def test_add_fixity_to_dof():
osi = o3.OpenSeesInstance(ndm=3, ndf=3)
n1 = o3.node.Node(osi, 1., 1., 1.)
o3.Fix3DOF(osi, n1, o3.cc.FIXED, o3.cc.FREE, o3.cc.FIXED)
o3.Fix3DOF(osi, n1, o3.cc.FREE, o3.cc.FREE, o3.cc.FREE)
# o3.Fix3DOF(osi, n1, o3.cc.FREE, o3.cc.FREE, o3.cc.FIXED) # fails with this
o3.add_fixity_to_dof(osi, o3.cc.DOF2D_ROTZ, [n1])
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 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_analysis(etype, asig, use_modal_damping=0):
osi = o3.OpenSeesInstance(ndm=2, ndf=3)
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, 5.5, 0.0),
o3.node.Node(osi, 0.0, 3.3),
o3.node.Node(osi, 5.5, 3.3)
]
o3.Mass2D(osi, nodes[2], 1e5, 1e5, 1e6)
o3.Mass2D(osi, nodes[3], 1e5, 1e5, 1e6)
o3.Fix3DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
steel_mat = o3.uniaxial_material.Steel01(osi, 300.0e6, 200.0e9, b=0.02)
# o3.element.DispBeamColumn(osi, [nodes[2], nodes[3]], )
tran = o3.geom_transf.Linear2D(osi)
e_mod = 200.0e9
iz = 1.0e-4
area = 0.01
# o3.element.ElasticBeamColumn2D(osi, [nodes[2], nodes[3]], 0.01, 200.0e9, iz=1.0e-4, transf=tran)
ei = e_mod * iz
ea = e_mod * area
phi_y = 0.001
my = ei * phi_y
print('my: ', my)
mat = o3.uniaxial_material.ElasticBilin(osi, ei, 0.01 * ei, phi_y)
mat_axial = o3.uniaxial_material.Elastic(osi, ea)
top_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
bot_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
centre_sect = o3.section.Elastic2D(osi, e_mod, area, iz)
lplas = 0.2
integ = o3.beam_integration.HingeMidpoint(osi, bot_sect, lplas, top_sect,
lplas, centre_sect)
beam = o3.element.ForceBeamColumn(osi, [nodes[2], nodes[3]], tran, integ)
o3.element.ElasticBeamColumn2D(osi, [nodes[0], nodes[2]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
o3.element.ElasticBeamColumn2D(osi, [nodes[1], nodes[3]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
a_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=a_series)
xi = 0.04
angular_freqs = np.array(o3.get_eigen(osi, n=4))**0.5
print('angular_freqs: ', angular_freqs)
periods = 2 * np.pi / angular_freqs
print('periods: ', periods)
if use_modal_damping: # Does not support modal damping
freqs = [0.5, 5]
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
else:
o3.ModalDamping(osi, [xi])
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=35, p_flag=0)
o3.numberer.RCM(osi)
if use_modal_damping:
o3_sys = o3.system.ProfileSPD # not sure why don't need to use FullGen here? since matrix is full?
else:
o3_sys = o3.system.ProfileSPD
if etype == 'implicit':
o3.algorithm.Newton(osi)
o3_sys(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
dt = 0.01
else:
o3.algorithm.Linear(osi, factor_once=True)
if etype == 'newmark_explicit':
o3_sys(osi)
o3.integrator.NewmarkExplicit(osi, gamma=0.5)
explicit_dt = periods[-1] / np.pi / 4
elif etype == 'central_difference':
o3_sys(osi)
o3.integrator.CentralDifference(osi)
explicit_dt = periods[-1] / np.pi / 4 # 0.5 is a factor of safety
elif etype == 'explicit_difference':
o3.system.Diagonal(osi)
o3.integrator.ExplicitDifference(osi)
explicit_dt = periods[-1] / np.pi / 4
else:
raise ValueError(etype)
print('explicit_dt: ', explicit_dt)
dt = explicit_dt
o3.analysis.Transient(osi)
roof_disp = o3.recorder.NodeToArrayCache(osi,
nodes[2],
dofs=[o3.cc.X],
res_type='disp')
time = o3.recorder.TimeToArrayCache(osi)
ele_resp = o3.recorder.ElementToArrayCache(osi, beam, arg_vals=['force'])
ttotal = 10.0
o3.analyze(osi, int(ttotal / dt), dt)
o3.wipe(osi)
return time.collect(), roof_disp.collect(), ele_resp.collect()
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 test_disp_control_cantilever_nonlinear():
osi = o3.OpenSeesInstance(ndm=2, state=3)
ele_len = 4.0
# Establish nodes
left_node = o3.node.Node(osi, 0, 0)
right_node = o3.node.Node(osi, ele_len, 0)
# Fix bottom node
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, right_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FREE)
e_mod = 200.0
i_sect = 0.1
area = 0.5
lp_i = 0.1
lp_j = 0.1
m_cap = 0.30
b = 0.05
phi = m_cap / (e_mod * i_sect)
# mat_flex = o3.uniaxial_material.Steel01(osi, m_cap, e0=e_mod * i_sect, b=b)
mat_flex = o3.uniaxial_material.ElasticBilin(osi, e_mod * i_sect,
e_mod * i_sect * b, phi)
mat_axial = o3.uniaxial_material.Elastic(osi, e_mod * area)
left_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex, o3.cc.M_Y]])
right_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
centre_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i, right_sect,
lp_j, centre_sect)
beam_transf = o3.geom_transf.Linear2D(osi, )
ele = o3.element.ForceBeamColumn(osi, [left_node, right_node], beam_transf,
integ)
# start displacement controlled
d_inc = 0.01
# opy.wipeAnalysis()
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
o3.test_check.NormUnbalance(osi, 2, max_iter=10, p_flag=0)
# o3.test_check.FixedNumIter(osi, max_iter=10)
# o3.test_check.NormDispIncr(osi, 0.002, 10, p_flag=0)
o3.algorithm.Newton(osi)
o3.integrator.DisplacementControl(osi, right_node, o3.cc.Y, d_inc)
o3.analysis.Static(osi)
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
o3.Load(osi, right_node, [0.0, 1.0, 0])
o3.analyze(osi, 4)
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
r = o3.get_ele_response(osi, ele, 'force')[:3]
k = r[1] / -end_disp
k_elastic_expected = 1. / (ele_len**3 / (3 * e_mod * i_sect))
assert np.isclose(k, k_elastic_expected)
o3.analyze(osi, 6)
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
r = o3.get_ele_response(osi, ele, 'force')[:3]
k = r[1] / -end_disp
assert k < 0.95 * k_elastic_expected
def get_inelastic_response(fb, asig, extra_time=0.0, xi=0.05, analysis_dt=0.001):
"""
Run seismic analysis of a nonlinear FrameBuilding
Parameters
----------
fb: sfsimodels.Frame2DBuilding object
asig: eqsig.AccSignal object
extra_time
xi
analysis_dt
Returns
-------
"""
osi = o3.OpenSeesInstance(ndm=2)
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):
nd[f"C{cc}-S{ss}"] = o3.node.Node(osi, 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)
o3.set_node_mass(osi, nd[f"C{cc}-S{ss}"], node_mass, 0., 0.)
