def add_nodes(joints_df, mass_df, list_new_joints, dict_of_hinges):
# Identify the joints that were auto created by ETABS (like COM joints)
points_df = joints_df[joints_df.IsAuto == 'Yes'].copy()
# create joints in opensees mdoel
joints_df.apply(lambda row: op.node(row.UniqueName, row.X, row.Y, row.Z),
axis='columns')
# add restraints to the joints
joints_df.apply(
lambda row: op.fix(row.UniqueName, *[int(r) for r in row.Restraints]),
axis='columns')
# special joint restraints for the COM joints
points_df.apply(lambda row: op.fix(row.UniqueName, *[0, 0, 1, 1, 1, 0]),
axis='columns')
op.constraints('Transformation')
# if the model diaphragm is rigid, define rigidity on each floor
if rigid_dia:
# obtain the list of floors in terms of the elevation (Z coordinate)
floor_list = set(joints_df[joints_df.Z > joints_df.Z.min()].Z)
# iterate through each floor to define rigid diaphragm
for floor in floor_list:
nodes_list = list(
joints_df.loc[joints_df.Z == floor]['UniqueName'])
remove_list = list(set(nodes_list) & set(list_new_joints)) + list(
dict_of_hinges.keys())
nodes = [i for i in nodes_list if i not in remove_list]
op.rigidDiaphragm(3, *nodes)
# apply mass to the respective nodes
mass_df.apply(lambda row: op.mass(row.PointElm, row.UX, row.UY, row.UZ, row
.RX, row.RY, row.RZ),
axis='columns')
return
def RunAnalysis():
AnalysisType = 'Pushover'
# Pushover Gravity
## ------------------------------
## Start of model generation
## -----------------------------
# remove existing model
ops.wipe()
# set modelbuilder
ops.model('basic', '-ndm', 2, '-ndf', 3)
import math
############################################
### Units and Constants ###################
############################################
inch = 1
kip = 1
sec = 1
# Dependent units
sq_in = inch * inch
ksi = kip / sq_in
ft = 12 * inch
# Constants
g = 386.2 * inch / (sec * sec)
pi = math.acos(-1)
#######################################
##### Dimensions
#######################################
# Dimensions Input
H_story = 10.0 * ft
W_bayX = 16.0 * ft
W_bayY_ab = 5.0 * ft + 10.0 * inch
W_bayY_bc = 8.0 * ft + 4.0 * inch
W_bayY_cd = 5.0 * ft + 10.0 * inch
# Calculated dimensions
W_structure = W_bayY_ab + W_bayY_bc + W_bayY_cd
################
### Material
################
# Steel02 Material
matTag = 1
matConnAx = 2
matConnRot = 3
Fy = 60.0 * ksi
# Yield stress
Es = 29000.0 * ksi
# Modulus of Elasticity of Steel
v = 0.2
# Poisson's ratio
Gs = Es / (1 + v)
# Shear modulus
b = 0.10
# Strain hardening ratio
params = [18.0, 0.925, 0.15] # R0,cR1,cR2
R0 = 18.0
cR1 = 0.925
cR2 = 0.15
a1 = 0.05
a2 = 1.00
a3 = 0.05
a4 = 1.0
sigInit = 0.0
alpha = 0.05
ops.uniaxialMaterial('Steel02', matTag, Fy, Es, b, R0, cR1, cR2, a1, a2,
a3, a4, sigInit)
# ##################
# ## Sections
# ##################
colSecTag1 = 1
colSecTag2 = 2
beamSecTag1 = 3
beamSecTag2 = 4
beamSecTag3 = 5
# COMMAND: section('WFSection2d', secTag, matTag, d, tw, bf, tf, Nfw, Nff)
ops.section('WFSection2d', colSecTag1, matTag, 10.5 * inch, 0.26 * inch,
