# define the recorder
#---------------------
# recorder Node -file Data/Node.out -time -node l1 -dof 2 disp
# define load pattern
#---------------------
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(l1, 0.0, -1.0)
ops.load(l2, 0.0, -1.0)
# --------------------------------------------------------------------
# Start of static analysis (creation of the analysis & analysis itself)
# --------------------------------------------------------------------
# Load control with variable load steps
# init Jd min max
ops.integrator('LoadControl', 1.0, 1, 1.0, 10.0)
# Convergence test
# tolerance maxIter displayCode
ops.test('EnergyIncr', 1.0e-12, 10, 0)
# Solution algorithm
ops.algorithm('Newton')
# DOF numberer
ops.numberer('RCM')
# Cosntraint handler
ops.constraints('Plain')
# System of equations solver
ops.system('ProfileSPD')
# Type of analysis analysis
ops.analysis('Static')
# Perform the analysis
ops.analyze(10)
# --------------------------
# End of static analysis
# --------------------------
# -------------------------------------
# create display for transient analysis
#--------------------------------------
# windowTitle xLoc yLoc xPixels yPixels
# recorder display "Simply Supported Beam" 10 10 800 200 -wipe
# prp 20 5.0 1.0 # 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 -30 30 -10 10 # coordiantes of the window relative to prp
# display 10 0 5
# the 1st arg. is the tag for display mode
# the 2nd arg. is magnification factor for nodes, the 3rd arg. is magnif. factor of deformed shape
# ---------------------------------------
# Create and Perform the dynamic analysis
# ---------------------------------------
#define damping
evals = ops.eigen(1)
ops.rayleigh(0., 0., 0., 2 * 0.02 / sqrt(evals[0]))
# Remove the static analysis & reset the time to 0.0
ops.wipeAnalysis()
ops.setTime(0.0)
# Now remove the loads and let the beam vibrate
ops.remove('loadPattern', 1)
uy1 = ops.nodeDisp(9, 2)
print("uy(9) = ", uy1)
# Create the transient analysis
ops.test('EnergyIncr', 1.0e-12, 10, 0)
ops.algorithm('Newton')
ops.numberer('RCM')
ops.constraints('Plain')
ops.integrator('Newmark', 0.5, 0.25)
ops.system('BandGeneral')
ops.analysis('Transient')
# Perform the transient analysis (50 sec)
ops.analyze(1500, 0.5)
uy2 = ops.nodeDisp(9, 2)
print("uy(9) = ", uy2)
assert abs(uy1 + 0.39426414168933876514) < 1e-12 and abs(
uy2 + 0.00736847273806807632) < 1e-12
print("========================================")
for step in range(n_steps):
ops.analyze(1, dt)
timeV[step] = ops.getTime()
# collect disp for element nodes
for el_i, ele_tag in enumerate(el_tags):
nd1, nd2 = ops.eleNodes(ele_tag)
Eds[step, el_i, :] = [ops.nodeDisp(nd1)[0],
ops.nodeDisp(nd1)[1],
ops.nodeDisp(nd1)[2],
ops.nodeDisp(nd2)[0],
ops.nodeDisp(nd2)[1],
ops.nodeDisp(nd2)[2]]
# 1. animate the deformated shape
anim = opsv.anim_defo(Eds, timeV, sfac_a, interpFlag=1, xlim=[-1, 7],
ylim=[-1, 5], fig_wi_he=(30., 22.))
plt.show()
# 2. after closing the window, animate the specified mode shape
eigVals = ops.eigen(5)
modeNo = 2 # specify which mode to animate
f_modeNo = np.sqrt(eigVals[modeNo-1])/(2*np.pi) # i-th natural frequency
anim = opsv.anim_mode(modeNo, interpFlag=1, xlim=[-1, 7], ylim=[-1, 5],
fig_wi_he=(30., 22.))
