def run(out_folder):
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
x_centre = 0.0
y_centre = 0.0
top_node = o3.node.Node(osi, x_centre, y_centre)
o3db = connect_to_db_and_obj_holder('db/truss_ops')
# o3db = O3ObjectDatabase()
o3db.add_obj(top_node, 'top_node')
bot_nodes = []
sf_eles = []
o3.Mass(osi, top_node, 10, 10)
fy = 500
k = 1.0e4
b = 0.1
pro_params = [5, 0.925, 0.15]
# sf_mat = o3.uniaxial_material.SteelMPF(osi, fy, fy, k, b, b, params=pro_params)
sf_mat = o3.uniaxial_material.Elastic(osi, k)
diff_pos = 0.5
depth = 1
bot_nodes.append(o3.node.Node(osi, x_centre - diff_pos, y_centre - depth))
o3.Fix2DOF(osi, bot_nodes[0], o3.cc.FIXED, o3.cc.FIXED)
bot_nodes.append(o3.node.Node(osi, x_centre + diff_pos, y_centre - depth))
o3.Fix2DOF(osi, bot_nodes[1], o3.cc.FIXED, o3.cc.FIXED)
sf_eles.append(
o3.element.Truss(osi, [top_node, bot_nodes[0]], big_a=1.0, mat=sf_mat))
sf_eles.append(
o3.element.Truss(osi, [top_node, bot_nodes[1]], big_a=1.0, mat=sf_mat))
o3db.add_objs(sf_eles, 'sf_eles')
save_db_state_and_objs(1, o3db)
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
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.DOF2D_ROTZ])
# nodal mass (weight / g):
o3.Mass(osi, top_node, 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
values = list(-1 * motion) # should be negative
acc_series = o3.time_series.Path(osi, dt, values)
o3.pattern.UniformExcitation(osi, o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freq2 = o3.get_eigen(osi, solver='fullGenLapack', n=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
o3.wipe_analysis(osi)
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": [], "force": []}
o3.record(osi)
curr_time = o3.get_time(osi)
while curr_time < analysis_time:
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(-o3.get_node_reaction(
osi, bot_node, o3.cc.X)) # Negative since diff node
o3.analyze(osi, 1, analysis_dt)
curr_time = o3.get_time(osi)
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def get_response(bd, asig, dtype, l_ph):
"""
Compute the response of a nonlinear lollipop on a foundation with linear/nonlinear soil
Units are N, m, s
:param bd:
SDOF building object
:param asig:
Acceleration signal object
:return:
"""
osi = o3.OpenSeesInstance(ndm=2, state=3)
# Establish nodes
top_ss_node = o3.node.Node(osi, 0, bd.h_eff)
bot_ss_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, bot_ss_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# nodal mass (weight / g):
o3.Mass(osi, top_ss_node, bd.mass_eff, 0.0, 0)
# Define a column element with a plastic hinge at base
transf = o3.geom_transf.Linear2D(osi, []) # can change for P-delta effects
area = 1.0
e_mod = 200.0e9
iz = bd.k_eff * bd.h_eff ** 3 / (3 * e_mod)
ele_nodes = [bot_ss_node, top_ss_node]
# Superstructure element
vert_ele = o3.element.ElasticBeamColumn2D(osi, ele_nodes, area=area, e_mod=e_mod, iz=iz, transf=transf)
omega = 2 * np.pi / bd.t_fixed
# define superstructure damping using rotational spring approach from Millen et al. (2017) to avoid double damping
if dtype == 'rot_dashpot':
cxx = bd.xi * 2 * np.sqrt(bd.mass_eff * bd.k_eff)
equiv_c_rot = cxx * (2.0 / 3) ** 2 * bd.h_eff ** 2
ss_rot_dashpot_mat = o3.uniaxial_material.Viscous(osi, equiv_c_rot, alpha=1.)