5.77 * inch, 0.44 * inch, 15, 16) # outer Column
ops.section('WFSection2d', colSecTag2, matTag, 10.5 * inch, 0.26 * inch,
5.77 * inch, 0.44 * inch, 15, 16) # Inner Column
ops.section('WFSection2d', beamSecTag1, matTag, 8.3 * inch, 0.44 * inch,
8.11 * inch, 0.685 * inch, 15, 15) # outer Beam
ops.section('WFSection2d', beamSecTag2, matTag, 8.2 * inch, 0.40 * inch,
8.01 * inch, 0.650 * inch, 15, 15) # Inner Beam
ops.section('WFSection2d', beamSecTag3, matTag, 8.0 * inch, 0.40 * inch,
7.89 * inch, 0.600 * inch, 15, 15) # Inner Beam
# Beam size - W10x26
Abeam = 7.61 * inch * inch
IbeamY = 144. * (inch**4)
# Inertia along horizontal axis
IbeamZ = 14.1 * (inch**4)
# inertia along vertical axis
# BRB input data
Acore = 2.25 * inch
Aend = 10.0 * inch
LR_BRB = 0.55
# ###########################
# ##### Nodes
# ###########################
# Create All main nodes
ops.node(1, 0.0, 0.0)
ops.node(2, W_bayX, 0.0)
ops.node(3, 2 * W_bayX, 0.0)
ops.node(11, 0.0, H_story)
ops.node(12, W_bayX, H_story)
ops.node(13, 2 * W_bayX, H_story)
ops.node(21, 0.0, 2 * H_story)
ops.node(22, W_bayX, 2 * H_story)
ops.node(23, 2 * W_bayX, 2 * H_story)
ops.node(31, 0.0, 3 * H_story)
ops.node(32, W_bayX, 3 * H_story)
ops.node(33, 2 * W_bayX, 3 * H_story)
# Beam Connection nodes
ops.node(1101, 0.0, H_story)
ops.node(1201, W_bayX, H_story)
ops.node(1202, W_bayX, H_story)
ops.node(1301, 2 * W_bayX, H_story)
ops.node(2101, 0.0, 2 * H_story)
ops.node(2201, W_bayX, 2 * H_story)
ops.node(2202, W_bayX, 2 * H_story)
ops.node(2301, 2 * W_bayX, 2 * H_story)
ops.node(3101, 0.0, 3 * H_story)
ops.node(3201, W_bayX, 3 * H_story)
ops.node(3202, W_bayX, 3 * H_story)
ops.node(3301, 2 * W_bayX, 3 * H_story)
# ###############
# Constraints
# ###############
ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
ops.fix(3, 1, 1, 1)
# #######################
# ### Elements
# #######################
# ### Assign beam-integration tags
ColIntTag1 = 1
ColIntTag2 = 2
BeamIntTag1 = 3
BeamIntTag2 = 4
BeamIntTag3 = 5
ops.beamIntegration('Lobatto', ColIntTag1, colSecTag1, 4)
ops.beamIntegration('Lobatto', ColIntTag2, colSecTag2, 4)
ops.beamIntegration('Lobatto', BeamIntTag1, beamSecTag1, 4)
ops.beamIntegration('Lobatto', BeamIntTag2, beamSecTag2, 4)
ops.beamIntegration('Lobatto', BeamIntTag3, beamSecTag3, 4)
# Assign geometric transformation
ColTransfTag = 1
BeamTranfTag = 2
ops.geomTransf('PDelta', ColTransfTag)
ops.geomTransf('Linear', BeamTranfTag)
# Assign Elements ##############
# ## Add non-linear column elements
ops.element('forceBeamColumn', 1, 1, 11, ColTransfTag, ColIntTag1, '-mass',
0.0)
ops.element('forceBeamColumn', 2, 2, 12, ColTransfTag, ColIntTag2, '-mass',
0.0)
ops.element('forceBeamColumn', 3, 3, 13, ColTransfTag, ColIntTag1, '-mass',
0.0)
ops.element('forceBeamColumn', 11, 11, 21, ColTransfTag, ColIntTag1,
'-mass', 0.0)
ops.element('forceBeamColumn', 12, 12, 22, ColTransfTag, ColIntTag2,
'-mass', 0.0)
ops.element('forceBeamColumn', 13, 13, 23, ColTransfTag, ColIntTag1,