plt.title(f'Mode {modeNo}, f_{modeNo}: {f_modeNo:.3f} Hz')
plt.show()
nep,
fmt_interp='b-',
az_el=(-68., 39.),
fig_wi_he=fig_wi_he,
endDispFlag=0)
plt.title('3d 3-element cantilever beam')
# - 2
opsv.plot_defo(sfac, 19, fmt_interp='b-', az_el=(6., 30.), fig_wi_he=fig_wi_he)
plt.title('3d 3-element cantilever beam')
# - 3
nfreq = 6
eigValues = ops.eigen(nfreq)
modeNo = 6
sfac = 2.0e1
opsv.plot_mode_shape(modeNo,
sfac,
19,
fmt_interp='b-',
az_el=(106., 46.),
fig_wi_he=fig_wi_he)
plt.title(f'Mode {modeNo}')
sfacN = 1.e-2
sfacVy = 5.e-2
sfacVz = 1.e-2
def test_EigenFrameExtra():
eleTypes = [
'elasticBeam', 'forceBeamElasticSection', 'dispBeamElasticSection',
'forceBeamFiberSectionElasticMaterial',
'dispBeamFiberSectionElasticMaterial'
]
for eleType in eleTypes:
ops.wipe()
ops.model('Basic', '-ndm', 2)
# units kip, ft
# properties
bayWidth = 20.0
storyHeight = 10.0
numBay = 10
numFloor = 9
A = 3.0 #area = 3ft^2
E = 432000.0 #youngs mod = 432000 k/ft^2
I = 1.0 #second moment of area I=1ft^4
M = 3.0 #mas/length = 4 kip sec^2/ft^2
coordTransf = "Linear" # Linear, PDelta, Corotational
massType = "-lMass" # -lMass, -cMass
nPts = 3 # numGauss Points
# an elastic material
ops.uniaxialMaterial('Elastic', 1, E)
# an elastic section
ops.section('Elastic', 1, E, A, I)
# a fiber section with A=3 and I = 1 (b=1.5, d=2) 2d bending about y-y axis
# b 1.5 d 2.0
y = 2.0
z = 1.5
numFiberY = 2000 # note we only need so many to get the required accuracy on eigenvalue 1e-7!
numFiberZ = 1
ops.section('Fiber', 2)
# patch rect 1 numFiberY numFiberZ 0.0 0.0 z y
ops.patch('quad', 1, numFiberY, numFiberZ, -y / 2.0, -z / 2.0, y / 2.0,
-z / 2.0, y / 2.0, z / 2.0, -y / 2.0, z / 2.0)
# add the nodes
# - floor at a time
nodeTag = 1
yLoc = 0.
for j in range(0, numFloor + 1):
xLoc = 0.
for i in range(numBay + 1):
ops.node(nodeTag, xLoc, yLoc)
xLoc += bayWidth
nodeTag += 1
yLoc += storyHeight
# fix base nodes
for i in range(1, numBay + 2):
ops.fix(i, 1, 1, 1)
# add column element
transfTag = 1
ops.geomTransf(coordTransf, transfTag)
integTag1 = 1
ops.beamIntegration('Lobatto', integTag1, 1, nPts)
integTag2 = 2
ops.beamIntegration('Lobatto', integTag2, 2, nPts)
eleTag = 1
for i in range(numBay + 1):
end1 = i + 1
end2 = end1 + numBay + 1
for j in range(numFloor):
if eleType == "elasticBeam":
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E,
I, 1, '-mass', M, massType)
elif eleType == "forceBeamElasticSection":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M)
elif eleType == "dispBeamElasticSection":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M, massType)
elif eleType == "forceBeamFiberSectionElasticMaterial":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M)
elif eleType == "dispBeamFiberSectionElasticMaterial":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M, massType)
else:
print("BARF")
end1 = end2
end2 = end1 + numBay + 1
eleTag += 1
# add beam elements
for j in range(1, numFloor + 1):