sfi_dashpot_ele = o3.element.TwoNodeLink(osi, [bot_ss_node, top_ss_node], mats=[ss_rot_dashpot_mat],
dirs=[o3.cc.DOF2D_ROTZ])
elif dtype == 'horz_dashpot':
cxx = bd.xi * 2 * np.sqrt(bd.mass_eff * bd.k_eff)
ss_rot_dashpot_mat = o3.uniaxial_material.Viscous(osi, cxx, alpha=1.)
sfi_dashpot_ele = o3.element.ZeroLength(osi, [bot_ss_node, top_ss_node], mats=[ss_rot_dashpot_mat],
dirs=[o3.cc.X])
else:
beta_k = 2 * bd.xi / omega
o3.rayleigh.Rayleigh(osi, 0, 0, beta_k_init=beta_k, beta_k_comm=0.0)
# Define the input motion for the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
print('loaded gm')
o3.wipe_analysis(osi)
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, 0.5, 0.25)
o3.analysis.Transient(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10)
analysis_time = asig.time[-1]
analysis_dt = 0.001
# define outputs of analysis
od = {
"time": o3.recorder.TimeToArrayCache(osi),
"rel_deck_disp": o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_X], 'disp'),
"deck_accel": o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_X], 'accel'),
"deck_rot": o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_ROTZ], 'disp'),
"chord_rots": o3.recorder.ElementToArrayCache(osi, vert_ele, arg_vals=['chordRotation']),
"col_forces": o3.recorder.ElementToArrayCache(osi, vert_ele, arg_vals=['force']),
}
if dtype in ['rot_dashpot', 'horz_dashpot']:
od['dashpot_force'] = o3.recorder.ElementToArrayCache(osi, sfi_dashpot_ele, arg_vals=['force'])
o3.analyze(osi, int(analysis_time / analysis_dt), analysis_dt)
o3.wipe(osi)
for item in od:
od[item] = od[item].collect()
od['col_shear'] = -od['col_forces'][:, 0]
od['col_moment'] = od['col_forces'][:, 2]
od['hinge_rotation'] = od['chord_rots'][:, 1]
od['hinge_rotation1'] = -od['chord_rots'][:, 2]
del od['col_forces']
del od['chord_rots']
return od
def run_analysis(asig, period, xi, f_yield, etype):
# Load a ground motion
# Define inelastic SDOF
mass = 1.0
r_post = 0.0
# Initialise OpenSees instance
osi = o3.OpenSeesInstance(ndm=2, state=0)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
o3.Mass(osi, top_node, mass, 0., 0.)
# Define material
k_spring = 4 * np.pi**2 * mass / period**2
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
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 *
asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freqs = np.array(o3.get_eigen(osi, solver='fullGenLapack',
n=1))**0.5
beta_k = 2 * xi / angular_freqs[0]
print('angular_freqs: ', angular_freqs)
periods = 2 * np.pi / angular_freqs
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
o3.wipe_analysis(osi)
# Run the dynamic analysis
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0)
o3.numberer.RCM(osi)
if etype == 'implicit':
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
analysis_dt = 0.01
else:
o3.algorithm.Linear(osi, factor_once=True)
o3.system.FullGeneral(osi)
if etype == 'newmark_explicit':
o3.integrator.NewmarkExplicit(osi, gamma=0.6)
explicit_dt = periods[0] / np.pi / 32
elif etype == 'central_difference':
o3.integrator.CentralDifference(osi)
o3.opy.integrator('HHTExplicit')
explicit_dt = periods[0] / np.pi / 16 # 0.5 is a factor of safety
elif etype == 'explicit_difference':
o3.integrator.ExplicitDifference(osi)
explicit_dt = periods[0] / np.pi / 32
