def material_response(self, material, demand):
"""
Calculate the response of a material to a given load history.
Parameters
----------
material: Material
The material object to analyze.
demand: DemandProtocol
The load history the material shall be exposed to.
Returns
-------
response: DataFrame
The DataFrame includes columns for strain (eps) and stress (sig).
"""
# initialize the analysis
self._initialize()
# define the structure
struct = SDOF(Truss(material, l_tot=1., A_cs=1.))
struct.create_FEM(damping=False)
id_ctrl_node = struct.ctrl_node
load_dir = 1
# define the loading
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
if self.ndf == 1 and self.ndm == 1:
ops.load(id_ctrl_node, 1.)
# configure the analysis
ops.constraints('Plain')
ops.numberer('RCM')
ops.system('UmfPack')
ops.test('NormDispIncr', 1e-10, 100)
ops.algorithm('NewtonLineSearch', '-maxIter', 100)
# initialize the arrays for results
result_size = demand.length
response = pd.DataFrame(np.zeros((result_size + 1, 2)),
columns=['eps', 'sig'])
# perform the analysis
for i, disp_incr in enumerate(demand.increments):
ops.integrator('DisplacementControl', id_ctrl_node, load_dir,
disp_incr)
ops.analysis('Static')
ops.analyze(1)
response.loc[i + 1, 'eps'] = ops.nodeDisp(id_ctrl_node, load_dir)
# response.loc[i+1, 'sig'] = ops.eleResponse(1, 'axialForce')[0] #![4]
response.loc[i + 1, 'sig'] = ops.eleResponse(1,
'axialForce') #![4]
return response
ops.node(9, 2.5, .5) # comment for quad8n element
ops.element('tri6n', 1, 1, 2, 3, 5, 6, 9, thk, 'PlaneStress', 1)
ops.element('tri6n', 2, 1, 3, 4, 9, 7, 8, thk, 'PlaneStress', 1)
ops.fix(1, 1, 1)
ops.fix(4, 1, 0)
ops.fix(8, 1, 0)
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(2, P, 0.)
ops.load(3, -P, 0.)
ops.analysis('Static')
ops.analyze(1)
ops.printModel()
stressAtNodes_ele1 = ops.eleResponse(1, 'stressAtNodes')
print(f'\nTip vertical displacement (node 2) is {ops.nodeDisp(2, 2):.4f}')
print(f'Stress sigma_xx at node 1 is {stressAtNodes_ele1[0]:.1f}')
# verification:
# tip vertical displacement (node 2 and 3) = 0.0075
# bottom extreme stress_xx (extrapolated) = 60000.0
exit()
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_PlanarTruss():
A = 10.0
E = 3000.
L = 200.0
alpha = 30.0
P = 200.0
sigmaYP = 60.0
pi = 2.0*asin(1.0)
alphaRad = alpha*pi/180.
cosA = cos(alphaRad)
sinA = sin(alphaRad)
# EXACT RESULTS per Popov
F1 = P/(2*cosA*cosA*cosA + 1)
F2 = F1*cosA*cosA
disp = -F1*L/(A*E)
# create the finite element model
ops.wipe()
ops.model('Basic', '-ndm', 2, '-ndf', 2)
dX = L*tan(alphaRad)
ops.node( 1, 0.0, 0.0)
ops.node( 2, dX, 0.0)
ops.node( 3, 2.0*dX, 0.0)
ops.node( 4, dX, -L )
ops.fix( 1, 1, 1)
ops.fix( 2, 1, 1)
ops.fix( 3, 1, 1)
ops.uniaxialMaterial('Elastic', 1, E)
ops.element('Truss', 1, 1, 4, A, 1)
ops.element('Truss', 2, 2, 4, A, 1)
ops.element('Truss', 3, 3, 4, A, 1)
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load( 4, 0., -P)
ops.numberer( 'Plain')
ops.constraints( 'Plain')
ops.algorithm( 'Linear')
ops.system('ProfileSPD')
ops.integrator('LoadControl', 1.0)
ops.analysis('Static')
ops.analyze(1)
# determine PASS/FAILURE of test
testOK = 0
#
# print table of camparsion
#
comparisonResults = F2, F1, F2