end1 = (numBay + 1) * j + 1
end2 = end1 + 1
for i in range(numBay):
if eleType == "elasticBeam":
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E,
I, 1, '-mass', M, massType)
elif eleType == "forceBeamElasticSection":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M)
elif eleType == "dispBeamElasticSection":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M, massType)
elif eleType == "forceBeamFiberSectionElasticMaterial":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M)
elif eleType == "dispBeamFiberSectionElasticMaterial":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M, massType)
else:
print("BARF")
# element(elasticBeamColumn eleTag end1 end2 A E I 1 -mass M
end1 = end2
end2 = end1 + 1
eleTag += 1
# calculate eigenvalues
numEigen = 3
eigenValues = ops.eigen(numEigen)
PI = 2 * asin(1.0)
# determine PASS/FAILURE of test
testOK = 0
# print table of camparsion
# Bathe & Wilson Peterson SAP2000 SeismoStruct
comparisonResults = [[0.589541, 5.52695, 16.5878],
[0.589541, 5.52696, 16.5879],
[0.589541, 5.52696, 16.5879],
[0.58955, 5.527, 16.588]]
print("\n\nEigenvalue Comparisons for eleType:", eleType)
tolerances = [9.99e-7, 9.99e-6, 9.99e-5]
formatString = '{:>15}{:>15}{:>15}{:>15}{:>15}'
print(
formatString.format('OpenSees', 'Bathe&Wilson', 'Peterson',
'SAP2000', 'SeismoStruct'))
formatString = '{:>15.5f}{:>15.4f}{:>15.4f}{:>15.4f}{:>15.3f}'
for i in range(numEigen):
lamb = eigenValues[i]
print(
formatString.format(lamb, comparisonResults[0][i],
comparisonResults[1][i],
comparisonResults[2][i],
comparisonResults[3][i]))
resultOther = comparisonResults[2][i]
tol = tolerances[i]
if abs(lamb - resultOther) > tol:
testOK = -1
print("failed->", abs(lamb - resultOther), tol)
assert testOK == 0
solverTypes = [
'-genBandArpack', '-fullGenLapack', '-UmfPack', '-SuperLU',
'-ProfileSPD'
]
for solverType in solverTypes:
eleType = 'elasticBeam'
ops.wipe()
ops.model('Basic', '-ndm', 2)
# units kip, ft
# properties
bayWidth = 20.0
storyHeight = 10.0
numBay = 10
numFloor = 9
A = 3.0 #area = 3ft^2
E = 432000.0 #youngs mod = 432000 k/ft^2
I = 1.0 #second moment of area I=1ft^4
M = 3.0 #mas/length = 4 kip sec^2/ft^2
coordTransf = "Linear" # Linear, PDelta, Corotational
massType = "-lMass" # -lMass, -cMass
nPts = 3 # numGauss Points
# an elastic material
ops.uniaxialMaterial('Elastic', 1, E)
# an elastic section
ops.section('Elastic', 1, E, A, I)
# a fiber section with A=3 and I = 1 (b=1.5, d=2) 2d bending about y-y axis
# b 1.5 d 2.0
y = 2.0
z = 1.5
numFiberY = 2000 # note we only need so many to get the required accuracy on eigenvalue 1e-7!
numFiberZ = 1
ops.section('Fiber', 2)
# patch rect 1 numFiberY numFiberZ 0.0 0.0 z y
ops.patch('quad', 1, numFiberY, numFiberZ, -y / 2.0, -z / 2.0, y / 2.0,
-z / 2.0, y / 2.0, z / 2.0, -y / 2.0, z / 2.0)
# add the nodes
# - floor at a time
nodeTag = 1
yLoc = 0.
for j in range(0, numFloor + 1):
xLoc = 0.