# 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):
o3.set_equal_dof(osi, nd[f"C1-S{ss}"], nd[f"C{cc}-S{ss}"], o3.cc.X)
# Fix all base nodes
for cc in range(1, n_cols + 1):
o3.Fix3DOF(osi, nd[f"C{cc}-S0"], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Coordinate transformation
transf = o3.geom_transf.Linear2D(osi, [])
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) * 10 # TODO: re-evaluate
# Define beams and columns
# 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)
md = OrderedDict() # material dict
sd = OrderedDict() # section dict
ed = OrderedDict() # element dict
for ss in range(fb.n_storeys):
# set columns
for cc in range(1, fb.n_cols + 1):
lp_i = 0.4
lp_j = 0.4 # plastic hinge length
ele_str = f"C{cc}-S{ss}S{ss+1}"
top_sect = o3.section.Elastic2D(osi, e_conc, a_columns[ss][cc - 1], i_columns[ss][cc - 1])
bot_sect = o3.section.Elastic2D(osi, e_conc, a_columns[ss][cc - 1], i_columns[ss][cc - 1])
centre_sect = o3.section.Elastic2D(osi, e_conc, a_columns[ss][cc - 1], i_columns[ss][cc - 1])
sd[ele_str + "T"] = top_sect
sd[ele_str + "B"] = bot_sect
sd[ele_str + "C"] = centre_sect
integ = o3.beam_integration.HingeMidpoint(osi, bot_sect, lp_i, top_sect, lp_j, centre_sect)
bot_node = nd[f"C{cc}-S{ss}"]
top_node = nd[f"C{cc}-S{ss+1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi, [bot_node, top_node], transf, integ)
# Set beams
for bb in range(1, fb.n_bays + 1):
lp_i = 0.5
lp_j = 0.5
ele_str = f"C{bb-1}C{bb}-S{ss}"
mat = o3.uniaxial_material.ElasticBilin(osi, ei_beams[ss][bb - 1], 0.05 * ei_beams[ss][bb - 1], phi_y_beam[ss][bb - 1])
md[ele_str] = mat
left_sect = o3.section.Uniaxial(osi, mat, quantity=o3.cc.M_Z)
right_sect = o3.section.Uniaxial(osi, mat, quantity=o3.cc.M_Z)
centre_sect = o3.section.Elastic2D(osi, e_conc, a_beams[ss][bb - 1], i_beams[ss][bb - 1])
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i, right_sect, lp_j, centre_sect)
left_node = nd[f"C{bb}-S{ss+1}"]
right_node = nd[f"C{bb+1}-S{ss+1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi, [left_node, right_node], transf, integ)
# Define the dynamic analysis
a_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=a_series)
# set damping based on first eigen mode
angular_freq_sqrd = o3.get_eigen(osi, solver='fullGenLapack', n=1)
if hasattr(angular_freq_sqrd, '__len__'):
angular_freq = angular_freq_sqrd[0] ** 0.5
else:
angular_freq = angular_freq_sqrd ** 0.5
if isinstance(angular_freq, complex):
raise ValueError("Angular frequency is complex, issue with stiffness or mass")
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)
tol = 1.0e-4
iter = 4
o3.test_check.EnergyIncr(osi, tol, iter, 0, 2)
analysis_time = (len(asig.values) - 1) * asig.dt + extra_time
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": [],
"ele_mom": [],
"ele_curve": [],
}
print("Analysis starting")
while o3.get_time(osi) < analysis_time:
curr_time = opy.getTime()
o3.analyze(osi, 1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(o3.get_node_disp(osi, nd["C%i-S%i" % (1, fb.n_storeys)], o3.cc.X))
outputs["rel_vel"].append(o3.get_node_vel(osi, nd["C%i-S%i" % (1, fb.n_storeys)], o3.cc.X))
outputs["rel_accel"].append(o3.get_node_accel(osi, nd["C%i-S%i" % (1, fb.n_storeys)], o3.cc.X))
# outputs['ele_mom'].append(opy.eleResponse('-ele', [ed['B%i-S%i' % (1, 0)], 'basicForce']))
o3.gen_reactions(osi)
react = 0
for cc in range(1, fb.n_cols):
react += -o3.get_node_reaction(osi, nd["C%i-S%i" % (cc, 0)], o3.cc.X)
outputs["force"].append(react) # Should be negative since diff node
o3.wipe(osi)
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def run_analysis(etype, asig, xi, sdt, use_modal_damping=0):
osi = o3.OpenSeesInstance(ndm=2, ndf=3)
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, 5.5, 0.0),
o3.node.Node(osi, 0.0, 3.3),
o3.node.Node(osi, 5.5, 3.3)
]
o3.Mass2D(osi, nodes[2], 1e5, 1e5, 1e6)
o3.Mass2D(osi, nodes[3], 1e5, 1e5, 1e6)
o3.Fix3DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
steel_mat = o3.uniaxial_material.Steel01(osi, 300.0e6, 200.0e9, b=0.02)
tran = o3.geom_transf.Linear2D(osi)
o3.element.ElasticBeamColumn2D(osi, [nodes[2], nodes[3]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
o3.element.ElasticBeamColumn2D(osi, [nodes[0], nodes[2]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
o3.element.ElasticBeamColumn2D(osi, [nodes[1], nodes[3]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
a_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=a_series)
angular_freqs = np.array(o3.get_eigen(osi, n=5))**0.5
print('angular_freqs: ', angular_freqs)
periods = 2 * np.pi / angular_freqs
print('periods: ', periods)
if use_modal_damping:
o3.ModalDamping(osi, [xi])
else:
freqs = [0.5, 5]
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=35, p_flag=0)
o3.numberer.RCM(osi)
if etype == 'implicit':
o3.algorithm.Newton(osi)
o3.system.FullGeneral(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
dt = 0.01
else:
o3.algorithm.Linear(osi)
if etype == 'newmark_explicit':
o3.system.FullGeneral(osi)
o3.integrator.NewmarkExplicit(osi, gamma=0.5)
explicit_dt = periods[-1] / np.pi / 8