'-mass', 0.0)
ops.element('forceBeamColumn', 21, 21, 31, ColTransfTag, ColIntTag1,
'-mass', 0.0)
ops.element('forceBeamColumn', 22, 22, 32, ColTransfTag, ColIntTag2,
'-mass', 0.0)
ops.element('forceBeamColumn', 23, 23, 33, ColTransfTag, ColIntTag1,
'-mass', 0.0)
# ### Add linear main beam elements, along x-axis
#element('elasticBeamColumn', 101, 1101, 1201, Abeam, Es, Gs, Jbeam, IbeamY, IbeamZ, beamTransfTag, '-mass', 0.0)
ops.element('forceBeamColumn', 101, 1101, 1201, BeamTranfTag, BeamIntTag1,
'-mass', 0.0)
ops.element('forceBeamColumn', 102, 1202, 1301, BeamTranfTag, BeamIntTag1,
'-mass', 0.0)
ops.element('forceBeamColumn', 201, 2101, 2201, BeamTranfTag, BeamIntTag2,
'-mass', 0.0)
ops.element('forceBeamColumn', 202, 2202, 2301, BeamTranfTag, BeamIntTag2,
'-mass', 0.0)
ops.element('forceBeamColumn', 301, 3101, 3201, BeamTranfTag, BeamIntTag3,
'-mass', 0.0)
ops.element('forceBeamColumn', 302, 3202, 3301, BeamTranfTag, BeamIntTag3,
'-mass', 0.0)
# Assign constraints between beam end nodes and column nodes (RIgid beam column connections)
ops.equalDOF(11, 1101, 1, 2, 3)
ops.equalDOF(12, 1201, 1, 2, 3)
ops.equalDOF(12, 1202, 1, 2, 3)
ops.equalDOF(13, 1301, 1, 2, 3)
ops.equalDOF(21, 2101, 1, 2, 3)
ops.equalDOF(22, 2201, 1, 2, 3)
ops.equalDOF(22, 2202, 1, 2, 3)
ops.equalDOF(23, 2301, 1, 2, 3)
ops.equalDOF(31, 3101, 1, 2, 3)
ops.equalDOF(32, 3201, 1, 2, 3)
ops.equalDOF(32, 3202, 1, 2, 3)
ops.equalDOF(33, 3301, 1, 2, 3)
AllNodes = ops.getNodeTags()
massX = 0.49
for nodes in AllNodes:
ops.mass(nodes, massX, massX, 0.00001)
################
## Gravity Load
################
# create TimeSeries
ops.timeSeries("Linear", 1)
# create a plain load pattern
ops.pattern("Plain", 1, 1)
# Create the nodal load
ops.load(11, 0.0, -5.0 * kip, 0.0)
ops.load(12, 0.0, -6.0 * kip, 0.0)
ops.load(13, 0.0, -5.0 * kip, 0.0)
ops.load(21, 0., -5. * kip, 0.0)
ops.load(22, 0., -6. * kip, 0.0)
ops.load(23, 0., -5. * kip, 0.0)
ops.load(31, 0., -5. * kip, 0.0)
ops.load(32, 0., -6. * kip, 0.0)
ops.load(33, 0., -5. * kip, 0.0)
###############################
### PUSHOVER ANALYSIS
###############################
if (AnalysisType == "Pushover"):
print("<<<< Running Pushover Analysis >>>>")
# Create load pattern for pushover analysis
# create a plain load pattern
ops.pattern("Plain", 2, 1)
ops.load(11, 1.61, 0.0, 0.0)
ops.load(21, 3.22, 0.0, 0.0)
ops.load(31, 4.83, 0.0, 0.0)
ControlNode = 31
ControlDOF = 1
MaxDisp = 0.15 * H_story
DispIncr = 0.1
NstepsPush = int(MaxDisp / DispIncr)
Model = 'test'
LoadCase = 'Pushover'
dt = 0.2
opp.createODB(Model, LoadCase, Nmodes=3)
ops.system("ProfileSPD")
ops.numberer("Plain")
ops.constraints("Plain")
ops.integrator("DisplacementControl", ControlNode, ControlDOF,
DispIncr)
ops.algorithm("Newton")
ops.test('NormUnbalance', 1e-8, 10)
ops.analysis("Static")
# analyze(NstepsPush)
ops.analyze(100)
print("Pushover analysis complete")
E = 25.0e6
G = 9615384.6
# Lx, Ly, Lz = 4., 3., 5.
Lx, Ly, Lz = 4., 4., 4.