for i in range(numBay + 1):
ops.node(nodeTag, xLoc, yLoc)
xLoc += bayWidth
nodeTag += 1
yLoc += storyHeight
# fix base nodes
for i in range(1, numBay + 2):
ops.fix(i, 1, 1, 1)
# add column element
transfTag = 1
ops.geomTransf(coordTransf, transfTag)
integTag1 = 1
ops.beamIntegration('Lobatto', integTag1, 1, nPts)
integTag2 = 2
ops.beamIntegration('Lobatto', integTag2, 2, nPts)
eleTag = 1
for i in range(numBay + 1):
end1 = i + 1
end2 = end1 + numBay + 1
for j in range(numFloor):
if eleType == "elasticBeam":
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E,
I, 1, '-mass', M, massType)
elif eleType == "forceBeamElasticSection":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M)
elif eleType == "dispBeamElasticSection":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M, massType)
elif eleType == "forceBeamFiberSectionElasticMaterial":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M)
elif eleType == "dispBeamFiberSectionElasticMaterial":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M, massType)
else:
print("BARF")
end1 = end2
end2 = end1 + numBay + 1
eleTag += 1
# add beam elements
for j in range(1, numFloor + 1):
end1 = (numBay + 1) * j + 1
end2 = end1 + 1
for i in range(numBay):
if eleType == "elasticBeam":
ops.element('elasticBeamColumn', eleTag, end1, end2, A, E,
I, 1, '-mass', M, massType)
elif eleType == "forceBeamElasticSection":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M)
elif eleType == "dispBeamElasticSection":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag1, '-mass', M, massType)
elif eleType == "forceBeamFiberSectionElasticMaterial":
ops.element('forceBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M)
elif eleType == "dispBeamFiberSectionElasticMaterial":
ops.element('dispBeamColumn', eleTag, end1, end2,
transfTag, integTag2, '-mass', M, massType)
else:
print("BARF")
# element(elasticBeamColumn eleTag end1 end2 A E I 1 -mass M
end1 = end2
end2 = end1 + 1
eleTag += 1
# calculate eigenvalues
numEigen = 3
eigenValues = ops.eigen(solverType, numEigen)
PI = 2 * asin(1.0)
# determine PASS/FAILURE of test
testOK = 0
# print table of camparsion
# Bathe & Wilson Peterson SAP2000 SeismoStruct
comparisonResults = [[0.589541, 5.52695, 16.5878],
[0.589541, 5.52696, 16.5879],
[0.589541, 5.52696, 16.5879],
[0.58955, 5.527, 16.588]]
print("\n\nEigenvalue Comparisons for solverType:", solverType)
tolerances = [9.99e-7, 9.99e-6, 9.99e-5]
formatString = '{:>15}{:>15}{:>15}{:>15}{:>15}'
print(
formatString.format('OpenSees', 'Bathe&Wilson', 'Peterson',
'SAP2000', 'SeismoStruct'))
formatString = '{:>15.5f}{:>15.4f}{:>15.4f}{:>15.4f}{:>15.3f}'
for i in range(numEigen):
lamb = eigenValues[i]
print(
formatString.format(lamb, comparisonResults[0][i],
comparisonResults[1][i],
comparisonResults[2][i],
comparisonResults[3][i]))
resultOther = comparisonResults[2][i]
tol = tolerances[i]
if abs(lamb - resultOther) > tol:
testOK = -1
print("failed->", abs(lamb - resultOther), tol)
assert testOK == 0
def get_inelastic_response(mass,
k_spring,
f_yield,
motion,
dt,
xi=0.05,
r_post=0.0):
"""
Run seismic analysis of a nonlinear SDOF
:param mass: SDOF mass
:param k_spring: spring stiffness
:param f_yield: yield strength
:param motion: list, acceleration values
:param dt: float, time step of acceleration values
:param xi: damping ratio
:param r_post: post-yield stiffness
:return:
"""
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
# Establish nodes
bot_node = 1
top_node = 2
opy.node(bot_node, 0., 0.)
opy.node(top_node, 0., 0.)
# Fix bottom node
opy.fix(top_node, opc.FREE, opc.FIXED, opc.FIXED)
opy.fix(bot_node, opc.FIXED, opc.FIXED, opc.FIXED)
# Set out-of-plane DOFs to be slaved
opy.equalDOF(1, 2, *[2, 3])
# nodal mass (weight / g):
opy.mass(top_node, mass, 0., 0.)