elif etype == 'central_difference':
if use_modal_damping:
o3.system.FullGeneral(osi)
explicit_dt = periods[
-1] / np.pi / 1.5 * sdt # 1.5 is a factor of safety for damping
else:
o3.system.ProfileSPD(osi)
explicit_dt = periods[-1] / np.pi / 1.1 * sdt
o3.integrator.CentralDifference(osi)
elif etype == 'explicit_difference':
o3.system.Diagonal(osi)
o3.integrator.ExplicitDifference(osi)
explicit_dt = periods[-1] / np.pi / 1.5
else:
raise ValueError(etype)
print('explicit_dt: ', explicit_dt)
dt = explicit_dt
o3.analysis.Transient(osi)
roof_disp = o3.recorder.NodeToArrayCache(osi,
nodes[2],
dofs=[o3.cc.X],
res_type='disp')
time = o3.recorder.TimeToArrayCache(osi)
ttotal = 15.0
while o3.get_time(osi) < ttotal:
if o3.analyze(osi, 10, dt):
print('failed')
break
ddisp = o3.get_node_disp(osi, nodes[2], dof=o3.cc.X)
if abs(ddisp) > 0.1:
print('Break')
break
o3.wipe(osi)
return time.collect(), roof_disp.collect()
def get_inelastic_response(fb,
roof_drift_ratio=0.05,
elastic=False,
w_sfsi=False,
out_folder=''):
"""
Run seismic analysis of a nonlinear FrameBuilding
Units: Pa, N, m, s
Parameters
----------
fb: sfsimodels.Frame2DBuilding object
xi
Returns
-------
"""
osi = o3.OpenSeesInstance(ndm=2, state=3)
q_floor = 7.0e3 # Pa
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):
nd[f"C{cc}-S{ss}"] = o3.node.Node(osi, 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)
o3.set_node_mass(osi, nd[f"C{cc}-S{ss}"], node_mass, 0., 0.)
# Set all nodes on a storey to have the same displacement
for ss in range(0, fb.n_storeys + 1):
for cc in range(2, n_cols + 1):
o3.set_equal_dof(osi, nd[f"C1-S{ss}"], nd[f"C{cc}-S{ss}"], o3.cc.X)
# Fix all base nodes
for cc in range(1, n_cols + 1):
o3.Fix3DOF(osi, nd[f"C{cc}-S0"], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
# Define material
e_conc = 30.0e9 # kPa
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
# 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)
md = OrderedDict() # material dict
sd = OrderedDict() # section dict
ed = OrderedDict() # element dict
for ss in range(fb.n_storeys):
# set columns
lp_i = 0.4
lp_j = 0.4 # plastic hinge length
col_transf = o3.geom_transf.Linear2D(
osi, ) # d_i=[0.0, lp_i], d_j=[0.0, -lp_j]
for cc in range(1, fb.n_cols + 1):
ele_str = f"C{cc}-S{ss}S{ss + 1}"
if elastic:
top_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
bot_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
else:
m_cap = ei_columns[ss][cc - 1] * phi_y_col[ss][cc - 1]
mat = o3.uniaxial_material.ElasticBilin(
osi, ei_columns[ss][cc - 1], 0.05 * ei_columns[ss][cc - 1],
1 * phi_y_col[ss][cc - 1])
mat_axial = o3.uniaxial_material.Elastic(
osi, e_conc * a_columns[ss][cc - 1])
top_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
bot_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat, o3.cc.M_Z]])
centre_sect = o3.section.Elastic2D(osi, e_conc,
a_columns[ss][cc - 1],
i_columns[ss][cc - 1])
sd[ele_str + "T"] = top_sect
sd[ele_str + "B"] = bot_sect
sd[ele_str + "C"] = centre_sect
integ = o3.beam_integration.HingeMidpoint(osi, bot_sect, lp_i,
top_sect, lp_j,
centre_sect)
bot_node = nd[f"C{cc}-S{ss}"]
top_node = nd[f"C{cc}-S{ss + 1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi, [bot_node, top_node],
col_transf, integ)
print('mc: ', ei_columns[ss][cc - 1] * phi_y_col[ss][cc - 1])
# Set beams
lp_i = 0.4
lp_j = 0.4
beam_transf = o3.geom_transf.Linear2D(osi, )
for bb in range(1, fb.n_bays + 1):
ele_str = f"C{bb}C{bb + 1}-S{ss + 1}"
print('mb: ', ei_beams[ss][bb - 1] * phi_y_beam[ss][bb - 1])
print('phi_b: ', phi_y_beam[ss][bb - 1])
if elastic:
left_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
right_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
else:
m_cap = ei_beams[ss][bb - 1] * phi_y_beam[ss][bb - 1]
# mat_flex = o3.uniaxial_material.ElasticBilin(osi, ei_beams[ss][bb - 1], 0.05 * ei_beams[ss][bb - 1], phi_y_beam[ss][bb - 1])
mat_flex = o3.uniaxial_material.Steel01(osi,
m_cap,
e0=ei_beams[ss][bb -
1],
b=0.05)
mat_axial = o3.uniaxial_material.Elastic(
osi, e_conc * a_beams[ss][bb - 1])
left_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex, o3.cc.M_Y]])
right_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex,
o3.cc.M_Y]])
centre_sect = o3.section.Elastic2D(osi, e_conc,
a_beams[ss][bb - 1],
i_beams[ss][bb - 1])
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i,
right_sect, lp_j,
centre_sect)
left_node = nd[f"C{bb}-S{ss + 1}"]
right_node = nd[f"C{bb + 1}-S{ss + 1}"]
ed[ele_str] = o3.element.ForceBeamColumn(osi,
[left_node, right_node],
beam_transf, integ)
# Apply gravity loads
gravity = 9.8 * 1e-2
# If true then load applied along beam
g_beams = 0 # TODO: when this is true and analysis is inelastic then failure
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
for ss in range(1, fb.n_storeys + 1):
print('ss:', ss)
if g_beams:
for bb in range(1, fb.n_bays + 1):
ele_str = f"C{bb}C{bb + 1}-S{ss}"
o3.EleLoad2DUniform(osi, ed[ele_str],
-trib_mass_per_length * gravity)
else:
for cc in range(1, fb.n_cols + 1):
if cc == 1 or cc == n_cols:
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)