else:
raise ValueError(etype)
print('explicit_dt: ', explicit_dt)
analysis_dt = explicit_dt
o3.analysis.Transient(osi)
analysis_time = asig.time[-1]
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, 1, analysis_dt)
curr_time = o3.get_time(osi)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(-o3.get_node_reaction(
osi, bot_node, o3.cc.X)) # Negative since diff node
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def run(out_folder):
osi = o3.OpenSeesInstance(ndm=2, ndf=2, state=3)
x_centre = 0.0
y_centre = 0.0
top_node = o3.node.Node(osi, x_centre, y_centre)
fd_area = 1
fd_e_mod = 1e9
fd_iz = 1e6
top_nodes = []
bot_nodes = []
sf_eles = []
fd_eles = []
o3.Mass(osi, top_node, 10, 10)
fy = 500
k = 1.0e4
b = 0.1
pro_params = [5, 0.925, 0.15]
sf_mat = o3.uniaxial_material.SteelMPF(osi,
fy,
fy,
k,
b,
b,
params=pro_params)
diff_pos = 0.5
depth = 1
bot_nodes.append(o3.node.Node(osi, x_centre - diff_pos, y_centre - depth))
o3.Fix2DOF(osi, bot_nodes[0], o3.cc.FIXED, o3.cc.FIXED)
bot_nodes.append(o3.node.Node(osi, x_centre + diff_pos, y_centre - depth))
o3.Fix2DOF(osi, bot_nodes[1], o3.cc.FIXED, o3.cc.FIXED)
top_nodes.append(o3.node.Node(osi, x_centre, y_centre))
sf_eles.append(
o3.element.Truss(osi, [top_nodes[0], bot_nodes[0]],
big_a=1.0,
mat=sf_mat))
sf_eles.append(
o3.element.Truss(osi, [top_nodes[0], bot_nodes[1]],
big_a=1.0,
mat=sf_mat))
o3.EqualDOF(osi,
top_node,
top_nodes[0],
dofs=[o3.cc.DOF2D_X, o3.cc.DOF2D_Y])
ts0 = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts0)
o3.Load(osi, top_node, [100, -500])
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.FullGeneral(osi)
n_steps_gravity = 15
d_gravity = 1. / n_steps_gravity
o3.integrator.LoadControl(osi, d_gravity, num_iter=10)
# o3.rayleigh.Rayleigh(osi, a0, a1, 0.0, 0.0)
o3.analysis.Static(osi)
o3r = o3.results.Results2D(cache_path=out_folder, dynamic=True)
o3r.pseudo_dt = 0.1
o3r.start_recorders(osi, dt=0.1)
nr = o3.recorder.NodeToArrayCache(osi, top_node,
[o3.cc.DOF2D_X, o3.cc.DOF2D_Y], 'disp')
er = o3.recorder.ElementToArrayCache(osi, sf_eles[0], arg_vals=['force'])
for i in range(n_steps_gravity):
o3.analyze(osi, num_inc=1)
o3.load_constant(osi, time=0.0)
import o3seespy.extensions
o3.extensions.to_py_file(osi, 'ofile.py')
print('init_disp: ', o3.get_node_disp(osi, top_node, o3.cc.DOF2D_Y))
print('init_disp: ', o3.get_node_disp(osi, top_nodes[0], o3.cc.DOF2D_Y))
print('init_disp: ', o3.get_node_disp(osi, top_nodes[-1], o3.cc.DOF2D_Y))
o3.wipe(osi)
o3r.save_to_cache()
# o3r.coords = o3.get_all_node_coords(osi)
# o3r.ele2node_tags = o3.get_all_ele_node_tags_as_dict(osi)
data = nr.collect()
edata = er.collect()
# bf, sps = plt.subplots(nrows=2)
# sps[0].plot(data[:, 0])
# sps[0].plot(data[:, 1])
# sps[1].plot(edata[:, 0])
# # sps[0].plot(data[1])
# plt.show()
o3r.load_from_cache()
o3plot.replot(o3r)
def run(show=0):
# Load a ground motion
record_filename = 'test_motion_dt0p01.txt'
asig = eqsig.load_asig(ap.MODULE_DATA_PATH + 'gms/' + record_filename,
m=0.5)
# Define inelastic SDOF
period = 1.0
xi = 0.05
mass = 1.0
f_yield = 1.5 # Reduce this to make it nonlinear
r_post = 0.0
# Initialise OpenSees instance
osi = o3.OpenSeesInstance(ndm=2, state=0)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
o3.Mass(osi, top_node, mass, 0., 0.)