# Define material
bilinear_mat_tag = 1
mat_type = "Steel01"
mat_props = [f_yield, k_spring, r_post]
opy.uniaxialMaterial(mat_type, bilinear_mat_tag, *mat_props)
# Assign zero length element
beam_tag = 1
opy.element('zeroLength', beam_tag, bot_node, top_node, "-mat",
bilinear_mat_tag, "-dir", 1, '-doRayleigh', 1)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * motion) # should be negative
opy.timeSeries('Path', load_tag_dynamic, '-dt', dt, '-values', *values)
opy.pattern('UniformExcitation', pattern_tag_dynamic, opc.X, '-accel',
load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = opy.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2**0.5
alpha_m = 0.0
beta_k = 2 * xi / angular_freq
beta_k_comm = 0.0
beta_k_init = 0.0
opy.rayleigh(alpha_m, beta_k, beta_k_init, beta_k_comm)
# Run the dynamic analysis
opy.wipeAnalysis()
opy.algorithm('Newton')
opy.system('SparseGeneral')
opy.numberer('RCM')
opy.constraints('Transformation')
opy.integrator('Newmark', 0.5, 0.25)
opy.analysis('Transient')
tol = 1.0e-10
iterations = 10
opy.test('EnergyIncr', tol, iterations, 0, 2)
analysis_time = (len(values) - 1) * dt
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while opy.getTime() < analysis_time:
curr_time = opy.getTime()
opy.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(opy.nodeDisp(top_node, 1))
outputs["rel_vel"].append(opy.nodeVel(top_node, 1))
outputs["rel_accel"].append(opy.nodeAccel(top_node, 1))
opy.reactions()
outputs["force"].append(
-opy.nodeReaction(bot_node, 1)) # Negative since diff node
opy.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
# row= 0
#
# gravity_load_data[:,0]= node_data[wall.shape[0]:node_data.shape[0],0]
#
# for story in range(num_story):
# gravity_load_data[row:row+ wall.shape[0],3]= -1*np.multiply(wall_data_arr[:,18],wall_data_arr[:,19])*original_bldg.iat[bldg_num,38]**2*0.0254**2*(1200+bldg.iat[bldg_num,8]*conc_mat[4]*9.81)
#
# row= row+ wall.shape[0]
# for i in range(gravity_load_data.shape[0]):
# ops.load(int(gravity_load_data[i,0]), gravity_load_data[i,1], gravity_load_data[i,2], gravity_load_data[i,3], gravity_load_data[i,4], gravity_load_data[i,5], gravity_load_data[i,6])
# =============================================================================
# Analysis Generation
# =============================================================================
#eigen command
eigen_values= ops.eigen(num_eigen)
period= 2*math.pi/np.sqrt(eigen_values)
period_data[bldg_num,:]= period
# render the model after defining all the nodes and elements
#plot_model()
ops.wipe()
#plot period vs. story
plt.plot(period_data[:,0], bldg_arr[:,3], 'o', color='black',markersize=5)
plt.ylim(0, 35)
plt.xlim(0, 6)
plt.xlabel('Fundamental period (s)')
def test_EigenAnal_twoStoryFrame1():
ops.wipe()
#input
m = 100.0 / 386.0
numModes = 2
#material
A = 63.41
I = 320.0
E = 29000.0
#geometry
L = 240.
h = 120.
# define the model
#---------------------------------
#model builder
ops.model('BasicBuilder', '-ndm', 2, '-ndf', 3)
# nodal coordinates:
ops.node(1, 0., 0.)
ops.node(2, L, 0.)
ops.node(3, 0., h)
ops.node(4, L, h)
ops.node(5, 0., 2 * h)
ops.node(6, L, 2 * h)
# Single point constraints -- Boundary Conditions
ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
# assign mass
ops.mass(3, m, 0., 0.)
ops.mass(4, m, 0., 0.)
ops.mass(5, m / 2., 0., 0.)
ops.mass(6, m / 2., 0., 0.)
