def PushoverLcD(Nsteps):
ControlNode = 4
ControlNodeDof = 1
du = 0.00001*m
# Define time series
# timeSeries('Constant', tag, '-factor', factor=1.0)
op.timeSeries('Constant',1)
op.timeSeries('Linear', 2)
# define loads
op.pattern('Plain',1 , 2)
op.sp(ControlNode, ControlNodeDof, du)
# Define Analysis Options
# create SOE
op.system("BandGeneral")
# create DOF number
op.numberer("Plain")
# create constraint handler
op.constraints("Transformation")
# create integrator
op.integrator("LoadControl", .1)
# create algorithm
op.algorithm("Newton")
# create analysis object
op.analysis("Static")
# Create Test
op.test('NormDispIncr', 1.*10**-8, 50)
# Run Analysis
op.record()
ok = op.analyze(Nsteps)
nn = 0
def analysis(P, steps, tol, max_iter):
tsTag = 1
ops.timeSeries('Linear', tsTag)
pattTag = 1
ops.pattern('Plain', pattTag, tsTag)
ops.load(2, *P)
##########################################################################
ops.constraints('Plain')
ops.numberer('RCM')
ops.system('BandGeneral')
ops.test('NormUnbalance', tol, max_iter)
ops.algorithm('Newton')
temp = 1 / steps
ops.integrator('LoadControl', temp)
ops.analysis('Static')
ops.analyze(steps)
##########################################################################
opsplt.plot_model()
##########################################################################
ops.wipe()
def analyse(self, num_incr):
'''
Analyse the system.
Args:
num_incr: An integer number of load increments.
return_node_disp:
'''
ops.constraints('Transformation')
ops.numberer('RCM')
ops.system('BandGeneral')
ops.test('NormUnbalance', 2e-8, num_incr)
ops.algorithm('Newton')
ops.integrator('LoadControl', 1 / num_incr)
ops.record()
ops.analysis('Static')
ok = ops.analyze(num_incr)
# Report analysis status
if ok == 0: print("Analysis done.")
else: print("Convergence issue.")
op.recorder('Node', '-file', 'Data-2c/DBase.out','-time', '-node', 1, '-dof', 1,2,3, 'disp')
op.recorder('Node', '-file', 'Data-2c/RBase.out','-time', '-node', 1, '-dof', 1,2,3, 'reaction')
#op.recorder('Drift', '-file', 'Data-2c/Drift.out','-time', '-node', 1, '-dof', 1,2,3, 'disp')
op.recorder('Element', '-file', 'Data-2c/FCol.out','-time', '-ele', 1, 'globalForce')
op.recorder('Element', '-file', 'Data-2c/ForceColSec1.out','-time', '-ele', 1, 'section', 1, 'force')
#op.recorder('Element', '-file', 'Data-2c/DCol.out','-time', '-ele', 1, 'deformations')
#defining gravity loads
op.timeSeries('Linear', 1)
op.pattern('Plain', 1, 1)
op.load(2, 0.0, -PCol, 0.0)
Tol = 1e-8 # convergence tolerance for test
NstepGravity = 10
DGravity = 1/NstepGravity
op.integrator('LoadControl', DGravity) # determine the next time step for an analysis
op.numberer('Plain') # renumber dof's to minimize band-width (optimization), if you want to
op.system('BandGeneral') # how to store and solve the system of equations in the analysis
op.constraints('Plain') # how it handles boundary conditions
op.test('NormDispIncr', Tol, 6) # determine if convergence has been achieved at the end of an iteration step
op.algorithm('Newton') # use Newton's solution algorithm: updates tangent stiffness at every iteration
op.analysis('Static') # define type of analysis static or transient
op.analyze(NstepGravity) # apply gravity
op.loadConst('-time', 0.0) #maintain constant gravity loads and reset time to zero
#applying Dynamic Ground motion analysis
GMdirection = 1
GMfile = 'BM68elc.acc'
GMfact = 1.0
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
def get_pile_m(pile_z0=0, pile_z1=-30, pile_d=2, m0=7.5, pile_f=0, pile_m=0):
pile_h = pile_z0 - pile_z1
pile_a = np.pi * (pile_d / 2) ** 2
pile_i = np.pi * pile_d ** 4 / 64
pile_b1 = 0.9 * (1.5 + 0.5 / pile_d) * 1 * pile_d
# 建立模型
ops.wipe()
ops.model('basic', '-ndm', 2, '-ndf', 3)
# 建立节点
node_z = np.linspace(pile_z0, pile_z1, elem_num + 1)
for i, j in enumerate(node_z):
ops.node(i + 1, 0, j)
ops.node(i + 201, 0, j)
# 约束
for i in range(len(node_z)):
ops.fix(i + 1, 0, 1, 0)
ops.fix(i + 201, 1, 1, 1)
# 建立材料
ops.uniaxialMaterial('Elastic', 1, 3e4)
for i in range(len(node_z)):
pile_depth = i * (pile_h / elem_num)
pile_depth_nominal = 10 if pile_depth <= 10 else pile_depth
soil_k = m0 * pile_depth_nominal * pile_b1 * (pile_h / elem_num)
if i == 0:
ops.uniaxialMaterial('Elastic', 100 + i, soil_k / 2)
continue
ops.uniaxialMaterial('Elastic', 100 + i, soil_k)
# 装配
ops.geomTransf('Linear', 1)
# 建立单元
for i in range(elem_num):
ops.element('elasticBeamColumn', i + 1, i + 1, i + 2, pile_a, 3e10, pile_i, 1)
# 建立弹簧
for i in range(len(node_z)):
ops.element('zeroLength', i + 201, i + 1, i + 201, '-mat', 100 + i, '-dir', 1)
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(1, pile_f, 0, pile_m)
ops.system('BandGeneral')
ops.numberer('Plain')
ops.constraints('Plain')
ops.integrator('LoadControl', 0.01)
ops.test('EnergyIncr', 1e-6, 200)
ops.algorithm('Newton')
ops.analysis('Static')
ops.analyze(100)
# 绘制位移图
node_disp = []
for i in range(101):
node_disp.append(ops.nodeDisp(i + 1))
node_disp = np.array(node_disp) * 1000
plt.figure()
plt.subplot(121)
for i, j in enumerate(node_z):
if abs(node_disp[:, 0][i]) > max(abs(node_disp[:, 0])) / 50:
if i == 0:
plt.plot([0, node_disp[:, 0][i]], [j, j], linewidth=1.5, color='grey')
else:
plt.plot([0, node_disp[:, 0][i]], [j, j], linewidth=0.7, color='grey')
if abs(node_disp[:, 0][i]) == max(abs(node_disp[:, 0])):
plt.annotate(f'{node_disp[:, 0][i]:.1f} mm', xy=(node_disp[:, 0][i], j),
xytext=(0.3, 0.5), textcoords='axes fraction',
bbox=dict(boxstyle="round", fc="0.8"),
arrowprops=dict(arrowstyle='->', connectionstyle="arc3,rad=-0.3"))
plt.plot([0, 0], [node_z[0], node_z[-1]], linewidth=1.5, color='dimgray')
plt.plot(node_disp[:, 0], node_z, linewidth=1.5, color='midnightblue')
plt.xlabel('Displacement(mm)')
plt.ylabel('Pile Depth(m)')
# 绘制弯矩图
elem_m = []
for i in range(100):
elem_m.append(ops.eleForce(i + 1))
elem_m = np.array(elem_m) / 1000
plt.subplot(122)
for i, j in enumerate(node_z[:-1]):
if abs(elem_m[:, 2][i]) > max(abs(elem_m[:, 2])) / 50:
if i == 0:
plt.plot([0, elem_m[:, 2][i]], [j, j], linewidth=1.5, color='grey')
else:
plt.plot([0, elem_m[:, 2][i]], [j, j], linewidth=0.7, color='grey')
if abs(elem_m[:, 2][i]) == max(abs(elem_m[:, 2])):
plt.annotate(f'{elem_m[:, 2][i]:.1f} kN.m', xy=(elem_m[:, 2][i], j),