# This works
o3.Load(osi, nd[f"C{cc}-S{ss}"], [0, -node_mass * gravity, 0])
tol = 1.0e-3
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
o3.test_check.NormDispIncr(osi, tol, 10)
o3.algorithm.Newton(osi)
n_steps_gravity = 10
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)
o3.gen_reactions(osi)
print('b1_int: ', o3.get_ele_response(osi, ed['C1C2-S1'], 'force'))
print('c1_int: ', o3.get_ele_response(osi, ed['C1-S0S1'], 'force'))
# o3.extensions.to_py_file(osi, 'po.py')
o3.load_constant(osi, time=0.0)
# Define the analysis
# set damping based on first eigen mode
angular_freq = o3.get_eigen(osi, solver='fullGenLapack', n=1)[0]**0.5
if isinstance(angular_freq, complex):
raise ValueError(
"Angular frequency is complex, issue with stiffness or mass")
print('angular_freq: ', angular_freq)
response_period = 2 * np.pi / angular_freq
print('response period: ', response_period)
# Run the analysis
o3r = o3.results.Results2D()
o3r.cache_path = out_folder
o3r.dynamic = True
o3r.pseudo_dt = 0.001 # since analysis is actually static
o3.set_time(osi, 0.0)
o3r.start_recorders(osi)
# o3res.coords = o3.get_all_node_coords(osi)
# o3res.ele2node_tags = o3.get_all_ele_node_tags_as_dict(osi)
d_inc = 0.0001
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
# o3.test_check.NormUnbalance(osi, 2, max_iter=10, p_flag=2)
# o3.test_check.FixedNumIter(osi, max_iter=10)
o3.test_check.NormDispIncr(osi, 0.002, 10, p_flag=0)
o3.algorithm.Newton(osi)
o3.integrator.DisplacementControl(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X,
d_inc)
o3.analysis.Static(osi)
d_max = 0.05 * fb.max_height # TODO: set to 5%
print('d_max: ', d_max)
# n_steps = int(d_max / d_inc)
print("Analysis starting")
print('int_disp: ',
o3.get_node_disp(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X))
# opy.recorder('Element', '-file', 'ele_out.txt', '-time', '-ele', 1, 'force')
tt = 0
outputs = {
'h_disp': [],
'vb': [],
'REACT-C1C2-S1': [],
'REACT-C1-S0S1': [],
}
hd = 0
n_max = 2
n_cycs = 0
xs = fb.heights / fb.max_height # TODO: more sophisticated displacement profile
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
for i, xp in enumerate(xs):
o3.Load(osi, nd[f"C1-S{i + 1}"], [xp, 0.0, 0])
# o3.analyze(osi, 2)
# n_max = 0
time = [0]
while n_cycs < n_max:
print('n_cycles: ', n_cycs)
for i in range(2):
if i == 0:
o3.integrator.DisplacementControl(osi,
nd[f"C1-S{fb.n_storeys}"],
o3.cc.X, d_inc)
else:
o3.integrator.DisplacementControl(osi,
nd[f"C1-S{fb.n_storeys}"],
o3.cc.X, -d_inc)
while hd * (-1)**i < d_max:
ok = o3.analyze(osi, 10)
time.append(time[len(time) - 1] + 1)
hd = o3.get_node_disp(osi, nd[f"C1-S{fb.n_storeys}"], o3.cc.X)
outputs['h_disp'].append(hd)
o3.gen_reactions(osi)
vb = 0
for cc in range(1, fb.n_cols + 1):
vb += o3.get_node_reaction(osi, nd[f"C{cc}-S0"], o3.cc.X)
outputs['vb'].append(-vb)
outputs['REACT-C1C2-S1'].append(
o3.get_ele_response(osi, ed['C1C2-S1'], 'force'))
outputs['REACT-C1-S0S1'].append(
o3.get_ele_response(osi, ed['C1-S0S1'], 'force'))
n_cycs += 1
o3.wipe(osi)
o3r.save_to_cache()
for item in outputs:
outputs[item] = np.array(outputs[item])
print('complete')
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 test_fix3dof():
osi = o3.OpenSeesInstance(ndm=2, ndf=3)
node = o3.node.Node(osi, 3, 4)
o3.Fix3DOF(osi, node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
sn = o3.node.build_regular_node_mesh(osi, [3, 4], [1, 6])
o3.Fix3DOFMulti(osi, sn[0], o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
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
def run_w_settings(ele_len, e_mod, i_sect, pload, udl, beam_in_parts,
use_pload):
osi = o3.OpenSeesInstance(ndm=2, state=3)
# Establish nodes
left_node = o3.node.Node(osi, 0, 0)
right_node = o3.node.Node(osi, ele_len, 0)
# Fix bottom node
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, right_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FREE)
area = 0.5
lp_i = 0.2
lp_j = 0.2
if beam_in_parts:
elastic = 1
if elastic:
left_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
else:
m_cap = 600.0
b = 0.05
phi = m_cap / (e_mod * i_sect)
# mat_flex = o3.uniaxial_material.Steel01(osi, m_cap, e0=e_mod * i_sect, b=b)
mat_flex = o3.uniaxial_material.ElasticBilin(
osi, e_mod * i_sect, e_mod * i_sect * b, phi)
mat_axial = o3.uniaxial_material.Elastic(osi, e_mod * area)
left_sect = o3.section.Aggregator(osi,
mats=[
mat_axial.tag, o3.cc.P,
mat_flex.tag, o3.cc.M_Z,
mat_flex.tag, o3.cc.M_Y
])
right_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
centre_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i,
right_sect, lp_j,
centre_sect)
beam_transf = o3.geom_transf.Linear2D(osi, )
ele = o3.element.ForceBeamColumn(osi, [left_node, right_node],
beam_transf, integ)
else:
beam_transf = o3.geom_transf.Linear2D(osi)
ele = o3.element.ElasticBeamColumn2D(osi, [left_node, right_node],
area, e_mod, i_sect,
beam_transf)
# Apply gravity loads
# If true then load applied along beam
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
if use_pload:
o3.Load(osi, right_node, [0, -pload, 0])
else:
o3.EleLoad2DUniform(osi, ele, -udl)