ops.node(1, 0., 0., 0.)
ops.node(2, 0., 0., Lz)
ops.node(3, Lx, 0., Lz)
ops.node(4, Lx, Ly, Lz)
ops.fix(1, 1, 1, 1, 1, 1, 1)
lmass = 200.
ops.mass(2, lmass, lmass, lmass, 0.001, 0.001, 0.001)
ops.mass(3, lmass, lmass, lmass, 0.001, 0.001, 0.001)
ops.mass(4, lmass, lmass, lmass, 0.001, 0.001, 0.001)
gTTagz = 1
gTTagx = 2
gTTagy = 3
coordTransf = 'Linear'
ops.geomTransf(coordTransf, gTTagz, 0., -1., 0.)
ops.geomTransf(coordTransf, gTTagx, 0., -1., 0.)
ops.geomTransf(coordTransf, gTTagy, 1., 0., 0.)
ops.element('elasticBeamColumn', 1, 1, 2, A, E, G, J, Iy, Iz, gTTagz)
ops.element('elasticBeamColumn', 2, 2, 3, A, E, G, J, Iy, Iz, gTTagx)
ops.element('elasticBeamColumn', 3, 3, 4, A, E, G, J, Iy, Iz, gTTagy)
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_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(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
#print(path1)
h = 432.0
w = 504.0
op.node(1, 0.0, 0.0)
op.node(2, h, 0.0)
op.node(3, 0.0, w)
op.node(4, h, w)
op.fix(1, 1,1,1)
op.fix(2, 1,1,1)
op.fix(3, 0,0,0)
op.fix(4, 0,0,0)
op.mass(3, 5.18, 0.0, 0.0)
op.mass(4, 5.18, 0.0, 0.0)
op.geomTransf('Linear', 1)
A = 3600000000.0
E = 4227.0
Iz = 1080000.0
A1 = 5760000000.0
Iz1 = 4423680.0
op.element('elasticBeamColumn', 1, 1, 3, A, E, Iz, 1)
op.element('elasticBeamColumn', 2, 2, 4, A, E, Iz, 1)
op.element('elasticBeamColumn', 3, 3, 4, A1, E, Iz1, 1)
op.recorder('Node', '-file', 'Data-1b/DFree.out','-time', '-node', 3,4, '-dof', 1,2,3, 'disp')
op.recorder('Node', '-file', 'Data-1b/DBase.out','-time', '-node', 1,2, '-dof', 1,2,3, 'disp')
ABeam = HBeam * BBeam IzCol = (BCol * math.pow(HCol, 3)) / 12 # Column moment of inertia IzBeam = (BBeam * math.pow(HBeam, 3)) / 12 # Beam moment of inertia op.node(1, 0.0, 0.0) op.node(2, LBeam, 0.0) op.node(3, 0.0, LCol) op.node(4, LBeam, LCol) op.fix(1, 1, 1, 0) op.fix(2, 1, 1, 0) IDctrlNode = 2 IDctrlDOF = 1 op.mass(3, Mass, 0.0, 0.0) op.mass(4, Mass, 0.0, 0.0) ColSecTag = 1 # assign a tag number to the column section BeamSecTag = 2 # assign a tag number to the beam section coverCol = 6.0 * inch # Column cover to reinforcing steel NA. numBarsCol = 10 # number of longitudinal-reinforcement bars in column. (symmetric top & bot) barAreaCol = 2.25 * inch2 # area of longitudinal-reinforcement bars # MATERIAL parameters IDconcU = 1 # material ID tag -- unconfined cover concrete (here used for complete section) IDreinf = 2 # material ID tag -- reinforcement # nominal concrete compressive strength fc = -4.0 * ksi # CONCRETE Compressive Strength (+Tension, -Compression)
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
# loaded nodes
mid = int(((nx + 1) * (ny + 1) + 1) / 2)
side1 = int((nx + 2) / 2)
side2 = int((nx + 1) * (ny + 1) - side1 + 1)