xytext=(0.5, 0.5), textcoords='axes fraction',
bbox=dict(boxstyle="round", fc="0.8"),
arrowprops=dict(arrowstyle='->', connectionstyle="arc3,rad=0.3"))
plt.plot([0, 0], [node_z[0], node_z[-1]], linewidth=1.5, color='dimgray')
plt.plot(elem_m[:, 2], node_z[:-1], linewidth=1.5, color='brown')
plt.xlabel('Moment(kN.m)')
# plt.ylabel('Pile Depth(m)')
plt.show()
return abs(max(elem_m[:, 2]))
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 analisis_opensees(path, permutaciones): #helper, #win
ops.wipe()
# bucle para generar los x análisis
for i in range(len(permutaciones)):
perfil = str(permutaciones[i][0])
nf = permutaciones[i][2]
amort = permutaciones[i][3]
den = permutaciones[i][4]
vel = permutaciones[i][5]
capas = len(permutaciones[i][6])
nstep = permutaciones[i][30]
dt = float(permutaciones[i][31])
# creación de elementos
sElemX = permutaciones[i][1] # elementos en X
sElemZ = permutaciones[i][46] # espesor en Z
# =============================================================================
# ######## geometría de la columna ######
# =============================================================================
# límite entre capas
limite_capa = []
anterior = 0
for j in range(capas):
espesor = permutaciones[i][8][j]
limite_capa.append(espesor + anterior)
anterior = limite_capa[j]
print('Límite de capa: ' + str(limite_capa[j]))
# creación de elementos y nodos en x
nElemX = 1 # elementos en x
nNodeX = 2 * nElemX + 1 # nodos en x
# creación de elementos y nodos para z
nElemZ = 1
# creación de elementos y nodos en Y y totales
nElemY = [] # elementos en y
sElemY = [] # dimension en y
nElemT = 0
for j in range(capas):
espesor = permutaciones[i][8][j]
nElemY.append(2 * espesor)
nElemT += nElemY[j]
print('Elementos en capa ' + str(j + 1) + ': ' + str(nElemY[j]))
sElemY.append(permutaciones[i][8][j] / nElemY[j])
print('Tamaño de los elementos en capa ' + str(j + 1) + ': ' +
str(sElemY[j]) + '\n')
# number of nodes in vertical direction in each layer
nNodeY = [] # dimension en y
nNodeT = 0
s = 0
for j in range(capas - 1):
nNodeY.append(4 * nElemY[j])
nNodeT += nNodeY[j]
s += 1
print('Nodos en capa ' + str(j + 1) + ': ' + str(nNodeY[j]))
nNodeY.append(4 * (nElemY[-1] + 1))
nNodeT += nNodeY[-1]
print('Nodos en capa ' + str(s + 1) + ': ' + str(nNodeY[s]))
print('Nodos totales: ' + str(nNodeT))
#win.ui.progressBar.setValue(15)
# =============================================================================
# ######### Crear nodos del suelo ##########
# =============================================================================
# creación de nodos de presión de poros
ops.model('basic', '-ndm', 3, '-ndf', 4)
with open(path + '/Post-proceso/' + perfil + '/ppNodesInfo.dat',
'w') as f:
count = 0.0
yCoord = 0.0
nodos = []
dryNode = []
altura_nf = 10 - nf
for k in range(capas):
for j in range(0, int(nNodeY[k]), 4):
ops.node(j + count + 1, 0.0, yCoord, 0.0)
ops.node(j + count + 2, 0.0, yCoord, sElemZ)
ops.node(j + count + 3, sElemX, yCoord, sElemZ)
ops.node(j + count + 4, sElemX, yCoord, 0.0)
f.write(
str(int(j + count + 1)) + '\t' + str(0.0) + '\t' +
str(yCoord) + '\t' + str(0.0) + '\n')
f.write(
str(int(j + count + 2)) + '\t' + str(0.0) + '\t' +
str(yCoord) + '\t' + str(sElemZ) + '\n')
f.write(
str(int(j + count + 3)) + '\t' + str(sElemX) + '\t' +
str(yCoord) + '\t' + str(sElemZ) + '\n')
f.write(
str(int(j + count + 4)) + '\t' + str(sElemX) + '\t' +
str(yCoord) + '\t' + str(0.0) + '\n')
nodos.append(str(j + count + 1))
nodos.append(str(j + count + 2))
nodos.append(str(j + count + 3))
nodos.append(str(j + count + 4))
#designate node sobre la superficie de agua
if yCoord >= altura_nf:
dryNode.append(j + count + 1)
dryNode.append(j + count + 2)
dryNode.append(j + count + 3)
dryNode.append(j + count + 4)
yCoord = (yCoord + sElemY[k])
count = (count + nNodeY[k])
print("Finished creating all soil nodes...")
# =============================================================================
# ####### Condiciones de contorno en la base de la columna #########
# =============================================================================
ops.fix(1, *[0, 1, 1, 0])
ops.fix(2, *[0, 1, 1, 0])
ops.fix(3, *[0, 1, 1, 0])
ops.fix(4, *[0, 1, 1, 0])
ops.equalDOF(1, 2, 1)
ops.equalDOF(1, 3, 1)
ops.equalDOF(1, 4, 1)
print('Fin de creación de nodos de la base de la columna\n\n')
# =============================================================================
# ####### Condiciones de contorno en los nudos restantes #########
# =============================================================================
count = 0
for k in range(5, int(nNodeT + 1), 4):
ops.equalDOF(k, k + 1, *[1, 2, 3])
ops.equalDOF(k, k + 2, *[1, 2, 3])
ops.equalDOF(k, k + 3, *[1, 2, 3])
print('Fin de creación equalDOF para nodos de presión de poros\n\n')
for j in range(len(dryNode)):
ops.fix(dryNode[j], *[0, 0, 0, 1])
print("Finished creating all soil boundary conditions...")
# =============================================================================
# ####### crear elemento y material de suelo #########
# =============================================================================
cargas = []
for j in range(capas):
pendiente = permutaciones[i][9][j]
slope = math.atan(pendiente / 100)
tipo_suelo = permutaciones[i][6][j]
rho = permutaciones[i][10][j]
Gr = permutaciones[i][12][j]
Br = permutaciones[i][13][j]
fric = permutaciones[i][15][j]
refpress = permutaciones[i][18][j]
gmax = permutaciones[i][19][j]
presscoef = permutaciones[i][20][j]
surf = permutaciones[i][21][j]
ev = permutaciones[i][22][j]
cc1 = permutaciones[i][23][j]
cc3 = permutaciones[i][24][j]
cd1 = permutaciones[i][25][j]
cd3 = permutaciones[i][26][j]
ptang = permutaciones[i][27][j]
coh = permutaciones[i][28][j]
if tipo_suelo == 'No cohesivo':
if float(surf) > 0:
ops.nDMaterial('PressureDependMultiYield02', j + 1, 3.0,
rho, Gr, Br, fric, gmax, refpress,
presscoef, ptang, cc1, cc3, cd1, cd3,
float(surf), 5.0, 3.0, *[1.0, 0.0], ev,
*[0.9, 0.02, 0.7, 101.0])
else:
ops.nDMaterial('PressureDependMultiYield02', j + 1, 3.0,
rho, Gr, Br, fric, gmax, refpress,
presscoef, ptang, cc1, cc3, cd1, cd3,
float(surf), *permutaciones[i][29][j], 5.0,
3.0, *[1.0,
0.0], ev, *[0.9, 0.02, 0.7, 101.0])