tol = 1.0e-3
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
n_steps_gravity = 10
o3.integrator.LoadControl(osi, 1. / n_steps_gravity, num_iter=10)
o3.test_check.NormDispIncr(osi, tol, 10)
o3.algorithm.Linear(osi)
o3.analysis.Static(osi)
o3.analyze(osi, n_steps_gravity)
o3.gen_reactions(osi)
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
return o3.get_ele_response(osi, ele, 'force')[:3], end_disp
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(apply_diff):
# If use_pload=true then apply point load at end, else apply distributed load along beam
osi = o3.OpenSeesInstance(ndm=2, state=3)
ele_len = 4.0
# Establish nodes
left_node = o3.node.Node(osi, 0, 0)
right_node = o3.node.Node(osi, ele_len, 0)
# Fix left node
if apply_diff:
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FREE, o3.cc.FREE)
o3.Fix3DOF(osi, left_node, o3.cc.FREE, o3.cc.FIXED, o3.cc.FIXED)
else:
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, right_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FREE)
e_mod = 200.0e2
i_sect = 0.1
area = 0.5
lp_i = 0.1
lp_j = 0.1
elastic = 0
if elastic:
left_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
else:
m_cap = 14.80
b = 0.05
phi = m_cap / (e_mod * i_sect)
# mat_flex = o3.uniaxial_material.Steel01(osi, m_cap, e0=e_mod * i_sect, b=b)
mat_flex = o3.uniaxial_material.ElasticBilin(osi, e_mod * i_sect,
e_mod * i_sect * b, phi)
mat_axial = o3.uniaxial_material.Elastic(osi, e_mod * area)
left_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex, o3.cc.M_Y]])
right_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
centre_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i, right_sect,
lp_j, centre_sect)
beam_transf = o3.geom_transf.Linear2D(osi, )
ele = o3.element.ForceBeamColumn(osi, [left_node, right_node], beam_transf,
integ)
use_pload = 1
w_gloads = 1
if w_gloads:
# Apply gravity loads
pload = 1.0 * ele_len
udl = 2.0
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
if use_pload:
o3.Load(osi, right_node, [0, -pload, 0])
else:
o3.EleLoad2DUniform(osi, ele, -udl)
tol = 1.0e-3
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
n_steps_gravity = 10
o3.integrator.LoadControl(osi, 1. / n_steps_gravity, num_iter=10)
o3.test_check.NormDispIncr(osi, tol, 10)
o3.algorithm.Linear(osi)
o3.analysis.Static(osi)
o3.analyze(osi, n_steps_gravity)
o3.gen_reactions(osi)
print('reactions: ', o3.get_ele_response(osi, ele, 'force')[:3])
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
print(f'end_disp: {end_disp}')
if use_pload:
disp_expected = pload * ele_len**3 / (3 * e_mod * i_sect)
print(f'v_expected: {pload}')
print(f'm_expected: {pload * ele_len}')
print(f'disp_expected: {disp_expected}')
else:
v_expected = udl * ele_len
m_expected = udl * ele_len**2 / 2
disp_expected = udl * ele_len**4 / (8 * e_mod * i_sect)
print(f'v_expected: {v_expected}')
print(f'm_expected: {m_expected}')
print(f'disp_expected: {disp_expected}')
rot_0 = o3.get_ele_response(osi,
ele,
'section',
extra_args=['1', 'deformation'])[1]
shear_0 = o3.get_ele_response(osi,
ele,
'section',
extra_args=['1', 'deformation'])[2]
print(
o3.get_ele_response(osi,
ele,
'section',
extra_args=['2', 'deformation']))
def get_moment_curvature(axial_load=100., max_curve=0.001, num_incr=500):
osi = o3.OpenSeesInstance(ndm=2, ndf=3, state=3)
fc = 4.0
# e_mod = 57000.0 * np.sqrt(fc * 1000.0) / 1e3
conc_conf = o3.uniaxial_material.Concrete01(osi, fpc=-5.0, epsc0=-0.005, fpcu=-3.5, eps_u=-0.02)
conc_unconf = o3.uniaxial_material.Concrete01(osi, fpc=-fc, epsc0=-0.002, fpcu=0.0, eps_u=-0.006)
rebar = o3.uniaxial_material.Steel01(osi, fy=60.0, e0=30000.0, b=0.02)
h = 18.0
b = 18.0
cover = 2.5
gj = 1.0E10
nf_core_y = 8
nf_core_z = 8
nf_cover_y = 10
nf_cover_z = 10
n_bars = 3
bar_area = 0.79
edge_y = h / 2.0
edge_z = b / 2.0
core_y = edge_y - cover
core_z = edge_z - cover
sect = o3.section.Fiber(osi, gj=gj)
# define the core patch
o3.patch.Quad(osi, conc_conf, nf_core_z, nf_core_y, # core, counter-clockwise (diagonals at corners)
crds_i=[-core_y, core_z],
crds_j=[-core_y, -core_z],
crds_k=[core_y, -core_z],
crds_l=[core_y, core_z])
o3.patch.Quad(osi, conc_unconf, 1, nf_cover_y, # right cover, counter-clockwise (diagonals at corners)
crds_i=[-edge_y, edge_z],
crds_j=[-core_y, core_z],
crds_k=[core_y, core_z],
crds_l=[edge_y, edge_z])
o3.patch.Quad(osi, conc_unconf, 1, nf_cover_y, # left cover
crds_i=[-core_y, -core_z],
crds_j=[-edge_y, -edge_z],
crds_k=[edge_y, -edge_z],
crds_l=[core_y, -core_z])
o3.patch.Quad(osi, conc_unconf, nf_cover_z, 1, # bottom cover
crds_i=[-edge_y, edge_z],
crds_j=[-edge_y, -edge_z],
crds_k=[-core_y, -core_z],
crds_l=[-core_y, core_z])
o3.patch.Quad(osi, conc_unconf, nf_cover_z, 1, # top cover
crds_i=[core_y, core_z],
crds_j=[core_y, -core_z],
crds_k=[edge_y, -edge_z],
crds_l=[edge_y, edge_z])
o3.layer.Straight(osi, rebar, n_bars, bar_area, start=[-core_y, core_z], end=[-core_y, -core_z])
o3.layer.Straight(osi, rebar, n_bars, bar_area, start=[core_y, core_z], end=[core_y, -core_z])
spacing_y = 2 * core_y / (n_bars - 1)
remaining_bars = n_bars - 2
