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
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 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_ts_custom_strain(mat, esig_v0, strains, osi=None, nu_dyn=None, target_d_inc=0.00001, k0=None, etype='newmark_explicit',
handle='silent', verbose=0, opyfile=None, dss=False, plain_strain=True, min_n=10, nl=True):
# if dss:
# raise ValueError('dss option is not working')
damp = 0.05
omega0 = 0.2
omega1 = 20.0
a1 = 2. * damp / (omega0 + omega1)
a0 = a1 * omega0 * omega1
if osi is None:
osi = o3.OpenSeesInstance(ndm=2, ndf=2)
mat.build(osi)
# Establish nodes
h_ele = 1.
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, h_ele, 0.0),
o3.node.Node(osi, h_ele, h_ele),
o3.node.Node(osi, 0.0, h_ele)
]
# Fix bottom node
o3.Fix2DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED)
if k0 is None:
o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, nodes[2], nodes[3], [o3.cc.X, o3.cc.Y])
else: # control k0 with node forces
o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FREE)
if plain_strain:
oop = 'PlaneStrain'
else:
oop = 'PlaneStress'
ele = o3.element.SSPquad(osi, nodes, mat, oop, 1, 0.0, 0.0)
angular_freqs = np.array(o3.get_eigen(osi, solver='fullGenLapack', n=2)) ** 0.5
print('angular_freqs: ', angular_freqs)
periods = 2 * np.pi / angular_freqs
xi = 0.03
o3.ModalDamping(osi, [xi, xi])
print('periods: ', periods)
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.FullGeneral(osi)
o3.integrator.Newmark(osi, gamma=0.5, beta=0.25)
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)
o3.update_material_stage(osi, mat, stage=0)
# dt = 0.00001
tload = 60
n_steps = tload / dt
# Add static vertical pressure and stress bias
time_series = o3.time_series.Path(osi, time=[0, tload, 1e10], values=[0, 1, 1])
o3.pattern.Plain(osi, time_series)
# ts0 = o3.time_series.Linear(osi, factor=1)
# o3.pattern.Plain(osi, ts0)
if k0:
o3.Load(osi, nodes[2], [-esig_v0 / 2, -esig_v0 / 2])
o3.Load(osi, nodes[3], [esig_v0 / 2, -esig_v0 / 2])
o3.Load(osi, nodes[1], [-esig_v0 / 2, 0])
# node 0 is fixed
else:
o3.Load(osi, nodes[2], [0, -esig_v0 / 2])
o3.Load(osi, nodes[3], [0, -esig_v0 / 2])
print('Apply init stress to elastic element')
o3.analyze(osi, num_inc=n_steps, dt=dt)
stresses = o3.get_ele_response(osi, ele, 'stress')
print('init_stress0: ', stresses)
o3.load_constant(osi, tload)
if hasattr(mat, 'update_to_nonlinear') and nl:
print('set to nonlinear')
mat.update_to_nonlinear()
o3.analyze(osi, 10000, dt=dt)
# if not nl:
# mat.update_to_linear()
if nu_dyn is not None:
mat.set_nu(nu_dyn, eles=[ele])
o3.analyze(osi, 10000, dt=dt)
# o3.extensions.to_py_file(osi)
stresses = o3.get_ele_response(osi, ele, 'stress')
print('init_stress1: ', stresses)
# Prepare for reading results
exit_code = None
stresses = o3.get_ele_response(osi, ele, 'stress')
if dss:
o3.gen_reactions(osi)
force0 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X)
force1 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X)
# force2 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X)
stress = [force1 + force0]
strain = [o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X)]
sxy_ind = None
gxy_ind = None
# iforce0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X)
# iforce1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X)
# iforce2 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X)
# iforce3 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X)
# print(iforce0, iforce1, iforce2, iforce3, stresses[2])
else:
ro = o3.recorder.load_recorder_options()
import pandas as pd
df = pd.read_csv(ro)
mat_type = ele.mat.type
dfe = df[(df['mat'] == mat_type) & (df['form'] == oop)]
df_sxy = dfe[dfe['recorder'] == 'stress']
outs = df_sxy['outs'].iloc[0].split('-')
sxy_ind = outs.index('sxy')
df_gxy = dfe[dfe['recorder'] == 'strain']
outs = df_gxy['outs'].iloc[0].split('-')
gxy_ind = outs.index('gxy')
stress = [stresses[sxy_ind]]
cur_strains = o3.get_ele_response(osi, ele, 'strain')
strain = [cur_strains[gxy_ind]]
time_series = o3.time_series.Path(osi, time=[0, tload, 1e10], values=[0, 1, 1])
o3.pattern.Plain(osi, time_series)
disps = list(np.array(strains) * 1)
d_per_dt = 0.01
diff_disps = np.diff(disps, prepend=0)
time_incs = np.abs(diff_disps) / d_per_dt
approx_n_steps = time_incs / dt
time_incs = np.where(approx_n_steps < 800, 800 * dt, time_incs)