cargas.append(
[0.0, -9.81 * math.cos(slope), -9.81 * math.sin(slope)])
print('Fin de la creación de material de suelo\n\n')
#-----------------------------------------------------------------------------------------
# 5. CREATE SOIL ELEMENTS
#-----------------------------------------------------------------------------------------
count = 0
alpha = 1.5e-6
with open(path + '/Post-proceso/' + perfil + '/ppElemInfo.dat',
'w') as f:
# crear elemento de suelo
for k in range(capas):
for j in range(int(nElemY[k])):
nI = 4 * (j + count + 1) - 3
nJ = nI + 1
nK = nI + 2
nL = nI + 3
nM = nI + 4
nN = nI + 5
nO = nI + 6
nP = nI + 7
f.write(
str(j + count + 1) + '\t' + str(nI) + '\t' + str(nJ) +
'\t' + str(nK) + '\t' + str(nL) + '\t' + str(nM) +
'\t' + str(nN) + '\t' + str(nO) + '\t' + str(nP) +
'\n')
Bc = permutaciones[i][14][k]
ev = permutaciones[i][22][k]
ops.element('SSPbrickUP', (j + count + 1),
*[nI, nJ, nK, nL, nM, nN, nO,
nP], (k + 1), float(Bc), 1.0, 1.0, 1.0, 1.0,
float(ev), alpha, cargas[k][0], cargas[k][1],
cargas[k][2])
count = (count + int(nElemY[k]))
print('Fin de la creación del elemento del suelo\n\n')
#win.ui.progressBar.setValue(25)
# =============================================================================
# ######### Amortiguamiento de Lysmer ##########
# =============================================================================
ops.model('basic', '-ndm', 3, '-ndf', 3)
# definir nodos y coordenadas del amortiguamiento
dashF = nNodeT + 1
dashX = nNodeT + 2
dashZ = nNodeT + 3
ops.node(dashF, 0.0, 0.0, 0.0)
ops.node(dashX, 0.0, 0.0, 0.0)
ops.node(dashZ, 0.0, 0.0, 0.0)
# definir restricciones para los nodos de amortiguamiento
ops.fix(dashF, 1, 1, 1)
ops.fix(dashX, 0, 1, 1)
ops.fix(dashZ, 1, 1, 0)
# definir equalDOF para el amortiguamiento en la base del suelo
ops.equalDOF(1, dashX, 1)
ops.equalDOF(1, dashZ, 3)
print(
'Fin de la creación de condiciones de contorno de los nodos de amortiguamiento\n\n'
)
# definir el material de amortiguamiento
colArea = sElemX * sElemZ
dashpotCoeff = vel * den * colArea
ops.uniaxialMaterial('Viscous', capas + 1, dashpotCoeff, 1.0)
# definir el elemento
ops.element('zeroLength', nElemT + 1, *[dashF, dashX], '-mat',
capas + 1, '-dir', *[1])
ops.element('zeroLength', nElemT + 2, *[dashF, dashZ], '-mat',
capas + 1, '-dir', *[3])
print('Fin de la creación del elemento de amortiguamiento\n\n')
#-----------------------------------------------------------------------------------------
# 9. DEFINE ANALYSIS PARAMETERS
#-----------------------------------------------------------------------------------------
# amortiguamiento de Rayleigh
# frecuencia menor
omega1 = 2 * math.pi * 0.2
# frecuencia mayor
omega2 = 2 * math.pi * 20
a0 = 2.0 * (amort / 100) * omega1 * omega2 / (omega1 + omega2)
a1 = 2.0 * (amort / 100) / (omega1 + omega2)
print('Coeficientes de amortiguamiento' + '\n' + 'a0: ' +
format(a0, '.6f') + '\n' + 'a1: ' + format(a1, '.6f') + '\n\n')
#win.ui.progressBar.setValue(35)
# =============================================================================
# ######## Determinación de análisis estático #########
# =============================================================================
#---DETERMINE STABLE ANALYSIS TIME STEP USING CFL CONDITION
# se determina a partir de un análisis transitorio de largo tiempo
duration = nstep * dt
# tamaño mínimo del elemento y velocidad máxima
minSize = sElemY[0]
vsMax = permutaciones[i][11][0]
for j in range(1, capas):
if sElemY[j] < minSize:
minSize = sElemY[j]
if permutaciones[i][11][j] > vsMax:
vsMax = permutaciones[i][11][j]
# trial analysis time step
kTrial = minSize / (vsMax**0.5)
# tiempo de análisis y pasos de tiempo
if dt <= kTrial:
nStep = nstep
dT = dt
else:
nStep = int(math.floor(duration / kTrial) + 1)
dT = duration / nStep
print('Número de pasos en el análisis: ' + str(nStep) + '\n')
print('Incremento de tiempo: ' + str(dT) + '\n\n')
#----------------------------------------------------------------------------------------
# 7. GRAVITY ANALYSIS
#-----------------------------------------------------------------------------------------
ops.model('basic', '-ndm', 3, '-ndf', 4)
ops.updateMaterialStage('-material', int(k + 1), '-stage', 0)
# algoritmo de análisis estático
ops.constraints(permutaciones[i][32][0],
float(permutaciones[i][32][1]),
float(permutaciones[i][32][2]))
ops.test(permutaciones[i][34][0], float(permutaciones[i][34][1]),
int(permutaciones[i][34][2]), int(permutaciones[i][34][3]))
ops.algorithm(permutaciones[i][38][0])
ops.numberer(permutaciones[i][33][0])
ops.system(permutaciones[i][36][0])
ops.integrator(permutaciones[i][35][0], float(permutaciones[i][35][1]),
float(permutaciones[i][35][2]))
ops.analysis(permutaciones[i][37][0])
print('Inicio de análisis estático elástico\n\n')
ops.start()
ops.analyze(20, 5.0e2)
print('Fin de análisis estático elástico\n\n')
#win.ui.progressBar.setValue(40)
# update materials to consider plastic behavior
# =============================================================================
ops.updateMaterialStage('-material', int(k + 1), '-stage', 1)
# =============================================================================
# plastic gravity loading
print('Inicio de análisis estático plástico\n\n')
ok = ops.analyze(40, 5.0e-2)
if ok != 0:
error = 'Error de convergencia en análisis estático de modelo' + str(
perfil) + '\n\n'
print(error)
break
print('Fin de análisis estático plástico\n\n')
#-----------------------------------------------------------------------------------------
# 11. UPDATE ELEMENT PERMEABILITY VALUES FOR POST-GRAVITY ANALYSIS
#-----------------------------------------------------------------------------------------
ini = 1
aum = 0
sum = 0
for j in range(capas):
#Layer 3
ops.setParameter(
'-val', permutaciones[i][16][j],
['-eleRange',
int(ini + aum),
int(nElemY[j] + sum)], 'xPerm')
ops.setParameter(
'-val', permutaciones[i][17][j],
['-eleRange',
int(ini + aum),
int(nElemY[j] + sum)], 'yPerm')
ops.setParameter(
'-val', permutaciones[i][16][j],
['-eleRange',
int(ini + aum),
int(nElemY[j] + sum)], 'zPerm')
ini = nElemY[j] + sum
sum += nElemY[j]
aum = 1
print("Finished updating permeabilities for dynamic analysis...")