# define geometric transformation:
TransfTag = 1
ops.geomTransf('Linear', TransfTag)
# define elements:
# columns
ops.element('elasticBeamColumn', 1, 1, 3, A, E, 2. * I, TransfTag)
ops.element('elasticBeamColumn', 2, 3, 5, A, E, I, TransfTag)
ops.element('elasticBeamColumn', 3, 2, 4, A, E, 2. * I, TransfTag)
ops.element('elasticBeamColumn', 4, 4, 6, A, E, I, TransfTag)
# beams
ops.element('elasticBeamColumn', 5, 3, 4, A, E, 2 * I, TransfTag)
ops.element('elasticBeamColumn', 6, 5, 6, A, E, I, TransfTag)
# record eigenvectors
#----------------------
# for { k 1 } { k <= numModes } { incr k } {
# recorder Node -file format "modes/mode%i.out" k -nodeRange 1 6 -dof 1 2 3 "eigen k"
# }
# perform eigen analysis
#-----------------------------
lamb = ops.eigen(numModes)
# calculate frequencies and periods of the structure
#---------------------------------------------------
omega = []
f = []
T = []
pi = 3.141593
for lam in lamb:
print("labmbda = ", lam)
omega.append(math.sqrt(lam))
f.append(math.sqrt(lam) / (2 * pi))
T.append((2 * pi) / math.sqrt(lam))
print("periods are ", T)
# write the output file cosisting of periods
#--------------------------------------------
period = "Periods.txt"
Periods = open(period, "w")
for t in T:
Periods.write(repr(t) + '\n')
Periods.close()
# 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)
#-----------------------------------------------------------------------
ops.integrator('LoadControl', 0.0, 1, 0.0, 0.0)
# Convergence test
# tolerance maxIter displayCode
ops.test('EnergyIncr', 1.0e-10, 100, 0)
# Solution algorithm
ops.algorithm('Newton')
# DOF numberer
ops.numberer('RCM')
# Constraint handler
ops.constraints('Transformation')
# System of equations solver
ops.system('ProfileSPD')
ops.analysis('Static')
res = ops.analyze(1)
if res < 0:
print("Modal analysis failed")
# get values of eigenvectors for translational DOFs
#---------------------------------------------------
f11 = ops.nodeEigenvector(3, 1, 1)
f21 = ops.nodeEigenvector(5, 1, 1)
f12 = ops.nodeEigenvector(3, 2, 1)
f22 = ops.nodeEigenvector(5, 2, 1)
print("eigenvector 1: ", [f11 / f21, f21 / f21])
print("eigenvector 2: ", [f12 / f22, f22 / f22])
assert abs(T[0] - 0.628538768190688) < 1e-12 and abs(
T[1] - 0.2359388635361575) < 1e-12 and abs(
f11 / f21 - 0.3869004256389493) < 1e-12 and abs(
f21 / f21 - 1.0) < 1e-12 and abs(f12 / f22 + 1.2923221761110006
) < 1e-12 and abs(f22 / f22 -
1.0) < 1e-12
def get_inelastic_response(fb, asig, extra_time=0.0, xi=0.05, analysis_dt=0.001):
"""
Run seismic analysis of a nonlinear FrameBuilding
:param fb: FrameBuilding object
:param asig: AccSignal object
:param extra_time: float, additional analysis time after end of ground motion
:param xi: damping ratio
:param analysis_dt: time step to perform the analysis
:return:
"""
op.wipe()
op.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
q_floor = 10000. # kPa
trib_width = fb.floor_length
trib_mass_per_length = q_floor * trib_width / 9.8
# Establish nodes and set mass based on trib area
# Nodes named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground level left
nd = OrderedDict()