approx_n_steps = time_incs / dt
assert min(approx_n_steps) >= 8, approx_n_steps
curr_time = o3.get_time(osi)
times = list(np.cumsum(time_incs) + curr_time)
disps.append(disps[-1])
times.append(1e10)
disps = list(disps)
n_steps_p2 = int((times[-2] - curr_time) / dt) + 10
print('n_steps: ', n_steps_p2)
times.insert(0, curr_time)
disps.insert(0, 0.0)
init_disp = o3.get_node_disp(osi, nodes[2], dof=o3.cc.X)
disps = list(np.array(disps) + init_disp)
ts0 = o3.time_series.Path(osi, time=times, values=disps, factor=1)
pat0 = o3.pattern.Plain(osi, ts0)
o3.SP(osi, nodes[2], dof=o3.cc.X, dof_values=[1])
o3.SP(osi, nodes[3], dof=o3.cc.X, dof_values=[1])
print('init_disp: ', init_disp)
print('path -times: ', times)
print('path -values: ', disps)
v_eff = [stresses[1]]
h_eff = [stresses[0]]
time = [o3.get_time(osi)]
for i in range(int(n_steps_p2 / 200)):
print(i / (n_steps_p2 / 200))
fail = o3.analyze(osi, 200, dt=dt)
o3.gen_reactions(osi)
stresses = o3.get_ele_response(osi, ele, 'stress')
v_eff.append(stresses[1])
h_eff.append(stresses[0])
if dss:
o3.gen_reactions(osi)
force0 = o3.get_node_reaction(osi, nodes[2], o3.cc.DOF2D_X)
force1 = o3.get_node_reaction(osi, nodes[3], o3.cc.DOF2D_X)
stress.append(force1 + force0)
strain.append(o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X))
else:
stress.append(stresses[sxy_ind])
cur_strains = o3.get_ele_response(osi, ele, 'strain')
strain.append(cur_strains[gxy_ind])
time.append(o3.get_time(osi))
if fail:
break
return np.array(stress), np.array(strain)-init_disp, np.array(v_eff), np.array(h_eff), np.array(time), exit_code
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(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 run_2d_strain_driver_iso(osi, base_mat, esig_v0, disps, target_d_inc=0.00001, max_steps=10000, handle='silent', da_strain_max=0.05, max_cycles=200, srate=0.0001, esig_v_min=1.0, k0_init=1, verbose=0,
cyc_lim_fail=True):
if not np.isclose(k0_init, 1., rtol=0.05):
raise ValueError(f'Only supports k0=1, current k0={k0_init:.3f}')
max_steps_per_half_cycle = 50000
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, 1.0, 0.0),
o3.node.Node(osi, 1.0, 1.0),
o3.node.Node(osi, 0.0, 1.0)
]
for node in nodes:
o3.Fix2DOF(osi, node, 1, 1)
mat = o3.nd_material.InitStressNDMaterial(osi, other=base_mat, init_stress=-esig_v0, n_dim=2)
ele = o3.element.SSPquad(osi, nodes, mat, 'PlaneStrain', 1, 0.0, 0.0)
# create analysis
o3.constraints.Penalty(osi, 1.0e15, 1.0e15)
o3.algorithm.Linear(osi)
o3.numberer.RCM(osi)
o3.system.FullGeneral(osi)
o3.analysis.Static(osi)
d_init = 0.0
d_max = 0.1 # element height is 1m
max_time = (d_max - d_init) / srate
ts0 = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts0)
o3.Load(osi, nodes[2], [1.0, 0.0])
o3.Load(osi, nodes[3], [1.0, 0.0])
o3.analyze(osi, 1)
o3.set_parameter(osi, value=1, eles=[ele], args=['materialState'])
o3.update_material_stage(osi, base_mat, 1)
o3.analyze(osi, 1)
exit_code = None
# loop through the total number of cycles
react = 0
strain = [0]
stresses = o3.get_ele_response(osi, ele, 'stress')
stress = [stresses[2]]
v_eff = [stresses[1]]
h_eff = [stresses[0]]
d_incs = np.diff(disps, prepend=0)
# orys = np.where(diffs >= 0, 1, -1)
for i in range(len(disps)):
d_inc_i = d_incs[i]
if target_d_inc < abs(d_inc_i):
n = int(abs(d_inc_i / target_d_inc))
d_step = d_inc_i / n
else:
n = 1
d_step = d_inc_i
for j in range(n):
o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_X, -d_step)
o3.Load(osi, nodes[2], [1.0, 0.0])
o3.Load(osi, nodes[3], [1.0, 0.0])
o3.analyze(osi, 1)
o3.gen_reactions(osi)
# react = o3.get_ele_response(osi, ele, 'force')[0]
stresses = o3.get_ele_response(osi, ele, 'stress')
v_eff.append(stresses[1])
h_eff.append(stresses[0])
force0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X)
force1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X)
stress.append(-force0 - force1)
# stress.append(stresses[2])
end_strain = -o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X)
strain.append(end_strain)
return -np.array(stress), np.array(strain), np.array(v_eff), np.array(h_eff), exit_code
def run_2d_strain_driver(osi, mat, esig_v0, disps, target_d_inc=0.00001, handle='silent', verbose=0):
k0 = 1.0
pois = k0 / (1 + k0)
damp = 0.05
omega0 = 0.2
omega1 = 20.0
a1 = 2. * damp / (omega0 + omega1)
a0 = a1 * omega0 * omega1
# Establish nodes
h_ele = 1.