# Define material
k_spring = 4 * np.pi**2 * mass / period**2
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
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 *
asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**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
o3.wipe_analysis(osi)
# Run the dynamic analysis
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = asig.time[-1]
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, 1, analysis_dt)
curr_time = o3.get_time(osi)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(-o3.get_node_reaction(
osi, bot_node, o3.cc.X)) # Negative since diff node
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
if show:
import matplotlib.pyplot as plt
plt.plot(outputs['time'], outputs['rel_disp'], label='o3seespy')
periods = np.array([period])
# Compare closed form elastic solution
from eqsig import sdof
resp_u, resp_v, resp_a = sdof.response_series(motion=asig.values,
dt=asig.dt,
periods=periods,
xi=xi)
plt.plot(asig.time, resp_u[0], ls='--', label='Elastic')
plt.legend()
plt.show()
def get_elastic_response(mass, k_spring, 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 motion: array_like,
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, state=3)
height = 5.
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, height)
# Fix bottom node
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FREE)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y])
# nodal mass (weight / g):
o3.Mass(osi, top_node, mass, 0., 0.)
# Define material
transf = o3.geom_transf.Linear2D(osi, [])
area = 1.0
e_mod = 1.0e6
iz = k_spring * height ** 3 / (3 * e_mod)
ele_nodes = [bot_node, top_node]
ele = o3.element.ElasticBeamColumn2D(osi, ele_nodes, area=area, e_mod=e_mod, iz=iz, transf=transf)
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=dt, values=-motion) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0] ** 0.5
response_period = 2 * np.pi / angular_freq
print('response_period: ', response_period)
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
o3.wipe_analysis(osi)
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, 0.5, 0.25)
o3.analysis.Transient(osi)
o3.extensions.to_py_file(osi, 'simple.py')
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = (len(motion) - 1) * dt
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, 1, analysis_dt)
curr_time = o3.get_time(osi)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(o3.get_ele_response(osi, ele, 'force'))
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def get_response(bd, asig, l_ph):
"""
Compute the response of a nonlinear lollipop on a foundation with linear/nonlinear soil
Units are N, m, s
:param bd:
SDOF building object
:param asig:
Acceleration signal object
:return:
"""
osi = o3.OpenSeesInstance(ndm=2, state=3)
# Establish nodes
top_ss_node = o3.node.Node(osi, 0, bd.h_eff)
bot_ss_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, bot_ss_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# nodal mass (weight / g):
o3.Mass(osi, top_ss_node, bd.mass_eff, 0.0, 0)
# Define a column element with a plastic hinge at base
transf = o3.geom_transf.Linear2D(osi, []) # can change for P-delta effects
area = 1.0
e_mod = 200.0e9
iz = bd.k_eff * bd.h_eff**3 / (3 * e_mod)
ele_nodes = [bot_ss_node, top_ss_node]
# Superstructure element
elastic_sect = o3.section.Elastic2D(osi, e_mod, area, iz)
integ = o3.beam_integration.HingeMidpoint(osi, elastic_sect, l_ph,
elastic_sect, l_ph, elastic_sect)
vert_ele = o3.element.ForceBeamColumn(osi, ele_nodes, transf, integ)
omega = 2 * np.pi / bd.t_fixed
beta_k = 2 * bd.xi / omega
o3.rayleigh.Rayleigh(osi, 0, 0, beta_k_init=beta_k, beta_k_comm=0.0)
# Define the input motion for the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt,
values=-asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