# generate the nodes and elements
# numX numY startNode startEle eleType eleArgs? coords?
ops.block2D(nx, ny, 1, 1, "ShellMITC4", 1, 1, -20.0, 0.0, 0.0, 2, -20.0, 0.0,
40.0, 3, 20.0, 0.0, 40.0, 4, 20.0, 0.0, 0.0, 5, -10.0, 10.0, 20.0,
7, 10.0, 10.0, 20.0, 9, 0.0, 10.0, 20.0)
# define the boundary conditions
ops.fixZ(0.0, 1, 1, 1, 0, 1, 1)
ops.fixZ(40.0, 1, 1, 1, 0, 1, 1)
ops.mass(20, 10.0, 10.0, 10.0, 0.0, 0.0, 0.0)
# create a Linear time series
ops.timeSeries("Linear", 1)
# add some loads
ops.pattern("Plain", 1, 1, "-fact", 1.0)
ops.load(mid, 0.0, -0.50, 0.0, 0.0, 0.0, 0.0)
ops.load(side1, 0.0, -0.25, 0.0, 0.0, 0.0, 0.0)
ops.load(side2, 0.0, -0.25, 0.0, 0.0, 0.0, 0.0)
# ------------------------
# Start of static analysis
# ------------------------
# Load control with variable load steps
# init Jd min max
def RectCFSTSteelHysteretic(length: float, secHeight: float, secWidth: float,
thickness: float, concrete_grade: float,
steel_grade: float, axial_load_ratio: float,
disp_control: Iterable[float]):
'''Peakstress: concrete peak stress \n crushstress: concrete crush stress
'''
#disp input
# dispControl=[3,-3,7,-7,14,-14,14,-14,14,-14,28,-28,28,-28,28,-28,42,-42,42,-42,42,-42,56,-56,0]
dispControl = tuple(disp_control)
#Geometry
# length=740
# secHeight=100
# secWidth=100
# thickness=7
#Materials
##steel_tube
point1Steel, point2Steel, point3Steel = [460, 0.00309], [460, 0.02721
], [530, 0.26969]
point1SteelNegative, point2SteelNegative, point3SteelNegative = [
-460, -0.00309
], [-460, -0.02721], [-736, -0.26969]
pinchX = 0.2
pinchY = 0.7
damagedFactor = 0.01
densitySteel = 7.8 / 1000000000
##concrete
peakPointConcrete, crushPointConcrete = [-221.76, -0.0102], [-195, -0.051]
unloadingLambda = 0.2
tensileStrength = 5.6
tensilePostStiffness = 0.01
densityConcrete = 2.4 / 1000000000
#axialLoadRatio
# axialLoadRatio=0.4
#fix condition
Fixed = 1
#section parameter
areaConcrete = (secHeight - 2 * thickness) * (secWidth - 2 * thickness)
areaSteel = secWidth * secHeight - areaConcrete
# fck,Ec,nuConcrete=128.1,4.34*10000,0.21
# fy,epsilonSteely,Es,nuSteel=444.6,3067/1000000,1.99*100000,0.29
fck = peakPointConcrete[0]
fy = point1Steel[0]
#Computate parameter
axialLoad = (areaConcrete * fck + areaSteel * fy) * axial_load_ratio
#loading control parameter
# for item in dispControlPercentage:
# dispControl.append(item*length)
# dispControl.append(-item*length)
# print('displist:'dispControl)
#wipe and build a model
ops.wipe()
ops.model('basic', '-ndm', 2, '-ndf', 3)
#node coordinates
meshNumLength = 5
meshVerticalSize = length / meshNumLength
meshSteelSize = 10
nodes = [(i + 1, meshVerticalSize * i)
for i in range(int(length / meshVerticalSize) + 1)]
for item in nodes:
ops.node(item[0], 0, item[1])
#boundary condition
ops.fix(1, 1, 1, 1)
# if bool(Fixed):
# ops.fix(int(length/meshVerticalSize)+1,0,0,1) ##uppper constrain condition: free or no-rotation
#mass defination(concentrate mass to nodes)
nodeMassSteel = areaSteel * meshVerticalSize * densitySteel
nodeMassConcrete = areaConcrete * meshVerticalSize * densityConcrete
nodeMass = nodeMassSteel + nodeMassConcrete
for i in range(len(nodes) - 1):
arg = [0., nodeMass, 0.]