nodes = [
o3.node.Node(osi, 0.0, 0.0),
o3.node.Node(osi, h_ele, 0.0),
o3.node.Node(osi, h_ele, h_ele),
o3.node.Node(osi, 0.0, h_ele)
]
# Fix bottom node
o3.Fix2DOF(osi, nodes[0], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, nodes[1], o3.cc.FIXED, o3.cc.FIXED)
o3.Fix2DOF(osi, nodes[2], o3.cc.FREE, o3.cc.FREE)
o3.Fix2DOF(osi, nodes[3], o3.cc.FREE, o3.cc.FREE)
# Set out-of-plane DOFs to be slaved
o3.EqualDOF(osi, nodes[2], nodes[3], [o3.cc.X, o3.cc.Y])
ele = o3.element.SSPquad(osi, nodes, mat, 'PlaneStrain', 1, 0.0, 0.0)
o3.constraints.Transformation(osi)
o3.test_check.NormDispIncr(osi, tol=1.0e-3, max_iter=35, p_flag=0)
o3.algorithm.Newton(osi)
o3.numberer.RCM(osi)
o3.system.FullGeneral(osi)
o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_Y, 0.005)
# o3.rayleigh.Rayleigh(osi, a0, a1, 0.0, 0.0)
o3.analysis.Static(osi)
o3.update_material_stage(osi, mat, stage=0)
# Add static vertical pressure and stress bias
# time_series = o3.time_series.Path(osi, time=[0, 100, 1e10], values=[0, 1, 1])
# o3.pattern.Plain(osi, time_series)
ts0 = o3.time_series.Linear(osi, factor=1)
o3.pattern.Plain(osi, ts0)
o3.Load(osi, nodes[2], [0, -esig_v0 / 2])
o3.Load(osi, nodes[3], [0, -esig_v0 / 2])
o3.analyze(osi, num_inc=100)
stresses = o3.get_ele_response(osi, ele, 'stress')
print('init_stress0: ', stresses)
# ts2 = o3.time_series.Path(osi, time=[110, 80000, 1e10], values=[1., 1., 1.], factor=1)
# o3.pattern.Plain(osi, ts2, fact=1.)
# y_vert = o3.get_node_disp(osi, nodes[2], o3.cc.Y)
# o3.SP(osi, nodes[3], dof=o3.cc.Y, dof_values=[y_vert])
# o3.SP(osi, nodes[2], dof=o3.cc.Y, dof_values=[y_vert])
#
# o3.analyze(osi, 25, dt=1)
o3.wipe_analysis(osi)
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)
o3.analysis.Static(osi)
o3.update_material_stage(osi, mat, stage=1)
o3.analyze(osi, 25, dt=1)
# o3.set_parameter(osi, value=sl.poissons_ratio, eles=[ele], args=['poissonRatio', 1])
# o3.extensions.to_py_file(osi)
stresses = o3.get_ele_response(osi, ele, 'stress')
print('init_stress1: ', stresses)
exit_code = None
strain = [0]
stresses = o3.get_ele_response(osi, ele, 'stress')
force0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X)
force1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X)
stress = [-force0 - force1]
v_eff = [stresses[1]]
h_eff = [stresses[0]]
d_incs = np.diff(disps, prepend=0)
for i in range(len(disps)):
d_inc_i = d_incs[i]
if target_d_inc < abs(d_inc_i):
n = int(abs(d_inc_i / target_d_inc))
d_step = d_inc_i / n
else:
n = 1
d_step = d_inc_i
for j in range(n):
o3.integrator.DisplacementControl(osi, nodes[2], o3.cc.DOF2D_X, -d_step)
o3.Load(osi, nodes[2], [1.0, 0.0])
o3.Load(osi, nodes[3], [1.0, 0.0])
o3.analyze(osi, 1)
o3.gen_reactions(osi)
stresses = o3.get_ele_response(osi, ele, 'stress')
print(stresses)
v_eff.append(stresses[1])
h_eff.append(stresses[0])
force0 = o3.get_node_reaction(osi, nodes[0], o3.cc.DOF2D_X)
force1 = o3.get_node_reaction(osi, nodes[1], o3.cc.DOF2D_X)
stress.append(-force0 - force1)
end_strain = o3.get_node_disp(osi, nodes[2], dof=o3.cc.DOF2D_X)
strain.append(end_strain)
return -np.array(stress), -np.array(strain), np.array(v_eff), np.array(h_eff), exit_code
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 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