col_xs = np.cumsum(fb.bay_lengths)
col_xs = np.insert(col_xs, 0, 0)
n_cols = len(col_xs)
sto_ys = fb.heights
sto_ys = np.insert(sto_ys, 0, 0)
for cc in range(1, n_cols + 1):
for ss in range(fb.n_storeys + 1):
n_i = cc * 100 + ss
nd["C%i-S%i" % (cc, ss)] = n_i
op.node(n_i, col_xs[cc - 1], sto_ys[ss])
if ss != 0:
if cc == 1:
node_mass = trib_mass_per_length * fb.bay_lengths[0] / 2
elif cc == n_cols:
node_mass = trib_mass_per_length * fb.bay_lengths[-1] / 2
else:
node_mass = trib_mass_per_length * (fb.bay_lengths[cc - 2] + fb.bay_lengths[cc - 1] / 2)
op.mass(n_i, node_mass)
# Set all nodes on a storey to have the same displacement
for ss in range(0, fb.n_storeys + 1):
for cc in range(1, n_cols + 1):
op.equalDOF(nd["C%i-S%i" % (1, ss)], nd["C%i-S%i" % (cc, ss)], opc.X)
# Fix all base nodes
for cc in range(1, n_cols + 1):
op.fix(nd["C%i-S%i" % (cc, 0)], opc.FIXED, opc.FIXED, opc.FIXED)
# Coordinate transformation
geo_tag = 1
trans_args = []
op.geomTransf("Linear", geo_tag, *[])
l_hinge = fb.bay_lengths[0] * 0.1
# Define material
e_conc = 30.0e6
i_beams = 0.4 * fb.beam_widths * fb.beam_depths ** 3 / 12
i_columns = 0.5 * fb.column_widths * fb.column_depths ** 3 / 12
a_beams = fb.beam_widths * fb.beam_depths
a_columns = fb.column_widths * fb.column_depths
ei_beams = e_conc * i_beams
ei_columns = e_conc * i_columns
eps_yield = 300.0e6 / 200e9
phi_y_col = calc_yield_curvature(fb.column_depths, eps_yield)
phi_y_beam = calc_yield_curvature(fb.beam_depths, eps_yield)
# Define beams and columns
md = OrderedDict() # material dict
sd = OrderedDict() # section dict
ed = OrderedDict() # element dict
# Columns named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground floor left
# Beams named as: B<bay-number>-S<storey-number>, first beam starts at B1-S1 = first storey left (foundation at S0)
for ss in range(fb.n_storeys):
# set columns
for cc in range(1, fb.n_cols + 1):
ele_i = cc * 100 + ss
md["C%i-S%i" % (cc, ss)] = ele_i
sd["C%i-S%i" % (cc, ss)] = ele_i
ed["C%i-S%i" % (cc, ss)] = ele_i
mat_props = elastic_bilin(ei_columns[ss][cc - 1], 0.05 * ei_columns[ss][cc - 1], phi_y_col[ss][cc - 1])
#print(opc.ELASTIC_BILIN, ele_i, *mat_props)
op.uniaxialMaterial(opc.ELASTIC_BILIN, ele_i, *mat_props)
# op.uniaxialMaterial("Elastic", ele_i, ei_columns[ss][cc - 1])
node_numbers = [nd["C%i-S%i" % (cc, ss)], nd["C%i-S%i" % (cc, ss + 1)]]
op.element(opc.ELASTIC_BEAM_COLUMN, ele_i,
*node_numbers,
a_columns[ss - 1][cc - 1],
e_conc,
i_columns[ss - 1][cc - 1],
geo_tag
)
# Set beams
for bb in range(1, fb.n_bays + 1):
ele_i = bb * 10000 + ss
md["B%i-S%i" % (bb, ss)] = ele_i
sd["B%i-S%i" % (bb, ss)] = ele_i
ed["B%i-S%i" % (bb, ss)] = ele_i
mat_props = elastic_bilin(ei_beams[ss][bb - 1], 0.05 * ei_beams[ss][bb - 1], phi_y_beam[ss][bb - 1])
op.uniaxialMaterial(opc.ELASTIC_BILIN, ele_i, *mat_props)
# op.uniaxialMaterial("Elastic", ele_i, ei_beams[ss][bb - 1])
node_numbers = [nd["C%i-S%i" % (bb, ss + 1)], nd["C%i-S%i" % (bb + 1, ss + 1)]]
print((opc.BEAM_WITH_HINGES, ele_i,
*node_numbers,
sd["B%i-S%i" % (bb, ss)], l_hinge,