ops.mass(i + 2, *arg)
#transformation:
ops.geomTransf('Linear', 1)
#material defination
##steel
ops.uniaxialMaterial('Hysteretic', 1001, *point1Steel, *point2Steel,
*point3Steel, *point1SteelNegative,
*point2SteelNegative, *point3SteelNegative, pinchX,
pinchY, damagedFactor, 0, 0.0)
##concrete
##using concrete01
#peakPointConcrete,crushPointConcrete=[110.6,0.00544],[22.11,0.09145]
#ops.uniaxialMaterial('Concrete01',1,*peakPointConcrete,*crushPointConcrete)
###using concrete02
ops.uniaxialMaterial('Concrete02', 1, *peakPointConcrete,
*crushPointConcrete, unloadingLambda, tensileStrength,
tensilePostStiffness)
#section defination
ops.section('Fiber', 1)
##inner concrete fiber
fiberPointI, fiberPointJ = [
-(secHeight - 2 * thickness) / 2, -(secWidth - 2 * thickness) / 2
], [(secHeight - 2 * thickness) / 2, (secWidth - 2 * thickness) / 2]
ops.patch('rect', 1, 10, 1, *fiberPointI, *fiberPointJ
) # https://opensees.berkeley.edu/wiki/index.php/Patch_Command
##outside steel fiber
steelFiberProperty = {
'height': meshSteelSize,
'area': meshSteelSize * thickness
}
steelFiberPropertyLeftAndRight = {
'height': secWidth,
'area': secWidth * thickness
}
###left and right
leftEdgeFiberY, rightEdgeFiberY = -(
secHeight - 2 * thickness) / 2 - thickness / 2, (
secHeight -
2 * thickness) / 2 + thickness / 2 #rightEdgeFiberY might be wrong
leftandRightEdgeFiberZ = [
-secWidth / 2 + steelFiberPropertyLeftAndRight['height'] * (1 / 2 + N)
for N in range(int(secWidth /
steelFiberPropertyLeftAndRight['height']))
]
###up and down
upEdgeFiberZ, downEdgeFiberZ = -(
secWidth - 2 * thickness) / 2 - thickness / 2, (
secWidth - 2 * thickness) / 2 + thickness / 2
upandDownEdgeFiberY = [
-secHeight / 2 + thickness + steelFiberProperty['height'] * (1 / 2 + N)
for N in range(
int((secHeight - 2 * thickness) / steelFiberProperty['height']))
]
for i in leftandRightEdgeFiberZ:
i = float(i)
ops.fiber(float(leftEdgeFiberY), i,
steelFiberPropertyLeftAndRight['area'], 1001)
ops.fiber(float(rightEdgeFiberY), i,
steelFiberPropertyLeftAndRight['area'], 1001)
for j in upandDownEdgeFiberY:
j = float(j)
ops.fiber(j, float(upEdgeFiberZ), steelFiberProperty['area'], 1001)
ops.fiber(j, float(downEdgeFiberZ), steelFiberProperty['area'], 1001)
#beamInergration defination
ops.beamIntegration('NewtonCotes', 1, 1, 5)
#element defination
for i in range(len(nodes) - 1):
ops.element('dispBeamColumn', i + 1, i + 1, i + 2, 1, 1)
#recorders
ops.recorder('Node', '-file', 'topLateralDisp.txt', '-time', '-node',
int(length / meshVerticalSize + 1), '-dof', 1, 2, 'disp')
ops.recorder('Node', '-file', 'topLateralForce.txt', '-time', '-node',
int(length / meshVerticalSize + 1), '-dof', 1, 2, 'reaction')
ops.recorder('Element', '-file', 'topElementForce.txt', '-time', '-ele',
int(length / meshVerticalSize), 'force')
#gravity load
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(int(length / meshVerticalSize + 1), 0, axialLoad, 0)
ops.constraints('Plain')
ops.numberer('RCM')
ops.system('BandGeneral')
##convertage test
tolerant, allowedIteralStep = 1 / 1000000, 6000
ops.test('NormDispIncr', tolerant, allowedIteralStep)
ops.algorithm('Newton')
ops.integrator('LoadControl', 0.1)
ops.analysis('Static')
ops.analyze(10)