o3.layer.Straight(osi, rebar, remaining_bars, bar_area,
start=[core_y - spacing_y, core_z],
end=[-core_y + spacing_y, core_z])
o3.layer.Straight(osi, rebar, remaining_bars, bar_area,
start=[core_y - spacing_y, -core_z],
end=[-core_y + spacing_y, -core_z])
n1 = o3.node.Node(osi, 0.0, 0.0)
n2 = o3.node.Node(osi, 0.0, 0.0)
o3.Fix3DOF(osi, n1, 1, 1, 1)
o3.Fix3DOF(osi, n2, 0, 1, 0)
ele = o3.element.ZeroLengthSection(osi, [n1, n2], sect)
nd = o3.recorder.NodeToArrayCache(osi, n2, dofs=[3], res_type='disp')
nm = o3.recorder.NodeToArrayCache(osi, n1, dofs=[3], res_type='reaction')
ts = o3.time_series.Constant(osi)
o3.pattern.Plain(osi, ts)
o3.Load(osi, n2, load_values=[axial_load, 0.0, 0.0])
o3.system.BandGeneral(osi)
o3.numberer.Plain(osi)
o3.constraints.Plain(osi)
o3.test.NormUnbalance(osi, tol=1.0e-9, max_iter=10)
o3.algorithm.Newton(osi)
o3.integrator.LoadControl(osi, incr=0.0)
o3.analysis.Static(osi)
o3.analyze(osi, 1)
#
ts = o3.time_series.Linear(osi)
o3.pattern.Plain(osi, ts)
o3.Load(osi, n2, load_values=[0.0, 0.0, 1.0])
d_cur = max_curve / num_incr
o3.integrator.DisplacementControl(osi, n2, o3.cc.DOF2D_ROTZ, d_cur, 1, d_cur, d_cur)
o3.analyze(osi, num_incr)
o3.wipe(osi)
curvature = nd.collect()
moment = -nm.collect()
return moment, curvature
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_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 run(use_pload):
# If pload=true then apply point load at end, else apply distributed load along beam
osi = o3.OpenSeesInstance(ndm=2, state=3)
ele_len = 4.0
# Establish nodes
left_node = o3.node.Node(osi, 0, 0)
right_node = o3.node.Node(osi, ele_len, 0)
# Fix bottom node
o3.Fix3DOF(osi, left_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, right_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FREE)
e_mod = 200.0e2
i_sect = 0.1
area = 0.5
lp_i = 0.1
lp_j = 0.1
elastic = 0
if elastic:
left_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
else:
m_cap = 14.80
b = 0.05
phi = m_cap / (e_mod * i_sect)
# mat_flex = o3.uniaxial_material.Steel01(osi, m_cap, e0=e_mod * i_sect, b=b)
mat_flex = o3.uniaxial_material.ElasticBilin(osi, e_mod * i_sect,
e_mod * i_sect * b, phi)
mat_axial = o3.uniaxial_material.Elastic(osi, e_mod * area)
left_sect = o3.section.Aggregator(osi,
mats=[[mat_axial, o3.cc.P],
[mat_flex, o3.cc.M_Z],
[mat_flex, o3.cc.M_Y]])
right_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
centre_sect = o3.section.Elastic2D(osi, e_mod, area, i_sect)
integ = o3.beam_integration.HingeMidpoint(osi, left_sect, lp_i, right_sect,
lp_j, centre_sect)
beam_transf = o3.geom_transf.Linear2D(osi, )
ele = o3.element.ForceBeamColumn(osi, [left_node, right_node], beam_transf,
integ)
w_gloads = 1
if w_gloads:
# Apply gravity loads
pload = 1.0 * ele_len
udl = 2.0
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
if use_pload:
o3.Load(osi, right_node, [0, -pload, 0])
else:
o3.EleLoad2DUniform(osi, ele, -udl)
tol = 1.0e-3
o3.constraints.Plain(osi)
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
n_steps_gravity = 10
o3.integrator.LoadControl(osi, 1. / n_steps_gravity, num_iter=10)
o3.test_check.NormDispIncr(osi, tol, 10)
o3.algorithm.Linear(osi)
o3.analysis.Static(osi)
o3.analyze(osi, n_steps_gravity)
o3.gen_reactions(osi)
print('reactions: ', o3.get_ele_response(osi, ele, 'force')[:3])
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
print(f'end_disp: {end_disp}')
if use_pload:
disp_expected = pload * ele_len**3 / (3 * e_mod * i_sect)
print(f'v_expected: {pload}')
print(f'm_expected: {pload * ele_len}')
print(f'disp_expected: {disp_expected}')
else:
v_expected = udl * ele_len
m_expected = udl * ele_len**2 / 2
disp_expected = udl * ele_len**4 / (8 * e_mod * i_sect)
print(f'v_expected: {v_expected}')
print(f'm_expected: {m_expected}')
print(f'disp_expected: {disp_expected}')
# o3.extensions.to_py_file(osi, 'temp4.py')
disp_load = 1
if disp_load:
# start displacement controlled
d_inc = -0.01
# opy.wipeAnalysis()
o3.numberer.RCM(osi)
o3.system.BandGeneral(osi)
o3.test_check.NormUnbalance(osi, 2, max_iter=10, p_flag=0)
# o3.test_check.FixedNumIter(osi, max_iter=10)
# o3.test_check.NormDispIncr(osi, 0.002, 10, p_flag=0)
o3.algorithm.Newton(osi)
o3.integrator.DisplacementControl(osi, right_node, o3.cc.Y, d_inc)
o3.analysis.Static(osi)
ts_po = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts_po)
o3.Load(osi, right_node, [0.0, 1.0, 0])
ok = o3.analyze(osi, 10)
end_disp = o3.get_node_disp(osi, right_node, dof=o3.cc.Y)
print(f'end_disp: {end_disp}')
r = o3.get_ele_response(osi, ele, 'force')[:3]
print('reactions: ', r)
k = r[1] / -end_disp
print('k: ', k)
k_elastic_expected = 1. / (ele_len**3 / (3 * e_mod * i_sect))
print('k_elastic_expected: ', k_elastic_expected)
def run_pm4sand_et(sl,
csr,
esig_v0=101.0e3,
static_bias=0.0,
n_lim=100,
k0=0.5,
strain_limit=0.03,
strain_inc=5.0e-6,
etype='implicit'):
nu_init = k0 / (1 + k0)
damp = 0.02
omega0 = 0.2
omega1 = 20.0
a1 = 2. * damp / (omega0 + omega1)
a0 = a1 * omega0 * omega1
# Initialise OpenSees instance
osi = o3.OpenSeesInstance(ndm=2, ndf=3, state=3)
# Establish nodes
h_ele = 1.