print("\nElement Force Comparison:")
tol = 1.0e-6
print('{:>10}{:>15}{:>15}'.format('Element','OpenSees','Popov'))
for i in range(1,4):
exactResult = comparisonResults[i-1]
eleForce = ops.eleResponse(i, 'axialForce')
print('{:>10d}{:>15.4f}{:>15.4f}'.format(i, eleForce[0], exactResult))
if abs(eleForce[0]-exactResult) > tol:
testOK = -1
print("failed force-> ", abs(eleForce[0]-exactResult), " ", tol)
print("\nDisplacement Comparison:")
osDisp = ops.nodeDisp( 4, 2)
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDisp,'Exact:', disp))
if abs(osDisp-disp) > tol:
testOK = -1
print("failed linear disp")
print("\n\n - NonLinear (Example2.23)")
#EXACT
# Exact per Popov
PA = (sigmaYP*A) * (1.0+2*cosA*cosA*cosA)
dispA = PA/P*disp
PB = (sigmaYP*A) * (1.0+2*cosA)
dispB = dispA / (cosA*cosA)
# create the new finite element model for nonlinear case
# will apply failure loads and calculate displacements
ops.wipe()
ops.model('Basic', '-ndm', 2, '-ndf', 2)
ops.node( 1, 0.0, 0.0)
ops.node( 2, dX, 0.0)
ops.node( 3, 2.0*dX, 0.0)
ops.node( 4, dX, -L )
ops.fix( 1, 1, 1)
ops.fix( 2, 1, 1)
ops.fix( 3, 1, 1)
ops.uniaxialMaterial( 'ElasticPP', 1, E, sigmaYP/E)
ops.element('Truss', 1, 1, 4, A, 1)
ops.element('Truss', 2, 2, 4, A, 1)
ops.element('Truss', 3, 3, 4, A, 1)
ops.timeSeries( 'Path', 1, '-dt', 1.0, '-values', 0.0, PA, PB, PB)
ops.pattern('Plain', 1, 1)
ops.load( 4, 0., -1.0)
ops.numberer('Plain')
ops.constraints('Plain')
ops.algorithm('Linear')
ops.system('ProfileSPD')
ops.integrator('LoadControl', 1.0)
ops.analysis('Static')
ops.analyze(1)
osDispA = ops.nodeDisp( 4, 2)
#print node 4
#print ele
ops.analyze(1)
osDispB = ops.nodeDisp( 4, 2)
#print node 4
#print ele
# determine PASS/FAILURE of test
testOK = 0
print("\nDisplacement Comparison:")
print("elastic limit state:")
osDisp = ops.nodeDisp( 4, 2)
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDispA,'Exact:',dispA))
if abs(osDispA-dispA) > tol:
testOK = -1
print("failed nonlineaer elastic limit disp")
print("collapse limit state:")
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDispB,'Exact:',dispB))
if abs(osDispB-dispB) > tol:
testOK = -1
print("failed nonlineaer collapse limit disp")
assert testOK == 0
mf.buildModel()
# Show Model
# opp.plot_model('node', 'elements')
# Create Database
Model = 'Cantilever'
LoadCase = 'PushoverLcD'
opp.createODB(Model, LoadCase)
eleNumber = 1
sectionNumber = 1
opp.saveFiberData2D(Model, LoadCase, eleNumber, sectionNumber)
# Run Analysis
af.PushoverLcD(0.05)
out = op.eleResponse(1, 'section', '1', 'fiberData')
op.wipe()
opp.plot_fiberResponse2D(Model, LoadCase, eleNumber, sectionNumber)
opp.plot_fiberResponse2D(Model,
LoadCase,
eleNumber,
sectionNumber,
InputType='strain')
#
ani = opp.animate_fiberResponse2D(Model, LoadCase, eleNumber, sectionNumber)
def test_PlanarTrussExtra():
A = 10.0
E = 3000.
L = 200.0
alpha = 30.0
P = 200.0
sigmaYP = 60.0
pi = 2.0*asin(1.0)
alphaRad = alpha*pi/180.
cosA = cos(alphaRad)
sinA = sin(alphaRad)
# EXACT RESULTS per Popov
F1 = P/(2*cosA*cosA*cosA + 1)
F2 = F1*cosA*cosA
disp = -F1*L/(A*E)
b = 1.0
d = A
z = A
y = 1.0
numFiberY = 10 # note we only need so many to get the required accuracy on eigenvalue 1e-7!