ops.loadConst('-time', 0)
#lateraldisp analysis
ops.pattern('Plain', 2, 1)
ops.load(int(length / meshVerticalSize + 1), 100, 0, 0)
for i in range(len(dispControl)):
if i == 0:
ops.integrator('DisplacementControl',
int(length / meshVerticalSize + 1), 1, 0.1)
ops.analyze(int(dispControl[i] / 0.1))
# print('Working on disp round',i)
else:
if dispControl[i] >= 0:
ops.integrator('DisplacementControl',
int(length / meshVerticalSize + 1), 1, 0.1)
ops.analyze(int(
abs(dispControl[i] - dispControl[i - 1]) / 0.1))
# print('Working on disp round',i)
else:
ops.integrator('DisplacementControl',
int(length / meshVerticalSize + 1), 1, -0.1)
ops.analyze(int(
abs(dispControl[i] - dispControl[i - 1]) / 0.1))
def RunAnalysis():
# ----------------------------
# Start of model generation
# ----------------------------
# remove existing model
ops.wipe()
ops.model("BasicBuilder", "-ndm", 3, "-ndf", 6)
# set default units
ops.defaultUnits("-force", "kip", "-length", "in", "-time", "sec", "-temp",
"F")
# Define the section
# ------------------
# secTag E nu h rho
ops.section("ElasticMembranePlateSection", 1, 3.0E3, 0.25, 1.175, 1.27)
# Define geometry
# ---------------
# these should both be even
nx = 10
ny = 2
# loaded nodes
mid = int(((nx + 1) * (ny + 1) + 1) / 2)
side1 = int((nx + 2) / 2)
side2 = int((nx + 1) * (ny + 1) - side1 + 1)
# generate the nodes and elements
# numX numY startNode startEle eleType eleArgs? coords?
ops.block2D(nx, ny, 1, 1, "ShellMITC4", 1, 1, -20.0, 0.0, 0.0, 2, -20.0,
0.0, 40.0, 3, 20.0, 0.0, 40.0, 4, 20.0, 0.0, 0.0, 5, -10.0,
10.0, 20.0, 7, 10.0, 10.0, 20.0, 9, 0.0, 10.0, 20.0)
# define the boundary conditions
ops.fixZ(0.0, 1, 1, 1, 0, 1, 1)
ops.fixZ(40.0, 1, 1, 1, 0, 1, 1)
ops.mass(20, 10.0, 10.0, 10.0, 0.0, 0.0, 0.0)
# create a Linear time series
ops.timeSeries("Linear", 1)
# add some loads
ops.pattern("Plain", 1, 1, "-fact", 1.0)
ops.load(mid, 0.0, -0.50, 0.0, 0.0, 0.0, 0.0)
ops.load(side1, 0.0, -0.25, 0.0, 0.0, 0.0, 0.0)
ops.load(side2, 0.0, -0.25, 0.0, 0.0, 0.0, 0.0)
# ------------------------
# Start of static analysis
# ------------------------
# Load control with variable load steps
# init Jd min max
ops.integrator("LoadControl", 1.0, 1, 1.0, 10.0)
ops.test("EnergyIncr", 1.0E-10, 20, 0)
ops.algorithm("Newton")
ops.numberer("RCM")
ops.constraints("Plain")
ops.system("SparseGeneral", "-piv")
ops.analysis("Static")
ops.analyze(5)
# ---------------------------------------
# Create and Perform the dynamic analysis
# ---------------------------------------
# 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)
Model = 'test'
LoadCase = 'Transient'
LoadCase2 = 'Transient_5s'
opp.createODB(Model, LoadCase, Nmodes=3, recorders=[])
opp.createODB(Model, LoadCase2, Nmodes=3, deltaT=5., recorders=[])
# Create the transient analysis
ops.test("EnergyIncr", 1.0E-10, 20, 0)
ops.algorithm("Newton")
ops.numberer("RCM")
ops.constraints("Plain")
ops.system("SparseGeneral", "-piv")
ops.integrator("Newmark", 0.50, 0.25)
ops.analysis("Transient")
# Perform the transient analysis (20 sec)
ops.analyze(100, 0.2)
M = 0.
coordTransf = "Linear" # Linear, PDelta, Corotational
massType = "-lMass" # -lMass, -cMass
nodeTag = 1
# add the nodes
# - floor at a time
zLoc = 0.