bl_node = o3.node.Node(osi, 0, 0)
br_node = o3.node.Node(osi, h_ele, 0)
tr_node = o3.node.Node(osi, h_ele, h_ele)
tl_node = o3.node.Node(osi, 0, h_ele)
all_nodes = [bl_node, br_node, tr_node, tl_node]
# Fix bottom node
o3.Fix3DOF(osi, bl_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, br_node, o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, tr_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FIXED)
o3.Fix3DOF(osi, tl_node, o3.cc.FREE, o3.cc.FREE, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, tr_node, tl_node, [o3.cc.X, o3.cc.Y])
# Define material
pm4sand = o3.nd_material.PM4Sand(osi,
sl.relative_density,
sl.g0_mod,
sl.h_po,
sl.unit_sat_mass,
101.3,
nu=nu_init)
# Note water bulk modulus is irrelevant since constant volume test - so as soil skeleton contracts
# the bulk modulus of the soil skeleton controls the change in effective stress
water_bulk_mod = 2.2e6
ele = o3.element.SSPquadUP(osi,
all_nodes,
pm4sand,
1.0,
water_bulk_mod,
1.,
sl.permeability,
sl.permeability,
sl.e_curr,
alpha=1.0e-5,
b1=0.0,
b2=0.0)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-6, max_iter=35, p_flag=0)
o3.numberer.RCM(osi)
omegas = np.array(o3.get_eigen(osi, n=1))**0.5
periods = 2 * np.pi / omegas
periods = [0.001]
if etype == 'implicit':
o3.algorithm.Newton(osi)
o3.system.FullGeneral(osi)
o3.integrator.Newmark(osi, gamma=5. / 6, beta=4. / 9)
dt = 0.01
else:
o3.algorithm.Linear(osi, factor_once=True)
o3.system.FullGeneral(osi)
if etype == 'newmark_explicit':
o3.integrator.NewmarkExplicit(osi, gamma=0.5)
explicit_dt = periods[0] / np.pi / 8
elif etype == 'central_difference':
o3.integrator.CentralDifference(osi)
explicit_dt = periods[0] / np.pi / 16 # 0.5 is a factor of safety
elif etype == 'hht_explicit':
o3.integrator.HHTExplicit(osi, alpha=0.5)
explicit_dt = periods[0] / np.pi / 8
elif etype == 'explicit_difference':
o3.integrator.ExplicitDifference(osi)
explicit_dt = periods[0] / np.pi / 4
else:
raise ValueError(etype)
print('explicit_dt: ', explicit_dt)
dt = explicit_dt
o3.analysis.Transient(osi)
freqs = [0.5, 10]
xi = 0.1
use_modal_damping = 0
if use_modal_damping:
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
else:
o3.ModalDamping(osi, [xi])
o3.update_material_stage(osi, pm4sand, stage=0)
# print('here1: ', o3.get_ele_response(osi, ele, 'stress'), esig_v0, csr)
all_stresses_cache = o3.recorder.ElementToArrayCache(osi,
ele,
arg_vals=['stress'])
all_strains_cache = o3.recorder.ElementToArrayCache(osi,
ele,
arg_vals=['strain'])
nodes_cache = o3.recorder.NodesToArrayCache(osi,
all_nodes,
dofs=[1, 2, 3],
res_type='disp')
o3.recorder.NodesToFile(osi,
'node_disp.txt',
all_nodes,
dofs=[1, 2, 3],
res_type='disp')
# Add static vertical pressure and stress bias
ttime = 30
time_series = o3.time_series.Path(osi,
time=[0, ttime, 1e10],
values=[0, 1, 1])
o3.pattern.Plain(osi, time_series)
o3.Load(osi, tl_node, [0, -esig_v0 / 2, 0])
o3.Load(osi, tr_node, [0, -esig_v0 / 2, 0])
o3.analyze(osi, num_inc=int(ttime / dt) + 10, dt=dt)
ts2 = o3.time_series.Path(osi,
time=[ttime, 80000, 1e10],
values=[1., 1., 1.],
factor=1)
o3.pattern.Plain(osi, ts2, fact=1.)