# =============================================================================
# ########### Grabadores dinámicos ##########
# =============================================================================
ops.setTime(0.0)
ops.wipeAnalysis()
ops.remove('recorders')
# tiempo de la grabadora
recDT = 10 * dt
path_acel = path + '/Post-proceso/' + perfil + '/dinamico/aceleraciones/'
ops.recorder('Node', '-file', path_acel + 'accelerationx.out', '-time',
'-dT', recDT, '-node', *nodos, '-dof', 1, 'accel')
print('Fin de creación de grabadores\n\n')
#win.ui.progressBar.setValue(50)
# =============================================================================
# ######### Determinación de análisis dinámico ##########
# =============================================================================
# objeto de serie temporal para el historial de fuerza
path_vel = path + '/Pre-proceso/' + perfil + '/TREASISL2.txt'
ops.timeSeries('Path', 1, '-dt', dt, '-filePath', path_vel, '-factor',
dashpotCoeff)
ops.pattern('Plain', 10, 1)
ops.load(1, *[1.0, 0.0, 0.0, 0.0]) #CAMBIO REALIZADO OJO
print('Fin de creación de carga dinámica\n\n')
# algoritmo de análisis dinámico
ops.constraints(permutaciones[i][39][0],
float(permutaciones[i][39][1]),
float(permutaciones[i][39][2]))
ops.test(permutaciones[i][41][0], float(permutaciones[i][41][1]),
int(permutaciones[i][41][2]), int(permutaciones[i][41][3]))
ops.algorithm(permutaciones[i][45][0])
ops.numberer(permutaciones[i][40][0])
ops.system(permutaciones[i][43][0])
ops.integrator(permutaciones[i][42][0], float(permutaciones[i][42][1]),
float(permutaciones[i][42][2]))
ops.analysis(permutaciones[i][44][0])
# =============================================================================
# ops.rayleigh(a0, a1, 0.0, 0.0)
# =============================================================================
print('Inicio de análisis dinámico\n\n')
#win.ui.progressBar.setValue(85)
ok = ops.analyze(nStep, dT)
if ok != 0:
error = 'Error de convergencia en análisis dinámico de modelo' + str(
permutaciones[i][0]) + '\n\n'
print(error)
curTime = ops.getTime()
mTime = curTime
print('cursTime:' + str(curTime))
curStep = (curTime / dT)
print('cursStep:' + str(curStep))
rStep = (nStep - curStep) * 2.0
remStep = int(nStep - curStep) * 2.0
print('remSTep:' + str(curStep))
dT = (dT / 2)
print('dT:' + str(dT))
ops.analyze(remStep, dT)
if ok != 0:
error = 'Error de convergencia en análisis dinámico de modelo' + str(
permutaciones[i][0]) + '\n\n'
print(error)
curTime = ops.getTime()
print('cursTime:' + str(curTime))
curStep = (curTime - mTime) / dT
print('cursStep:' + str(curStep))
remStep = int(rStep - curStep) * 2
print('remSTep:' + str(curStep))
dT = (dT / 2)
print('dT:' + str(dT))
ops.analyze(remStep, dT)
print('Fin de análisis dinámico\n\n')
ops.wipe()
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
ops.record()
# create constraint object
ops.constraints('Plain')
# create numberer object
ops.numberer('Plain')
# create convergence test object
ops.test('PFEM', 1e-5, 1e-5, 1e-5, 1e-5, 1e-15, 1e-15, 20, 3, 1, 2)
# create algorithm object
ops.algorithm('Newton')
# create integrator object
ops.integrator('PFEM')
# create SOE object
ops.system('PFEM', '-umfpack', '-print')
# create analysis object
ops.analysis('PFEM', dtmax, dtmin, b2)
# analysis
while ops.getTime() < totaltime:
# analysis
if ops.analyze() < 0:
break
ops.remesh(alpha)
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 test_PinchedCylinder():
P = 1
R = 300.
L = 600.
E = 3e6
thickness = R / 100.
uExact = -164.24 * P / (E * thickness)
formatString = '{:>20s}{:>15.5e}'
print("\n Displacement Under Applied Load:\n")
formatString = '{:>20s}{:>10s}{:>15s}{:>15s}{:>15s}'
print(
formatString.format("Element Type", " mesh ", "OpenSees", "Exact",
"%Error"))
for shellType in ['ShellMITC4', 'ShellDKGQ', 'ShellNLDKGQ']:
for numEle in [4, 16, 32]:
ops.wipe()
# ----------------------------
# Start of model generation
# ----------------------------
ops.model('basic', '-ndm', 3, '-ndf', 6)
radius = R
length = L / 2.
E = 3.0e6
v = 0.3
PI = 3.14159
ops.nDMaterial('ElasticIsotropic', 1, E, v)
ops.nDMaterial('PlateFiber', 2, 1)
ops.section('PlateFiber', 1, 2, thickness)
#section ElasticMembranePlateSection 1 E v thickness 0.
nR = numEle
nY = numEle
tipNode = (nR + 1) * (nY + 1)
#create nodes
nodeTag = 1
for i in range(nR + 1):
theta = i * PI / (2.0 * nR)
xLoc = 300 * cos(theta)
zLoc = 300 * sin(theta)
for j in range(nY + 1):
yLoc = j * length / (1.0 * nY)
ops.node(nodeTag, xLoc, yLoc, zLoc)
nodeTag += 1
#create elements
eleTag = 1
for i in range(nR):
iNode = i * (nY + 1) + 1
jNode = iNode + 1
lNode = iNode + (nY + 1)
kNode = lNode + 1
for j in range(nY):
ops.element(shellType, eleTag, iNode, jNode, kNode, lNode,
1)
eleTag += 1
iNode += 1
jNode += 1
kNode += 1
lNode += 1
# define the boundary conditions
ops.fixX(radius, 0, 0, 1, 1, 1, 0, '-tol', 1.0e-2)
ops.fixZ(radius, 1, 0, 0, 0, 1, 1, '-tol', 1.0e-2)
ops.fixY(0., 1, 0, 1, 0, 0, 0, '-tol', 1.0e-2)
ops.fixY(length, 0, 1, 0, 1, 0, 1, '-tol', 1.0e-2)
#define loads
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
ops.load(tipNode, 0., 0., -1. / 4.0, 0., 0., 0.)
ops.integrator('LoadControl', 1.0)
ops.test('EnergyIncr', 1.0e-10, 20, 0)
ops.algorithm('Newton')
ops.numberer('RCM')
ops.constraints('Plain')
ops.system('Umfpack')
ops.analysis('Static')
ops.analyze(1)
res = ops.nodeDisp(tipNode, 3)
err = abs(100 * (uExact - res) / uExact)
formatString = '{:>20s}{:>5d}{:>3s}{:>2d}{:>15.5e}{:>15.5e}{:>15.2f}'
print(
formatString.format(shellType, numEle, " x ", numEle, res,
uExact, err))
tol = 5.0
if abs(100 * (uExact - res) / uExact) > tol:
testOK = 1
else:
testOK = 0
assert testOK == 0
ops.node(2, 144.0, 0.0)
ops.node(3, 168.0, 0.0)
ops.node(4, 72.0, 96.0)
ops.fix(2, 1, 1)
ops.fix(3, 1, 1)
ops.element('Truss', 2, 2, 4, 5.0, 1)
ops.element('Truss', 3, 3, 4, 5.0, 1)
ops.constraints('Transformation')
ops.numberer('ParallelPlain')
ops.system('Mumps')
ops.test('NormDispIncr', 1e-6, 6, 2)
ops.algorithm('Newton')
ops.integrator('LoadControl', 0.1)
ops.analysis('Static')
ops.analyze(10)
print('Node 4: ', [ops.nodeCoord(4), ops.nodeDisp(4)])
ops.loadConst('-time', 0.0)
if pid == 0:
ops.pattern('Plain', 2, 1)
ops.load(4, 1.0, 0.0)
ops.domainChange()
ops.integrator('ParallelDisplacementControl', 4, 1, 0.1)
ops.analyze(10)
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
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
Hload = Weight
maxNumIter = 6
tol = 1e-8
op.timeSeries('Linear', 2)
op.pattern('Plain', 200, 2)
op.load(2, Hload, 0.0, 0.0)
op.wipeAnalysis()
op.constraints('Plain')
op.numberer('Plain')
op.system('BandGeneral')
op.test('EnergyIncr', Tol, maxNumIter)
op.algorithm('Newton')
op.integrator('DisplacementControl', IDctrlNode, IDctrlDOF, Dincr)
op.analysis('Static')
Nsteps = int(Dmax / Dincr)
ok = op.analyze(Nsteps)
print(ok)
# for gravity analysis, load control is fine, 0.1 is the load factor increment (http://opensees.berkeley.edu/wiki/index.php/Load_Control)
test = {
1: 'NormDispIncr',
2: 'RelativeEnergyIncr',
4: 'RelativeNormUnbalance',
5: 'RelativeNormDispIncr',
6: 'NormUnbalance'
def NSProcedure(ndm, ndf, NbaysX, NbaysZ, NStr, XbayL, ZbayL, StoryH, lon, lat,
SHL, Vso, gamma_soil, nu_soil, Re, fpc, Ec, gamma_conc, fy, E0,
bsteel, ColTransfType, BeamEffFact, ColEffFact, g, Qsd, Ql,
Qlr, EMs, R, Ie, StrType, BldTypCo, BldTypCm, DsgnType, dirs,
directory):
# The Nonlinear Static Procdure is executed in order to get responses
# of a defined building.
import openseespy.opensees as ops
import OPSDefsMOD as OPSDMOD
import OPSDefsAN as OPSDAN
from timeit import default_timer as timer
import ASCE716Seismic as ASCE716
import ASCE4117
import matplotlib.pyplot as plt
import pickle
import numpy as np
for mm in range(len(NbaysX)):
for nn in range(len(NStr)):
for oo in range(len(Vso)):
Teff = np.zeros(
(len(dirs)
)) # [s][LIST] effective lateral period of building.