for k in range(0, numFloor + 1):
xLoc = 0.
for i in range(0, numBayX + 1):
yLoc = 0.
for j in range(0, numBayY + 1):
ops.node(nodeTag, xLoc, yLoc, zLoc)
ops.mass(nodeTag, massX, massX, 0.01, 1.0e-10, 1.0e-10, 1.0e-10)
if k == 0:
ops.fix(nodeTag, 1, 1, 1, 1, 1, 1)
yLoc += bayWidthY
nodeTag += 1
xLoc += bayWidthX
if k < numFloor:
storyHeight = storyHeights[k]
zLoc += storyHeight
# add column element
ops.geomTransf(coordTransf, 1, 1, 0, 0)
# beam integration
inteTag = 1
numpts = 2
ops.beamIntegration('Legendre', inteTag, secTag, numpts)
# beam mesh
beamTag = 6
ndf = 3
ops.mesh('line', beamTag, 2, 12, 13, beam_id, ndf, h, 'dispBeamColumn',
transfTag, inteTag)
ndmass = bmass / len(ops.getNodeTags('-mesh', beamTag))
for nd in ops.getNodeTags('-mesh', beamTag):
ops.mass(nd, ndmass, ndmass, 0.0)
# fluid mesh
fluidTag = 4
ndf = 2
ops.mesh('line', 1, 10, 4, 5, 8, 9, 10, 11, 7, 6, 12, 2, wall_id, ndf, h)
ops.mesh('line', 2, 3, 2, 1, 4, wall_id, ndf, h)
ops.mesh('line', 3, 3, 2, 3, 4, water_bound_id, ndf, h)
eleArgs = ['PFEMElementBubble', rho, mu, b1, b2, thk, kappa]
ops.mesh('tri', fluidTag, 2, 2, 3, water_body_id, ndf, h, *eleArgs)
# wall mesh
wallTag = 5
ops.mesh('tri', wallTag, 2, 1, 2, wall_id, ndf, h)
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 __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
BCol = 5.0 * ft # Column Width
PCol = Weight # nodal dead-load weight per column
#g = 386.4
Mass = PCol / g
ACol = HCol * BCol # cross-sectional area
IzCol = (BCol * math.pow(HCol, 3)) / 12 # Column moment of inertia
op.node(1, 0.0, 0.0)
op.node(2, 0.0, LCol)
op.fix(1, 1, 1, 1)
IDctrlNode = 2
IDctrlDOF = 1
op.mass(2, Mass, 1e-9, 0.0)
ColSecTag = 1 # assign a tag number to the column section
coverCol = 5.0 * inch # Column cover to reinforcing steel NA.
numBarsCol = 20 # number of longitudinal-reinforcement bars in column. (symmetric top & bot)
barAreaCol = 2.25 * inch2 # area of longitudinal-reinforcement bars
# MATERIAL parameters
IDconcU = 1 # material ID tag -- unconfined cover concrete (here used for complete section)
IDreinf = 2 # material ID tag -- reinforcement
# nominal concrete compressive strength
fc = -4.0 * ksi # CONCRETE Compressive Strength (+Tension, -Compression)
Ec = 57 * ksi * math.sqrt(
-fc /
psi) # Concrete Elastic Modulus (the term in sqr root needs to be in psi
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(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
ops.section('Elastic', secTag, E, A, Iz)
# beam integration
inteTag = 1
numpts = 2
ops.beamIntegration('Legendre', inteTag, secTag, numpts)
coltag = 3
eleArgs = ['dispBeamColumn', transfTag, inteTag]
ops.mesh('line', coltag, 2, 1, 2, sid, ndf, h, *eleArgs)
# mass
sNodes = ops.getNodeTags('-mesh', coltag)
bmass = bmass / len(sNodes)
for nd in sNodes:
ops.mass(int(nd), bmass, bmass, 0.0)
# background mesh
lower = [-h, -h]
upper = [5 * L, 3 * L]
ops.mesh('bg', h, *lower, *upper, '-structure', sid, len(sNodes), *sNodes,
'-structure', sid, len(wallNodes), *wallNodes)
print('num nodes =', len(ops.getNodeTags()))
print('num particles =', nx * ny)
# create constraint object
ops.constraints('Plain')
# create numberer object