sd["B%i-S%i" % (bb, ss)], l_hinge,
sd["B%i-S%i" % (bb, ss)], geo_tag
))
# Old definition
# op.element(opc.BEAM_WITH_HINGES, ele_i,
# *[nd["C%i-S%i" % (bb, ss - 1)], nd["C%i-S%i" % (bb + 1, ss)]],
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# e_conc,
# a_beams[ss - 1][bb - 1],
# i_beams[ss - 1][bb - 1], geo_tag
# )
# New definition
# op.element(opc.BEAM_WITH_HINGES, ele_i,
# *node_numbers,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], geo_tag # TODO: make this elastic
#
# )
# Elastic definition
op.element(opc.ELASTIC_BEAM_COLUMN, ele_i,
*node_numbers,
a_beams[ss - 1][bb - 1],
e_conc,
i_beams[ss - 1][bb - 1],
geo_tag
)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * asig.values) # should be negative
op.timeSeries('Path', load_tag_dynamic, '-dt', asig.dt, '-values', *values)
op.pattern('UniformExcitation', pattern_tag_dynamic, opc.X, '-accel', load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = op.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2 ** 0.5
if isinstance(angular_freq, complex):
raise ValueError("Angular frequency is complex, issue with stiffness or mass")
alpha_m = 0.0
beta_k = 2 * xi / angular_freq
beta_k_comm = 0.0
beta_k_init = 0.0
period = angular_freq / 2 / np.pi
print("period: ", period)
op.rayleigh(alpha_m, beta_k, beta_k_init, beta_k_comm)
# Run the dynamic analysis
op.wipeAnalysis()
op.algorithm('Newton')
op.system('SparseGeneral')
op.numberer('RCM')
op.constraints('Transformation')
op.integrator('Newmark', 0.5, 0.25)
op.analysis('Transient')
#op.test("NormDispIncr", 1.0e-1, 2, 0)
tol = 1.0e-10
iter = 10
op.test('EnergyIncr', tol, iter, 0, 2) # TODO: make this test work
analysis_time = (len(values) - 1) * asig.dt + extra_time
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
print("Analysis starting")
while op.getTime() < analysis_time:
curr_time = op.getTime()
op.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(op.nodeDisp(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
outputs["rel_vel"].append(op.nodeVel(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
outputs["rel_accel"].append(op.nodeAccel(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
op.reactions()
react = 0
for cc in range(1, fb.n_cols):
react += -op.nodeReaction(nd["C%i-S%i" % (cc, 0)], opc.X)
outputs["force"].append(react) # Should be negative since diff node
op.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
rho = 2400 * kg / m**3
nu = 0.20 # Poisson's ratio of soil
E = 2460000 * N / cm**2
ops.nDMaterial('ElasticIsotropic', mTg, E, nu, rho)
# espesor de los elementos
B = 0.25 * m
# construccion de nodos
for i in range(nNode):
ops.node(i + 1, *Node[i][1:])
# construccion de elementos
for i in range(nEle):
if (Ele[i][0] == 1):
ops.element('quad', i + 1, *Ele[i][2:], B, 'PlaneStress', Ele[i][0])
# condiciones de frontera
boundFix(nNode, Node)
# calculo de los modos de vibracion
Nmodes = 6
Tmodes = ops.eigen(Nmodes)
for i in range(Nmodes):
Tmodes[i] = 2 * math.pi / Tmodes[i]**0.5
print(Tmodes)
# Grafico de la deformada
fig = plt.figure(figsize=(10, 10))
opsv.plot_mode_shape(4, sfac=10)
plt.show()