for ii in range(len(dirs)):
time_o = timer()
# Some previous definitions
# ----------------------------
if DsgnType in ('conv_dsgn'):
flex = 'no'
elif DsgnType in ('ssi_dsgn'):
flex = 'yes'
# SiteClass = ASCE716.detSiteClass(Vso[oo])
# Unpicklin' some stored parameters from design process.
# ------------------------------------------------------
workpath = directory + '\\RegularDesign\\' + str(NbaysX[mm])+'BayX'+str(NbaysZ)+\
'BayZ'+str(NStr[nn])+'FLRS'+str(Vso[oo])+'.pickle'
with open(workpath, 'rb') as f:
ColDims, Colreinf, XBDims, XBreinf, ZBDims, ZBreinf, _, _, _, _, _, _, _, _, _, _ = pickle.load(
f)
# Calculation of height vector
# ------------------------------
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
# [m][LIST] with level height starting from first level or from base if foundation flexibility is included.
hx = [0.0001]
else:
hx = []
for i in range(NStr[nn]):
hx.append((i + 1) * StoryH)
# Plan Dimensions of Building
B = NbaysZ * ZbayL # [m] short side of building plan.
L = NbaysX[mm] * XbayL # [m] long side of building plan.
# Determination of MCEr spectral acceleration parameters
# ------------------------------------------------------
(Sxs, Sx1) = ASCE4117.detSxi(lon, lat, Vso[oo], SHL)
# MODELING OF THE STRUCTURE USING OPENSEESPY
# ===========================================
ops.wipe()
OPSDMOD.ModelGen(ndm, ndf)
OPSDMOD.NodeGen(NbaysX[mm], NbaysZ, XbayL, ZbayL, StoryH,
NStr[nn], flex)
OPSDMOD.MastNodeGen(NbaysX[mm],
NbaysZ,
XbayL,
ZbayL,
StoryH,
NStr[nn],
flex,
coords=0)
OPSDMOD.SPConstGen(NbaysX[mm], NbaysZ, flex)
OPSDMOD.MPConstGen(NbaysX[mm], NbaysZ, NStr[nn], flex)
OPSDMOD.MatGenRCB(fpc, Ec, fy, E0, bsteel)
# OPSDMOD.GeomTransGen(ColTransfType,XBD=[min(XBDims[:,0]),min(XBDims[:,1])],\
# ZBD=[min(ZBDims[:,0]),min(ZBDims[:,1])],\
# ColD=[min(ColDims[:,0]),min(ColDims[:,1])])
OPSDMOD.GeomTransGen(
ColTransfType,
ColD=[min(ColDims[:, 0]),
min(ColDims[:, 1])])
# OPSDMOD.GeomTransGen(ColTransfType)
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
# Interface elements generation for foundation flexibility considerations.
# =========================================================================
# Materials generation: stiffness constants accounting for soil flexibility.
# ---------------------------------------------------------------------------
OPSDMOD.FoundFlexMaterials(NbaysX[mm],NbaysZ,XbayL,ZbayL,Sxs,Vso[oo],gamma_soil,nu_soil,B,L,Re,\
D=0,omega_soil=0,analtype='lat')
# Zero-Length elements creation for connecting base nodes.
OPSDMOD.FoundFlexZLElements(NbaysX[mm], NbaysZ, XbayL,
ZbayL, B, L, Re)
OPSDMOD.ElementGen(NbaysX[mm],NbaysZ,XbayL,ZbayL,NStr[nn],StoryH,XBDims,ZBDims,\
ColDims,BeamEffFact,ColEffFact,Ec,fy,EMs,\
XBreinf,ZBreinf,Colreinf,N=5,rec=0.0654,nuconc=0.2,dbar=0.025)
[Wx,MassInputMatr] = \
OPSDMOD.LumpedMassGen(NbaysX[mm],NbaysZ,XBDims,ZBDims,ColDims,gamma_conc,g,XbayL,ZbayL,NStr[nn],StoryH,Qsd,flex)
W = sum(Wx) # [kN] total weight of the building
# GRAVITY LOADS APPLIED TO MODEL ACCORDINGO TO ASCE4117
# ======================================================
# According to ASCE4117 Section 7.2.2, equation (7-3), the combination
# of gravitational loads mus be as follows:
# Qg = Qd + 0.25*Ql + Qs (7-3)
OPSDMOD.DeadLoadGen(NbaysX[mm], NbaysZ, NStr[nn], XBDims,
ZBDims, ColDims, gamma_conc)
OPSDMOD.SuperDeadLoadGen(NbaysX[mm], NbaysZ, NStr[nn],
XbayL, ZbayL, Qsd)
OPSDMOD.LiveLoadGen(NbaysX[mm], NbaysZ, NStr[nn], XbayL,
ZbayL, 0.25 * Ql, 0.25 * Qlr)
# GRAVITY-LOADS-CASE ANALYSIS.
# ============================
ops.system('ProfileSPD')
ops.constraints('Transformation')
ops.numberer('RCM')
ops.test('NormDispIncr', 1.0e-4, 100)
ops.algorithm('KrylovNewton')
ops.integrator('LoadControl', 1)
ops.analysis('Static')
ops.analyze(1)
# Vertical reactions Calculation for verification.
# ------------------------------------------------
ops.reactions()
YReact = 0
for i in range((NbaysX[mm] + 1) * (NbaysZ + 1)):
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
YReact += ops.nodeReaction(int(i + 1), 2)
else:
YReact += ops.nodeReaction(int(i + 1 + 1e4), 2)
# ==========================================================================
# MODAL ANALYSIS FOR DETERMINING FUNDAMENTAL PERIOD AND ITS DIRECTION.
# ==========================================================================
(T, Tmaxver,
Mast) = OPSDAN.ModalAnalysis(NStr[nn], B, L, Wx, flex)
print(T)
# ==================
# PUSHOVER ANALYSIS
# ==================
# Lateral Force used for analysis
# --------------------------------
# Using functions from ASCE716Seismic Module.
(_,_,_,_,_,_,_,_,_,_,_,FxF,_,_,_) = \
ASCE716.ELFP(Sxs,Sx1,Vso[oo],Wx,R,Ie,hx,StrType,T[0,ii])
# Aplication of forces to the model.
# ----------------------------------
ops.loadConst('-time', 0.0)
MdeShape = OPSDMOD.POForceGen(NStr[nn], FxF, dirs[ii],
flex)
# =============================================
# First Execution of the analysis and output results.
# =============================================
(results1,dtg1,tgfactor1) = \
OPSDAN.POAnalysisProc(lon,lat,Vso[oo],SHL,NbaysX[mm],NbaysZ,\
NStr[nn],StoryH,R,Ie,BldTypCo,BldTypCm,\
T[0,ii],W,dirs[ii],flex,\
DispIncr=0,beta=0.05,TL=8.,Tf=6.0,Npts=500,Vy=0,Te=0) # [Disp,Force]
# =====================================================
# Determining the first approximation of values of Vy
# and calculation of effective fundamental period for NSP
# =====================================================
(Delta_y, V_y, Delta_d, V_d, Ke, alpha1, alpha2) = \
ASCE4117.IFDC(dtg1,results1)
Ki = Mast[ii] * 4 * np.pi**2 / T[
0,
ii]**2 # [kN/m] elastic lateral stiffness of the building.
Teff[ii] = T[0, ii] * (
Ki / Ke
)**0.5 # [s] effctive fundamental period of building.