print('loaded gm')
o3.wipe_analysis(osi)
o3.algorithm.Newton(osi)
o3.system.SparseGeneral(osi)
o3.numberer.RCM(osi)
o3.constraints.Transformation(osi)
o3.integrator.Newmark(osi, 0.5, 0.25)
o3.analysis.Transient(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=10)
analysis_time = asig.time[-1]
analysis_dt = 0.001
# define outputs of analysis
od = {
"time":
o3.recorder.TimeToArrayCache(osi),
"rel_deck_disp":
o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_X],
'disp'),
"deck_accel":
o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_X],
'accel'),
"deck_rot":
o3.recorder.NodeToArrayCache(osi, top_ss_node, [o3.cc.DOF2D_ROTZ],
'disp'),
"chord_rots":
o3.recorder.ElementToArrayCache(osi,
vert_ele,
arg_vals=['chordRotation']),
"col_forces":
o3.recorder.ElementToArrayCache(osi, vert_ele, arg_vals=['force']),
}
o3.analyze(osi, int(analysis_time / analysis_dt), analysis_dt)
o3.wipe(osi)
for item in od:
od[item] = od[item].collect()
od['col_shear'] = -od['col_forces'][:, 0]
od['col_moment'] = od['col_forces'][:, 2]
od['hinge_rotation'] = od['chord_rots'][:, 1]
od['hinge_rotation1'] = -od['chord_rots'][:, 2]
del od['col_forces']
del od['chord_rots']
return od
def gen_response(period, xi, asig, etype, fos_for_dt=None):
# Define inelastic SDOF
mass = 1.0
f_yield = 1.5 # Reduce this to make it nonlinear
r_post = 0.0
# Initialise OpenSees instance
osi = o3.OpenSeesInstance(ndm=2, state=0)
# Establish nodes
bot_node = o3.node.Node(osi, 0, 0)
top_node = o3.node.Node(osi, 0, 0)
# Fix bottom node
o3.Fix3DOF(osi, top_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, bot_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, top_node, bot_node, [o3.cc.Y, o3.cc.ROTZ])
# nodal mass (weight / g):
o3.Mass(osi, top_node, mass, 0., 0.)
# Define material
k_spring = 4 * np.pi**2 * mass / period**2
# bilinear_mat = o3.uniaxial_material.Steel01(osi, fy=f_yield, e0=k_spring, b=r_post)
mat = o3.uniaxial_material.Elastic(osi, e_mod=k_spring)
# Assign zero length element, # Note: pass actual node and material objects into element
o3.element.ZeroLength(osi, [bot_node, top_node],
mats=[mat],
dirs=[o3.cc.DOF2D_X],
r_flag=1)
# Define the dynamic analysis
# Define the dynamic analysis
acc_series = o3.time_series.Path(osi, dt=asig.dt, values=-1 *
asig.values) # should be negative
o3.pattern.UniformExcitation(osi, dir=o3.cc.X, accel_series=acc_series)
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5
period = 2 * np.pi / angular_freq
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)
o3.set_time(osi, 0.0)
# Run the dynamic analysis
o3.wipe_analysis(osi)
# Run the dynamic analysis
o3.numberer.RCM(osi)
o3.system.FullGeneral(osi)
if etype == 'central_difference':
o3.algorithm.Linear(osi, factor_once=True)
o3.integrator.CentralDifference(osi)
explicit_dt = 2 / angular_freq / fos_for_dt
analysis_dt = explicit_dt
elif etype == 'implicit':
o3.algorithm.Newton(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
analysis_dt = 0.001
else:
raise ValueError()
o3.constraints.Transformation(osi)
o3.analysis.Transient(osi)
o3.test_check.EnergyIncr(osi, tol=1.0e-10, max_iter=10)
analysis_time = asig.time[-1]
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
rec_dt = 0.002
n_incs = int(analysis_dt / rec_dt)
n_incs = 1
while o3.get_time(osi) < analysis_time:
o3.analyze(osi, n_incs, analysis_dt)
curr_time = o3.get_time(osi)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, top_node, o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, top_node, o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, top_node, o3.cc.X))
o3.gen_reactions(osi)
outputs["force"].append(-o3.get_node_reaction(
osi, bot_node, o3.cc.X)) # Negative since diff node
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs