def step(self, action=0):
self.time = op.getTime()
assert (self.time < self.analysis_time)
# 選ばれたアクションに応じて減衰定数を変化させる
self.h = self.action[action]
self.hs.append(self.h)
self.beta_k = 2 * self.h / self.w0
op.rayleigh(self.alpha_m, self.beta_k, self.beta_k_init,
self.beta_k_comm)
op.analyze(1, self.dt)
op.reactions()
self.dis = op.nodeDisp(self.top_node, 1)
self.vel = op.nodeVel(self.top_node, 1)
self.acc = op.nodeAccel(self.top_node, 1)
self.a_acc = self.acc + self.values[self.i]
self.force = -op.nodeReaction(self.bot_node,
1) # Negative since diff node
self.resp["time"].append(self.time)
self.resp["dis"].append(self.dis)
self.resp["vel"].append(self.vel)
self.resp["acc"].append(self.acc)
self.resp["a_acc"].append(self.a_acc)
self.resp["force"].append(self.force)
next_time = op.getTime()
self.done = next_time >= self.analysis_time
self.i_pre = self.i
self.i += 1
self.i_next = self.i + 1 if not self.done else self.i
return self.reward, self.done
def test_ele_load_uniform():
osi = o3.OpenSeesInstance(ndm=2, state=3)
ele_len = 2.0
coords = [[0, 0], [ele_len, 0]]
ele_nodes = [o3.node.Node(osi, *coords[x]) for x in range(len(coords))]
transf = o3.geom_transf.Linear2D(osi, [])
ele = o3.element.ElasticBeamColumn2D(osi,
ele_nodes=ele_nodes,
area=1.0,
e_mod=1.0,
iz=1.0,
transf=transf,
mass=1.0,
c_mass="string")
for i, node in enumerate(ele_nodes):
if i == 0:
o3.Fix3DOF(osi, node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
else:
o3.Fix3DOF(osi, node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
udl = 10.
o3.EleLoad2DUniform(osi, ele, w_y=-udl)
tol = 1.0e-4
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
o3.test_check.NormDispIncr(osi, tol, 6)
o3.algorithm.Newton(osi)
n_steps_gravity = 1
d_gravity = 1. / n_steps_gravity
o3.integrator.LoadControl(osi, d_gravity, num_iter=10)
o3.analysis.Static(osi)
o3.analyze(osi, n_steps_gravity)
opy.reactions()
ele_loads = o3.get_ele_response(osi, ele, 'force')
assert np.isclose(ele_loads[0], 0.0)
assert np.isclose(ele_loads[1], udl * ele_len / 2)
assert np.isclose(ele_loads[2], udl * ele_len**2 / 12)
assert np.isclose(ele_loads[3], 0.0)
assert np.isclose(ele_loads[4], udl * ele_len / 2)
assert np.isclose(ele_loads[5], -udl * ele_len**2 / 12)
assert np.isclose(o3.get_node_reaction(osi, ele_nodes[0], o3.cc.Y),
udl * ele_len / 2)
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 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_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("==========================")
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.
# ==========================================================================
(Tver, Tmaxver, Mast) = OPSDAN.ModalAnalysis(NStr[0], B, L, Wx, flex)
import ASCE716SSI as SSI
if flex in ('Y', 'YES', 'Yes', 'yES', 'yes', 'y'):
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 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 run_sensitivity_pushover_analysis(ctrlNode,
baseNodes,
dof,
Dincr,
max_disp,
SensParam,
IOflag=False):
"""
Run pushover analysis with sensitivity
"""
ops.wipeAnalysis()
start_time = time.time()
ops.loadConst("-time", 0.0)
title("Running Displacement-Control Pushover Sensitivity Analysis ...")
testType = "NormDispIncr" # EnergyIncr
tolInit = 1.0E-8
iterInit = 10 # Set the initial Max Number of Iterations
algorithmType = "Newton" # Set the algorithm type
ops.system("BandGeneral")
ops.constraints("Transformation")
ops.numberer("RCM")
ops.test(testType, tolInit, iterInit)
ops.algorithm(algorithmType)
# Change the integration scheme to be displacement control
# node dof init Jd min max
ops.integrator("DisplacementControl", ctrlNode, dof, Dincr)
ops.analysis("Static")
ops.sensitivityAlgorithm(
"-computeAtEachStep"
) # automatically compute sensitivity at the end of each step
if IOflag:
print(
f"Single Pushover: Push node {ctrlNode} to {max_disp} {LunitTXT}.\n"
)
# Set some parameters
tCurrent = ops.getTime()
currentStep = 1
outputs = {
"time": np.array([]),
"disp": np.array([]),
"force": np.array([]),
}
for sens in SensParam:
outputs[f"sensLambda_{sens}"] = np.array([]),
nodeList = []
for node in baseNodes:
nodeList.append(f"- ops.nodeReaction({node}, dof) ")
nodeList = "".join(nodeList)
currentDisp = ops.nodeDisp(ctrlNode, dof)
ok = 0
while ok == 0 and currentDisp < max_disp:
ops.reactions()
ok = ops.analyze(1)
tCurrent = ops.getTime()
currentDisp = ops.nodeDisp(ctrlNode, dof)
if IOflag:
print(
f"Current displacement ==> {ops.nodeDisp(ctrlNode, dof):.3f} {LunitTXT}"
)
# if the analysis fails try initial tangent iteration
if ok != 0:
print("\n==> Trying relaxed convergence...")