# =============================================
# Second Execution of the analysis and output results.
# =============================================
ops.wipe()
OPSDMOD.ModelGen(ndm, ndf)
OPSDMOD.NodeGen(NbaysX[mm], NbaysZ, XbayL, ZbayL, StoryH,
NStr[nn], flex)
OPSDMOD.MastNodeGen(NbaysX[mm],
NbaysZ,
XbayL,
ZbayL,
StoryH,
NStr[nn],
flex,
coords=0)
OPSDMOD.SPConstGen(NbaysX[mm], NbaysZ, flex)
OPSDMOD.MPConstGen(NbaysX[mm], NbaysZ, NStr[nn], flex)
OPSDMOD.MatGenRCB(fpc, Ec, fy, E0, bsteel)
# OPSDMOD.GeomTransGen(ColTransfType,XBD=[min(XBDims[:,0]),min(XBDims[:,1])],\
# ZBD=[min(ZBDims[:,0]),min(ZBDims[:,1])],\
# ColD=[min(ColDims[:,0]),min(ColDims[:,1])])
OPSDMOD.GeomTransGen(
ColTransfType,
ColD=[min(ColDims[:, 0]),
min(ColDims[:, 1])])
# OPSDMOD.GeomTransGen(ColTransfType)
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
# Interface elements generation for foundation flexibility considerations.
# =========================================================================
# Materials generation: stiffness constants accounting for soil flexibility.
# ---------------------------------------------------------------------------
OPSDMOD.FoundFlexMaterials(NbaysX[mm],NbaysZ,XbayL,ZbayL,Sxs,Vso[oo],gamma_soil,nu_soil,B,L,Re,\
D=0,omega_soil=0,analtype='lat')
# Zero-Length elements creation for connecting base nodes.
OPSDMOD.FoundFlexZLElements(NbaysX[mm], NbaysZ, XbayL,
ZbayL, B, L, Re)
OPSDMOD.ElementGen(NbaysX[mm],NbaysZ,XbayL,ZbayL,NStr[nn],StoryH,XBDims,ZBDims,\
ColDims,BeamEffFact,ColEffFact,Ec,fy,EMs,\
XBreinf,ZBreinf,Colreinf,N=5,rec=0.0654,nuconc=0.2,dbar=0.025)
[Wx,MassInputMatr] = \
OPSDMOD.LumpedMassGen(NbaysX[mm],NbaysZ,XBDims,ZBDims,ColDims,gamma_conc,g,XbayL,ZbayL,NStr[nn],StoryH,Qsd,flex)
W = sum(Wx) # [kN] total weight of the building
# GRAVITY LOADS APPLIED TO MODEL ACCORDINGO TO ASCE4117
# ======================================================
OPSDMOD.DeadLoadGen(NbaysX[mm], NbaysZ, NStr[nn], XBDims,
ZBDims, ColDims, gamma_conc)
OPSDMOD.SuperDeadLoadGen(NbaysX[mm], NbaysZ, NStr[nn],
XbayL, ZbayL, Qsd)
OPSDMOD.LiveLoadGen(NbaysX[mm], NbaysZ, NStr[nn], XbayL,
ZbayL, 0.25 * Ql, 0.25 * Qlr)
# GRAVITY-LOADS-CASE ANALYSIS.
# ============================
ops.system('ProfileSPD')
ops.constraints('Transformation')
ops.numberer('RCM')
ops.test('NormDispIncr', 1.0e-4, 100)
ops.algorithm('KrylovNewton')
ops.integrator('LoadControl', 1)
ops.analysis('Static')
ops.analyze(1)
# ==================
# PUSHOVER ANALYSIS
# ==================
# Lateral Force used for analysis
# --------------------------------
# Using functions from ASCE716Seismic Module.
(_,_,_,_,_,_,_,_,_,_,_,FxF,_,_,_) = \
ASCE716.ELFP(Sxs,Sx1,Vso[oo],Wx,R,Ie,hx,StrType,Teff[ii])
# Aplication of forces to the model.
# ----------------------------------
ops.loadConst('-time', 0.0)
MdeShape = OPSDMOD.POForceGen(NStr[nn], FxF, dirs[ii],
flex)
# =============================================
# First Execution of the analysis and output results.
# =============================================
(results2,dtg2,tgfactor2) = \
OPSDAN.POAnalysisProc(lon,lat,Vso[oo],SHL,NbaysX[mm],NbaysZ,\
NStr[nn],StoryH,R,Ie,BldTypCo,BldTypCm,\
T[0,ii],W,dirs[ii],flex,\
DispIncr=0,beta=0.05,TL=8.,Tf=6.0,Npts=500,Vy=0,Te=Teff[ii]) # [Disp,Force].
# =====================================================
# Determining the "exact" values of Vy
# and calculation of effective fundamental period for NSP
# =====================================================
(Delta_y, V_y, Delta_d, V_d, Ke, alpha1, alpha2) = \
ASCE4117.IFDC(dtg1,results2)
Ki = Mast[ii] * 4 * np.pi**2 / T[
0,
ii]**2 # [kN/m] elastic lateral stiffness of the building.
Teff[ii] = T[0, ii] * (
Ki / Ke
)**0.5 # [s] effctive fundamental period of building.
ttime = timer() - time_o
print(f'Elapsed Time {round(ttime/60,2)} [m]')
plt.figure()
plt.plot(results2[:, 0], results2[:, 1])
plt.grid()
print('The mode shape is:')
print(MdeShape)
return (results1, results2), (dtg1, dtg2), (tgfactor1,
tgfactor2), (tgfactor1 * dtg1,
tgfactor2 * dtg2)
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
*wallnodes)
# create constraint object
ops.constraints('Plain')
# create numberer object
ops.numberer('Plain')
# create convergence test object
ops.test('PFEM', 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 1e-5, 10, 3, 1, 2)
# create algorithm object
ops.algorithm('Newton')
# create integrator object
ops.integrator('PFEM', 0.5, 0.25)
# create SOE object
ops.system('PFEM')
# ops.system('PFEM', '-mumps) Linux version can use mumps
# create analysis object
ops.analysis('PFEM', dtmax, dtmin, b2)
# analysis
while ops.getTime() < totaltime:
# analysis
if ops.analyze() < 0:
break
def run_sensitivity_analysis(ctrlNode,
dof,
baseNode,
SensParam,
steps=500,
IOflag=False):
"""
Run load-control sensitivity analysis
"""
ops.wipeAnalysis()
start_time = time.time()
title("Running Load-Control Sensitivity Analysis ...")
ops.system("BandGeneral")
ops.numberer("RCM")
ops.constraints("Transformation")
ops.test("NormDispIncr", 1.0E-12, 10, 3)
ops.algorithm("Newton") # KrylovNewton
ops.integrator("LoadControl", 1 / steps)
ops.analysis("Static")
ops.sensitivityAlgorithm(
"-computeAtEachStep"
) # automatically compute sensitivity at the end of each step
outputs = {
"time": np.array([]),
"disp": np.array([]),
"force": np.array([]),
}
for sens in SensParam:
outputs[f"sensDisp_{sens}"] = np.array([]),
for i in range(steps):
ops.reactions()
if IOflag:
print(
f"Single Cycle Response: Step #{i}, Node #{ctrlNode}: {ops.nodeDisp(ctrlNode, dof):.3f} {LunitTXT} / {-ops.nodeReaction(baseNode, dof):.2f} {FunitTXT}."
)
ops.analyze(1)
tCurrent = ops.getTime()
outputs["time"] = np.append(outputs["time"], tCurrent)
outputs["disp"] = np.append(outputs["disp"],
ops.nodeDisp(ctrlNode, dof))
outputs["force"] = np.append(outputs["force"],
-ops.nodeReaction(baseNode, dof))
for sens in SensParam:
# sensDisp(patternTag, paramTag)
outputs[f"sensDisp_{sens}"] = np.append(
outputs[f"sensDisp_{sens}"],
ops.sensNodeDisp(ctrlNode, dof, sens))
title("Sensitvity Analysis Completed!")
print(
f"Analysis elapsed time is {(time.time() - start_time):.3f} seconds.\n"
)
return outputs
def Analysis_Proc(Num: int, Node: int, dof: int, Dincr: float):
'''
brief KrylovNewton → Newton -SecantNewton → ModifiedNewton → NewtonWithLineSearch → BGFS → Broyden\n
pararm Num the number of analyze step\n
return analyze if successful return 0
if NOT successful return < 0\n
'''
for step in range(1, Num + 1):
logger.info("No. %d of Cyclic. Anaylsis KrylovNewton..", step)
ops.algorithm('KrylovNewton')
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info("No. %d of Cyclic. Anaylsis Trying SecantNewton ..",
step)
ops.algorithm('SecantNewton')
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info(
"NO. %d of Cyclic. Anaylsis Trying NewtonLineSearch ..", step)
ops.algorithm('NewtonLineSearch', True, False, True, False, 0.8,
1000, 0.1, 10.0)
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info("No. %d of Cyclic. Anaylsis Trying PeriodicNewton ..",
step)
ops.algorithm('PeriodicNewton')
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info(
"NO. %d of Cyclic. Anaylsis Trying NewtonWithLineSearch ..",
step)
ops.algorithm('NewtonLineSearch')
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info("No. %d of Cyclic. Anaylsis Trying BFGS ..", step)
ops.algorithm('BFGS', True, False, 10000000)
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info("No. %d of Cyclic. Anaylsis Trying Broyden ..", step)
ops.algorithm('Broyden')
ops.integrator("DisplacementControl", Node, dof, Dincr)
ops.analysis("Static")
ok = ops.analyze(1)
if ok != 0:
logger.info("No. $step of Cyclic. Analysis Convergence Failure!")
