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(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 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 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 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