ops.test(testType, tolInit / 0.01, iterInit * 50)
ok = ops.analyze(1)
if ok == 0:
print("==> that worked ... back to default analysis...\n")
ops.test(testType, tolInit, iterInit)
if ok != 0:
print("\n==> Trying Newton with initial then current...")
ops.test(testType, tolInit / 0.01, iterInit * 50)
ops.algorithm("Newton", "-initialThenCurrent")
ok = ops.analyze(1)
if ok == 0:
print("==> that worked ... back to default analysis...\n")
ops.algorithm(algorithmType)
ops.test(testType, tolInit, iterInit)
if ok != 0:
print("\n==> Trying ModifiedNewton with initial...")
ops.test(testType, tolInit / 0.01, iterInit * 50)
ops.algorithm("ModifiedNewton", "-initial")
ok = ops.analyze(1)
if ok == 0:
print("==> that worked ... back to default analysis...\n")
ops.algorithm(algorithmType)
ops.test(testType, tolInit, iterInit)
currentStep += 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"], eval(nodeList))
for sens in SensParam:
# sensLambda(patternTag, paramTag)
outputs[f"sensLambda_{sens}"] = np.append(
outputs[f"sensLambda_{sens}"], ops.sensLambda(1, sens))
# Print a message to indicate if analysis completed succesfully or not
if ok == 0:
title("Pushover Analysis Completed Successfully!")
else:
title("Pushover Analysis Completed Failed!")
print(
f"Analysis elapsed time is {(time.time() - start_time):.3f} seconds.\n"
)
return outputs
def get_inelastic_response(mass,
k_spring,
f_yield,
motion,
dt,
xi=0.05,
r_post=0.0):
"""
Run seismic analysis of a nonlinear SDOF
:param mass: SDOF mass
:param k_spring: spring stiffness
:param f_yield: yield strength
:param motion: list, acceleration values
:param dt: float, time step of acceleration values
:param xi: damping ratio
:param r_post: post-yield stiffness
:return:
"""
osi = o3.OpenSeesInstance(ndm=2)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
opy.fix(top_node.tag, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
opy.fix(bot_node.tag, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
opy.equalDOF(top_node.tag, bot_node.tag, *[o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
opy.mass(top_node.tag, mass, 0., 0.)
# Define material
bilinear_mat = o3.uniaxial_material.Steel01(osi,
fy=f_yield,
e0=k_spring,
b=r_post)
# Assign zero length element, # Note: pass actual node and material objects into element
o3.element.ZeroLength(osi, [bot_node, top_node],
mats=[bilinear_mat],
dirs=[o3.cc.DOF2D_X],
r_flag=1)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * motion) # should be negative
opy.timeSeries('Path', load_tag_dynamic, '-dt', dt, '-values', *values)
opy.pattern('UniformExcitation', pattern_tag_dynamic, o3.cc.X, '-accel',
load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = opy.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2**0.5
beta_k = 2 * xi / angular_freq
o3.rayleigh.Rayleigh(osi,
alpha_m=0.0,
beta_k=beta_k,
beta_k_init=0.0,
beta_k_comm=0.0)
# Run the dynamic analysis
opy.wipeAnalysis()
newmark_gamma = 0.5
newmark_beta = 0.25
o3.algorithm.Newton(osi)
o3.constraints.Transformation(osi)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.SparseGeneral(osi)
o3.integrator.Newmark(osi, newmark_gamma, newmark_beta)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = (len(values) - 1) * dt
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while opy.getTime() < analysis_time:
curr_time = opy.getTime()
opy.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(opy.nodeDisp(top_node.tag, o3.cc.X))
outputs["rel_vel"].append(opy.nodeVel(top_node.tag, o3.cc.X))
outputs["rel_accel"].append(opy.nodeAccel(top_node.tag, o3.cc.X))
opy.reactions()
outputs["force"].append(-opy.nodeReaction(
bot_node.tag, o3.cc.X)) # Negative since diff node
opy.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
print("Finished creating loading object...")
#----------------------------------------------------------
# create the analysis
#----------------------------------------------------------
op.integrator('LoadControl', 0.05)
op.numberer('RCM')
op.system('SparseGeneral')
op.constraints('Transformation')
op.test('NormDispIncr', 1e-5, 20, 1)
op.algorithm('Newton')
op.analysis('Static')
print("Starting Load Application...")
op.analyze(201)
print("Load Application finished...")
#print("Loading Analysis execution time: [expr $endT-$startT] seconds.")
#op.wipe
op.reactions()
Nodereactions = dict()
Nodedisplacements = dict()
for i in range(201, nodeTag + 1):
Nodereactions[i] = op.nodeReaction(i)
Nodedisplacements[i] = op.nodeDisp(i)
print('Node Reactions are: ', Nodereactions)
print('Node Displacements are: ', Nodedisplacements)