# ****************************************************************************
# GRAVITY ANALYSIS EXCECUTED ACCOUNING FOR LIVE, DEAD AND SUPERDEAD LOADS.
# ========================================================================
OPSDMOD.DeadLoadGen(NbaysX[0], NbaysZ, NStr[0], XBDims, ZBDims, ColDims,
gamma_conc)
OPSDMOD.SuperDeadLoadGen(NbaysX[0], NbaysZ, NStr[0], XbayL, ZbayL, Qsd)
OPSDMOD.LiveLoadGen(NbaysX[0], NbaysZ, NStr[0], XbayL, ZbayL, Ql, Qlr)
# GRAVITY-LOADS-CASE ANALYSIS.
# ============================
ops.system('ProfileSPD')
ops.constraints('Transformation')
ops.numberer('RCM')
ops.test('NormDispIncr', 1.0e-4, 100)
ops.algorithm('KrylovNewton')
ops.integrator('LoadControl', 1)
ops.analysis('Static')
ops.analyze(1)
# Vertical reactions Calculation for verification.
# ------------------------------------------------
ops.reactions()
YReact = 0
for i in range((NbaysX[0] + 1) * (NbaysZ + 1)):
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
YReact += ops.nodeReaction(99000 + i + 1, 2)
else:
YReact += ops.nodeReaction(i + 1, 2)
print('>>> Gravity loads applied...')
# ==========================================================================
# MODAL ANALYSIS FOR DETERMINING FUNDAMENTAL PERIOD AND ITS DIRECTION.
tf = 0.2 * s
fr = 10 * Hz
prd = 1 / fr
ops.timeSeries('Trig', 1, ti, tf, prd)
# https://openseespydoc.readthedocs.io/en/latest/src/pathTs.html
ops.pattern('UniformExcitation', 1, 1, '-accel', 1)
# https://openseespydoc.readthedocs.io/en/latest/src/uniformExcitation.html
# amortiguamiento de rayleigh
ops.rayleigh(*setRayParam(0.05, 0.05, 0.2, 20))
# analysis commands
ops.constraints('Plain')
ops.numberer('Plain')
ops.system('UmfPack')
ops.algorithm('Linear')
ops.integrator('Newmark', 0.5, 0.25)
ops.analysis('Transient')
# analisis
# ops.analyze(400,0.001)
ops.start()
for i in range(400):
ops.analyze(1, 0.001)
print(i)
ops.stop()
# Grafico de la deformada
fig = plt.figure(figsize=(25, 5))
opsv.plot_defo(500)
plt.show()
dt = 0.01 # time step for input ground motion
GMfatt = 1.0 # data in input file is in g Unifts -- ACCELERATION TH
maxNumIter = 10
op.timeSeries('Path', 2, '-dt', dt, '-filePath', GMfile, '-factor', GMfact)
op.pattern('UniformExcitation', IDloadTag, GMdirection, '-accel', 2)
op.wipeAnalysis()
op.constraints('Transformation')
op.numberer('Plain')
op.system('BandGeneral')
op.test('EnergyIncr', Tol, maxNumIter)
op.algorithm('ModifiedNewton')
NewmarkGamma = 0.5
NewmarkBeta = 0.25
op.integrator('Newmark', NewmarkGamma, NewmarkBeta)
op.analysis('Transient')
DtAnalysis = 0.01 # time-step Dt for lateral analysis
TmaxAnalysis = 10.0 # maximum duration of ground-motion analysis
Nsteps = int(TmaxAnalysis / DtAnalysis)
ok = op.analyze(Nsteps, DtAnalysis)
tCurrent = op.getTime()
# for gravity analysis, load control is fine, 0.1 is the load factor increment (http://opensees.berkeley.edu/wiki/index.php/Load_Control)
test = {
1: 'NormDispIncr',
def get_multi_pile_m(
pile_layout,
cap_edge=0,
cap_thickness=2,
pile_z0=-2.5,
pile_z1=-30,
pile_d=2,
m0=7500000,
top_f=0.0,
top_h=0.0,
top_m=0.0
):
if cap_edge == 0:
if pile_d <= 1:
cap_edge = max(0.25, 0.5 * pile_d)
else:
cap_edge = max(0.5, 0.3 * pile_d)
cap_w = max(pile_layout[0]) - min(pile_layout[0]) + pile_d + cap_edge * 2
cap_l = max(pile_layout[1]) - min(pile_layout[1]) + pile_d + cap_edge * 2
top_f += cap_w * cap_l * cap_thickness * 26e3 # 承台自重
top_f += (cap_w * cap_l) * (-pile_z0 - cap_thickness) * 15e3 # 盖梁重量
pile_rows = len(pile_layout[1]) # 桩排数
top_f /= pile_rows # 桩顶力分配
top_h /= pile_rows # 桩顶水平力分配
top_m /= pile_rows # 桩顶弯矩分配
cap_i = cap_l * cap_thickness ** 3 / 12 / pile_rows # 承台横向刚度
pile_h = pile_z0 - pile_z1
pile_a = np.pi * (pile_d / 2) ** 2
pile_i = np.pi * pile_d ** 4 / 64
pile_b1 = 0.9 * (1.5 + 0.5 / pile_d) * 1 * pile_d
# 建立模型
ops.wipe()
ops.model('basic', '-ndm', 2, '-ndf', 3)
# 建立节点
cap_bot = pile_z0
# ops.node(1, 0, cap_top) # 承台竖向节点
if 0 not in pile_layout[0]:
ops.node(2, 0, cap_bot)
# 建立桩基节点
node_z = np.linspace(pile_z0, pile_z1, elem_num + 1)
for i, j in enumerate(pile_layout[0]):
node_start = 100 + i * 300
for m, n in enumerate(node_z):
ops.node(node_start + m + 1, j, n)
ops.node(node_start + m + 151, j, n)
nodes = {}
for i in ops.getNodeTags():
nodes[i] = ops.nodeCoord(i)
# 建立约束
for i, j in enumerate(pile_layout[0]):
node_start = 100 + i * 300
for m, n in enumerate(node_z):
ops.fix(node_start + m + 151, 1, 1, 1)
if n == node_z[-1]:
ops.fix(node_start + m + 1, 1, 1, 1)
# 建立材料
for i in range(len(node_z)):
pile_depth = i * (pile_h / elem_num)
pile_depth_nominal = 10 if pile_depth <= 10 else pile_depth
soil_k = m0 * pile_depth_nominal * pile_b1 * (pile_h / elem_num)
if i == 0:
ops.uniaxialMaterial('Elastic', 1 + i, soil_k / 2)
continue
ops.uniaxialMaterial('Elastic', 1 + i, soil_k)
# 装配
ops.geomTransf('Linear', 1)
# 建立单元
if len(pile_layout[0]) > 1: # 承台横向单元
cap_nodes = []
for i in nodes:
if nodes[i][1] == cap_bot:
if len(cap_nodes) == 0:
cap_nodes.append(i)
elif nodes[i][0] != nodes[cap_nodes[-1]][0]:
cap_nodes.append(i)
cap_nodes = sorted(cap_nodes, key=lambda x: nodes[x][0])
for i, j in enumerate(cap_nodes[:-1]):
ops.element('elasticBeamColumn', 10 + i, j, cap_nodes[i+1], cap_l * cap_thickness, 3e10, cap_i, 1)
pile_elem = []
for i, j in enumerate(pile_layout[0]): # 桩基单元
node_start = 100 + i * 300
pile_elem_i = []
for m, n in enumerate(node_z):
if n != pile_z1:
ops.element('elasticBeamColumn', node_start + m + 1, node_start + m + 1,
node_start + m + 2, pile_a, 3e10, pile_i, 1)
pile_elem_i.append(node_start + m + 1)
ops.element('zeroLength', node_start + m + 151, node_start + m + 151,
node_start + m + 1, '-mat', 1 + m, '-dir', 1)
pile_elem.append(pile_elem_i)
ops.timeSeries('Linear', 1)