numFiberZ = 1
# create the finite element model
for sectType in ['Fiber', 'Uniaxial']:
print(" - Linear (Example 2.14) sectType: ", sectType)
testOK = 0
ops.wipe()
ops.model( 'Basic', '-ndm', 2, '-ndf', 2)
dX = L*tan(alphaRad)
ops.node(1, 0.0, 0.0)
ops.node(2, dX , 0.0)
ops.node(3, 2.0*dX, 0.0)
ops.node(4, dX, -L )
ops.fix(1, 1, 1)
ops.fix(2, 1, 1)
ops.fix(3, 1, 1)
if sectType == "Uniaxial":
ops.uniaxialMaterial( 'Elastic', 1, A*E)
ops.section( 'Uniaxial', 1, 1, 'P')
else:
ops.uniaxialMaterial( 'Elastic', 1, E)
ops.section('Fiber', 1)
# patch rect 1 numFiberY numFiberZ [expr -z/2.0] [expr -y/2.0] [expr z/2.0] [expr y/2.0]
ops.patch( 'rect', 1, numFiberY, numFiberZ, -z, -y, 0., 0.)
ops.element('Truss', 1, 1, 4, 1)
ops.element('Truss', 2, 2, 4, 1)
ops.element('Truss', 3, 3, 4, 1)
ops.timeSeries( 'Linear', 1)
ops.pattern( 'Plain', 1, 1)
ops.load( 4, 0., -P)
ops.numberer( 'Plain')
ops.constraints( 'Plain')
ops.algorithm('Linear')
ops.system('ProfileSPD')
ops.integrator('LoadControl', 1.0)
ops.analysis('Static')
ops.analyze(1)
#
# print table of camparsion
#
comparisonResults = F2, F1, F2
print("\nElement Force Comparison:")
tol = 1.0e-6
print('{:>10}{:>15}{:>15}'.format('Element','OpenSees','Popov'))
for i in range(1,4):
exactResult = comparisonResults[i-1]
eleForce =ops.eleResponse( i, 'axialForce')
print('{:>10d}{:>15.4f}{:>15.4f}'.format(i, eleForce[0], exactResult))
if abs(eleForce[0]-exactResult) > tol:
testOK = -1
print("failed force-> ", abs(eleForce[0]-exactResult), " ", tol)
print("\nDisplacement Comparison:")
osDisp = ops.nodeDisp( 4, 2)
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDisp,'Exact:', disp))
if abs(osDisp-disp) > tol:
testOK = -1
print("failed linear disp")
print("\n\n - NonLinear (Example2.23) sectType: ", sectType)
#EXACT
# Exact per Popov
PA = (sigmaYP*A) * (1.0+2*cosA*cosA*cosA)
dispA = PA/P*disp
PB = (sigmaYP*A) * (1.0+2*cosA)
dispB = dispA / (cosA*cosA)
# create the new finite element model for nonlinear case
# will apply failure loads and calculate displacements
ops.wipe()
ops.model('Basic', '-ndm', 2, '-ndf', 2)
ops.node( 1, 0.0, 0.0)
ops.node( 2, dX, 0.0)
ops.node( 3, 2.0*dX, 0.0)
ops.node( 4, dX, -L )
ops.fix( 1, 1, 1)
ops.fix( 2, 1, 1)
ops.fix( 3, 1, 1)
if sectType == "Uniaxial":
ops.uniaxialMaterial( 'ElasticPP', 1, A*E, sigmaYP/E)
ops.section( 'Uniaxial', 1, 1, 'P')
else:
ops.uniaxialMaterial( 'ElasticPP', 1, E, sigmaYP/E)
ops.section( 'Fiber', 1)
ops.patch( 'rect', 1, numFiberY, numFiberZ, -z/2.0, -y/2.0, z/2.0, y/2.0)
ops.element('Truss', 1, 1, 4, 1)
ops.element('Truss', 2, 2, 4, 1)
ops.element('Truss', 3, 3, 4, 1)
ops.timeSeries( 'Path', 1, '-dt', 1.0, '-values', 0.0, PA, PB, PB)
ops.pattern('Plain', 1, 1)
ops.load( 4, 0., -1.0)
ops.numberer('Plain')
ops.constraints('Plain')
ops.algorithm('Linear')
ops.system('ProfileSPD')
ops.integrator('LoadControl', 1.0)
ops.analysis('Static')
ops.analyze(1)
osDispA = ops.nodeDisp( 4, 2)
ops.analyze(1)
osDispB = ops.nodeDisp( 4, 2)
print("\nDisplacement Comparison:")
print("elastic limit state:")
osDisp = ops.nodeDisp( 4, 2)
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDispA,'Exact:',dispA))
if abs(osDispA-dispA) > tol:
testOK = -1
print("failed nonlineaer elastic limit disp")
print("collapse limit state:")
print('{:>10}{:>15.8f}{:>10}{:>15.8f}'.format('OpenSees:',osDispB,'Exact:',dispB))
if abs(osDispB-dispB) > tol:
testOK = -1
print("failed nonlineaer collapse limit disp")
assert testOK == 0