y_vert = o3.get_node_disp(osi, tr_node, o3.cc.Y)
o3.SP(osi, tl_node, dof=o3.cc.Y, dof_values=[y_vert])
o3.SP(osi, tr_node, dof=o3.cc.Y, dof_values=[y_vert])
# Close the drainage valves
for node in all_nodes:
o3.remove_sp(osi, node, dof=3)
o3.analyze(osi, int(5 / dt), dt=dt)
print('here3: ', o3.get_ele_response(osi, ele, 'stress'), esig_v0, csr)
o3.update_material_stage(osi, pm4sand, stage=1)
o3.set_parameter(osi, value=0, eles=[ele], args=['FirstCall', pm4sand.tag])
o3.analyze(osi, int(5 / dt), dt=dt)
o3.set_parameter(osi,
value=sl.poissons_ratio,
eles=[ele],
args=['poissonRatio', pm4sand.tag])
o3.extensions.to_py_file(osi)
n_cyc = 0.0
target_strain = 1.1 * strain_limit
target_disp = target_strain * h_ele
limit_reached = 0
export = 1
while n_cyc < n_lim:
print('n_cyc: ', n_cyc)
h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X)
curr_time = o3.get_time(osi)
steps = target_strain / strain_inc
ts0 = o3.time_series.Path(osi,
time=[curr_time, curr_time + steps, 1e10],
values=[h_disp, target_disp, target_disp],
factor=1)
pat0 = o3.pattern.Plain(osi, ts0)
o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0])
curr_stress = o3.get_ele_response(osi, ele, 'stress')[2]
if math.isnan(curr_stress):
raise ValueError
if export:
o3.extensions.to_py_file(osi)
export = 0
while curr_stress < (csr - static_bias) * esig_v0:
o3.analyze(osi, int(0.1 / dt), dt=dt)
curr_stress = o3.get_ele_response(osi, ele, 'stress')[2]
h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X)
print(h_disp, target_disp)
if h_disp >= target_disp:
print('STRAIN LIMIT REACHED - on load')
limit_reached = 1
break
if limit_reached:
break
n_cyc += 0.25
print('load reversal, n_cyc: ', n_cyc)
curr_time = o3.get_time(osi)
o3.remove_load_pattern(osi, pat0)
o3.remove(osi, ts0)
o3.remove_sp(osi, tr_node, dof=o3.cc.X)
# Reverse cycle
steps = (h_disp + target_disp) / (strain_inc * h_ele)
ts0 = o3.time_series.Path(osi,
time=[curr_time, curr_time + steps, 1e10],
values=[h_disp, -target_disp, -target_disp],
factor=1)
pat0 = o3.pattern.Plain(osi, ts0)
o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0])
i = 0
while curr_stress > -(csr + static_bias) * esig_v0:
o3.analyze(osi, int(0.1 / dt), dt=dt)
curr_stress = o3.get_ele_response(osi, ele, 'stress')[2]
h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X)
if -h_disp >= target_disp:
print('STRAIN LIMIT REACHED - on reverse')
limit_reached = 1
break
i += 1
if i > steps:
break
if limit_reached:
break
n_cyc += 0.5
print('reload, n_cyc: ', n_cyc)
curr_time = o3.get_time(osi)
o3.remove_load_pattern(osi, pat0)
o3.remove(osi, ts0)
o3.remove_sp(osi, tr_node, dof=o3.cc.X)
# reload cycle
steps = (-h_disp + target_disp) / (strain_inc * h_ele)
ts0 = o3.time_series.Path(osi,
time=[curr_time, curr_time + steps, 1e10],
values=[h_disp, target_disp, target_disp],
factor=1)
pat0 = o3.pattern.Plain(osi, ts0)
o3.SP(osi, tr_node, dof=o3.cc.X, dof_values=[1.0])
while curr_stress < static_bias * esig_v0:
o3.analyze(osi, int(0.1 / dt), dt=dt)
curr_stress = o3.get_ele_response(osi, ele, 'stress')[2]
h_disp = o3.get_node_disp(osi, tr_node, o3.cc.X)
if h_disp >= target_disp:
print('STRAIN LIMIT REACHED - on reload')
limit_reached = 1
break
if limit_reached:
break
o3.remove_load_pattern(osi, pat0)
o3.remove(osi, ts0)
o3.remove_sp(osi, tr_node, dof=o3.cc.X)
n_cyc += 0.25
o3.wipe(osi)
all_stresses = all_stresses_cache.collect()
all_strains = all_strains_cache.collect()
disps = nodes_cache.collect()
stress = all_stresses[:, 2]
strain = all_strains[:, 2]
ppt = all_stresses[:, 1]
return stress, strain, ppt, disps
pass
def run_analysis(etype, asig, use_modal_damping=0):
osi = o3.OpenSeesInstance(ndm=2, ndf=3)
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, 5.5, 0.0),
o3.node.Node(osi, 0.0, 3.3),
o3.node.Node(osi, 5.5, 3.3)
]
o3.Mass2D(osi, nodes[2], 1e5, 1e5, 1e6)
o3.Mass2D(osi, nodes[3], 1e5, 1e5, 1e6)
o3.Fix3DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
o3.Fix3DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED, o3.cc.FIXED)
steel_mat = o3.uniaxial_material.Steel01(osi, 300.0e6, 200.0e9, b=0.02)
tran = o3.geom_transf.Linear2D(osi)
o3.element.ElasticBeamColumn2D(osi, [nodes[2], nodes[3]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
o3.element.ElasticBeamColumn2D(osi, [nodes[0], nodes[2]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
o3.element.ElasticBeamColumn2D(osi, [nodes[1], nodes[3]],
0.01,
200.0e9,
iz=1.0e-4,
transf=tran)
a_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=a_series)
xi = 0.1
angular_freqs = np.array(o3.get_eigen(
osi, n=5))**0.5 # There are vertical modes too!
print('angular_freqs: ', angular_freqs)
periods = 2 * np.pi / angular_freqs
print('periods: ', periods)
if use_modal_damping: # Does not support modal damping
freqs = [0.5, 5]
omega_1 = 2 * np.pi * freqs[0]
omega_2 = 2 * np.pi * freqs[1]
a0 = 2 * xi * omega_1 * omega_2 / (omega_1 + omega_2)
a1 = 2 * xi / (omega_1 + omega_2)
o3.rayleigh.Rayleigh(osi, a0, 0, a1, 0)
else:
o3.ModalDamping(osi, [xi])
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-5, max_iter=35, p_flag=0)
o3.numberer.RCM(osi)
if use_modal_damping:
o3_sys = o3.system.ProfileSPD # not sure why don't need to use FullGen here? since matrix is full?
else:
o3_sys = o3.system.ProfileSPD
if etype == 'implicit':
o3.algorithm.Newton(osi)
o3_sys(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
dt = 0.001
else:
o3.algorithm.Linear(osi, factor_once=True)
if etype == 'newmark_explicit':
o3_sys(osi)
o3.integrator.NewmarkExplicit(osi, gamma=0.5)
explicit_dt = periods[-1] / np.pi / 2.01
elif etype == 'central_difference':
o3_sys(osi)
o3.integrator.CentralDifference(osi)
if use_modal_damping:
explicit_dt = periods[
-1] / np.pi / 1.5 # 1.1 is a factor of safety
else:
explicit_dt = periods[-1] / np.pi / 1.5
elif etype == 'explicit_difference':
o3.system.Diagonal(osi)
o3.integrator.ExplicitDifference(osi)
explicit_dt = periods[-1] / np.pi / 1.6
else:
raise ValueError(etype)
print('explicit_dt: ', explicit_dt)
dt = explicit_dt
o3.analysis.Transient(osi)
roof_disp = o3.recorder.NodeToArrayCache(osi,
nodes[2],
dofs=[o3.cc.X],
res_type='disp')
time = o3.recorder.TimeToArrayCache(osi)
ttotal = 15.0
o3.analyze(osi, int(ttotal / dt), dt)
o3.wipe(osi)
return time.collect(), roof_disp.collect()