ops.pattern('Plain', 1, 1)
for i in nodes:
if nodes[i] == [0, pile_z0]:
ops.load(i, -top_h, -top_f, top_m) # 加载
ops.system('BandGeneral')
ops.numberer('Plain')
ops.constraints('Plain')
ops.integrator('LoadControl', 0.01)
ops.test('EnergyIncr', 1e-6, 200)
ops.algorithm('Newton')
ops.analysis('Static')
ops.analyze(100)
node_disp = {}
for i in ops.getNodeTags():
node_disp[i] = [j * 1000 for j in ops.nodeDisp(i)]
elem_m = {}
for i in pile_elem:
for j in i:
elem_m[j] = [k / 1000 for k in ops.eleForce(j)]
plt.figure()
for i, j in enumerate(pile_elem):
plt.subplot(f'1{len(pile_elem)}{i+1}')
if i == 0:
plt.ylabel('Pile Depth(m)')
node_disp_x = []
for m, n in enumerate(j):
node_1 = ops.eleNodes(n)[0]
if m == 0:
plt.plot([0, node_disp[node_1][0]], [nodes[node_1][1], nodes[node_1][1]],
linewidth=1.5, color='grey')
else:
plt.plot([0, node_disp[node_1][0]], [nodes[node_1][1], nodes[node_1][1]],
linewidth=0.7, color='grey')
node_disp_x.append(node_disp[node_1][0])
for m, n in enumerate(j):
node_1 = ops.eleNodes(n)[0]
if abs(node_disp[node_1][0]) == max([abs(i) for i in node_disp_x]):
side = 1 if node_disp[node_1][0] > 0 else -1
plt.annotate(f'{node_disp[node_1][0]:.1f} mm', xy=(node_disp[node_1][0], nodes[node_1][1]),
xytext=(0.4 + 0.1 * side, 0.5), textcoords='axes fraction',
bbox=dict(boxstyle="round", fc="0.8"),
arrowprops=dict(arrowstyle='->', connectionstyle=f"arc3,rad={side * 0.3}"))
break
plt.plot([0, 0], [node_z[0], node_z[-1]], linewidth=1.5, color='dimgray')
plt.plot(node_disp_x, node_z[:-1], linewidth=1.5, color='midnightblue')
plt.xlabel(f'Displacement_{i+1} (mm)')
plt.show()
plt.figure()
for i, j in enumerate(pile_elem):
plt.subplot(f'1{len(pile_elem)}{i + 1}')
if i == 0:
plt.ylabel('Pile Depth(m)')
elem_mi = []
for m, n in enumerate(j):
node_1 = ops.eleNodes(n)[0]
if m == 0:
plt.plot([0, elem_m[n][2]], [nodes[node_1][1], nodes[node_1][1]],
linewidth=1.5, color='grey')
else:
plt.plot([0, elem_m[n][2]], [nodes[node_1][1], nodes[node_1][1]],
linewidth=0.7, color='grey')
elem_mi.append(elem_m[n][2])
for m, n in enumerate(j):
node_1 = ops.eleNodes(n)[0]
if abs(elem_m[n][2]) == max([abs(i) for i in elem_mi]):
side = 1 if elem_m[n][2] > 0 else -1
plt.annotate(f'{elem_m[n][2]:.1f} kN.m', xy=(elem_m[n][2], nodes[node_1][1]),
xytext=(0.4 + 0.1 * side, 0.5), textcoords='axes fraction',
bbox=dict(boxstyle="round", fc="0.8"),
arrowprops=dict(arrowstyle='->', connectionstyle=f"arc3,rad={side * 0.3}"))
break
plt.plot([0, 0], [node_z[0], node_z[-1]], linewidth=1.5, color='dimgray')
plt.plot(elem_mi, node_z[:-1], linewidth=1.5, color='brown')
plt.xlabel(f'Moment_{i + 1} (kN.m)')
plt.show()
return pile_elem, elem_m
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("==========================")
op.recorder('Element', '-file', 'Data-4-inelasticFiber/DefoColSec1.out',
'-time', '-ele', 1, 2, 'section', 1, 'deformation')
#op.recorder('Element', '-file', 'Data-4-inelasticFiber/DCol.out','-time', '-ele', 1, 'deformations')
#defining gravity loads
WzBeam = Weight / LBeam
op.timeSeries('Linear', 1)
op.pattern('Plain', 1, 1)
op.eleLoad('-ele', 3, '-type', '-beamUniform', -WzBeam, 0.0, 0.0)
#op.load(2, 0.0, -PCol, 0.0)
Tol = 1e-8 # convergence tolerance for test
NstepGravity = 10
DGravity = 1 / NstepGravity
op.integrator('LoadControl',
DGravity) # determine the next time step for an analysis
op.numberer(
'Plain'
) # renumber dof's to minimize band-width (optimization), if you want to
op.system('BandGeneral'
) # how to store and solve the system of equations in the analysis
op.constraints('Plain') # how it handles boundary conditions
op.test(
'NormDispIncr', Tol, 6
) # determine if convergence has been achieved at the end of an iteration step
op.algorithm(
'Newton'
) # use Newton's solution algorithm: updates tangent stiffness at every iteration
op.analysis('Static') # define type of analysis static or transient
op.analyze(NstepGravity) # apply gravity
def test_Truss():
# remove existing model
ops.wipe()
# set modelbuilder
ops.model('basic', '-ndm', 2, '-ndf', 2)
# create nodes
ops.node(1, 0.0, 0.0)
ops.node(2, 144.0, 0.0)
ops.node(3, 168.0, 0.0)
ops.node(4, 72.0, 96.0)
# set boundary condition
ops.fix(1, 1, 1)
ops.fix(2, 1, 1)
ops.fix(3, 1, 1)
# define materials
ops.uniaxialMaterial("Elastic", 1, 3000.0)
# define elements
ops.element("Truss", 1, 1, 4, 10.0, 1)
ops.element("Truss", 2, 2, 4, 5.0, 1)
ops.element("Truss", 3, 3, 4, 5.0, 1)
# create TimeSeries
ops.timeSeries("Linear", 1)
# create a plain load pattern
ops.pattern("Plain", 1, 1)
# Create the nodal load - command: load nodeID xForce yForce
ops.load(4, 100.0, -50.0)
# ------------------------------
# Start of analysis generation
# ------------------------------
# create SOE
ops.system("BandSPD")
# create DOF number
ops.numberer("Plain")
# create constraint handler
ops.constraints("Plain")
# create integrator
ops.integrator("LoadControl", 1.0)
# create algorithm
ops.algorithm("Linear")
# create analysis object
ops.analysis("Static")
# perform the analysis
ops.analyze(1)
ux = ops.nodeDisp(4, 1)
uy = ops.nodeDisp(4, 2)
assert abs(ux - 0.53009277713228375450) < 1e-12 and abs(
uy + 0.17789363846931768864) < 1e-12
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)
ops.timeSeries('Linear',1)
ops.pattern('Plain',1,1)
fx = 0
fy = -10*kN
ops.load(2, fx, fy)
#for i in range(nNode):
# if (Node[i][0] == 2):
# ops.load(i+1, fx, fy)
ops.system('FullGeneral') # probar otros solvers: 'UmfPack' 'SparseSYM'
ops.numberer('Plain')
ops.constraints('Plain')
ops.integrator('LoadControl',1)
ops.algorithm('Linear')
ops.analysis('Static')
ops.analyze(1)
# Desplazamiento
disp = ops.nodeDisp(2,2)
print(disp)
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")