def test_beam_integration_mid_point_w_steel01():
lp_i = 0.1
lp_j = 0.2
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
section1_id = 1
section2_id = 2
section3_id = 3
uniaxial_steel01_section(section1_id)
uniaxial_steel01_section(section2_id)
uniaxial_steel01_section(section3_id)
integ_tag = 1
opy.beamIntegration('HingeMidpoint', integ_tag, section1_id, lp_i,
section2_id, lp_j, section3_id)
with_force_beam_column = 1
if with_force_beam_column:
# Establish nodes
bot_node = 1
top_node = 2
transf_tag = 1
opy.geomTransf('Linear', transf_tag, *[])
opy.node(bot_node, 0., 0.)
opy.node(top_node, 0., 5.)
ele_i = 1
opy.element('forceBeamColumn', ele_i, bot_node, top_node, transf_tag,
integ_tag)
def test_beam_integration_lobatto_w_steel01():
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
section_id = 1
uniaxial_steel01_material(section_id)
int_tag = 1
opy.beamIntegration('Lobatto', int_tag, section_id, 8)
assert 1 == 1 # This pass
def test_beam_integration_mid_point_w_elastic():
lp_i = 0.1
lp_j = 0.2
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
section_id = 1
elastic_section(section_id)
integ_tag = 1
opy.beamIntegration('HingeMidpoint', integ_tag, section_id, lp_i,
section_id, lp_j, section_id)
def get_inelastic_response(fb,
asig,
extra_time=0.0,
xi=0.05,
analysis_dt=0.001):
"""
Run seismic analysis of a nonlinear FrameBuilding
:param fb: FrameBuilding object
:param asig: AccSignal object
:param extra_time: float, additional analysis time after end of ground motion
:param xi: damping ratio
:param analysis_dt: time step to perform the analysis
:return:
"""
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
q_floor = 10000. # kPa
trib_width = fb.floor_length
trib_mass_per_length = q_floor * trib_width / 9.8
# Establish nodes and set mass based on trib area
# Nodes named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground level left
nd = OrderedDict()
col_xs = np.cumsum(fb.bay_lengths)
col_xs = np.insert(col_xs, 0, 0)
n_cols = len(col_xs)
sto_ys = fb.heights
sto_ys = np.insert(sto_ys, 0, 0)
for cc in range(1, n_cols + 1):
for ss in range(fb.n_storeys + 1):
n_i = cc * 100 + ss
nd["C%i-S%i" % (cc, ss)] = n_i
opy.node(n_i, col_xs[cc - 1], sto_ys[ss])
if ss != 0:
if cc == 1:
node_mass = trib_mass_per_length * fb.bay_lengths[0] / 2
elif cc == n_cols:
node_mass = trib_mass_per_length * fb.bay_lengths[-1] / 2
else:
node_mass = trib_mass_per_length * (
fb.bay_lengths[cc - 2] + fb.bay_lengths[cc - 1] / 2)
opy.mass(n_i, node_mass)
# Set all nodes on a storey to have the same displacement
for ss in range(0, fb.n_storeys + 1):
for cc in range(1, n_cols + 1):
opy.equalDOF(nd["C%i-S%i" % (1, ss)], nd["C%i-S%i" % (cc, ss)],
opc.X)
# Fix all base nodes
for cc in range(1, n_cols + 1):
opy.fix(nd["C%i-S%i" % (cc, 0)], opc.FIXED, opc.FIXED, opc.FIXED)
# Coordinate transformation
geo_tag = 1
trans_args = []
opy.geomTransf("Linear", geo_tag, *[])
l_hinge = fb.bay_lengths[0] * 0.1
# Define material
e_conc = 30.0e6
i_beams = 0.4 * fb.beam_widths * fb.beam_depths**3 / 12
i_columns = 0.5 * fb.column_widths * fb.column_depths**3 / 12
a_beams = fb.beam_widths * fb.beam_depths
a_columns = fb.column_widths * fb.column_depths
ei_beams = e_conc * i_beams
ei_columns = e_conc * i_columns
eps_yield = 300.0e6 / 200e9
phi_y_col = calc_yield_curvature(fb.column_depths, eps_yield)
phi_y_beam = calc_yield_curvature(fb.beam_depths, eps_yield)
# Define beams and columns
md = OrderedDict() # material dict
sd = OrderedDict() # section dict
ed = OrderedDict() # element dict
# Columns named as: C<column-number>-S<storey-number>, first column starts at C1-S0 = ground floor left
# Beams named as: B<bay-number>-S<storey-number>, first beam starts at B1-S1 = first storey left (foundation at S0)
for ss in range(fb.n_storeys):
# set columns
for cc in range(1, fb.n_cols + 1):
ele_i = cc * 100 + ss
md["C%i-S%i" % (cc, ss)] = ele_i
sd["C%i-S%i" % (cc, ss)] = ele_i
ed["C%i-S%i" % (cc, ss)] = ele_i
mat_props = elastic_bilin(ei_columns[ss][cc - 1],
0.05 * ei_columns[ss][cc - 1],
phi_y_col[ss][cc - 1])
#print(opc.ELASTIC_BILIN, ele_i, *mat_props)
opy.uniaxialMaterial(opc.ELASTIC_BILIN, ele_i, *mat_props)
# opy.uniaxialMaterial("Elastic", ele_i, ei_columns[ss][cc - 1])
node_numbers = [
nd["C%i-S%i" % (cc, ss)], nd["C%i-S%i" % (cc, ss + 1)]
]
opy.element(opc.ELASTIC_BEAM_COLUMN, ele_i, *node_numbers,
a_columns[ss - 1][cc - 1], e_conc,
i_columns[ss - 1][cc - 1], geo_tag)
# Set beams
for bb in range(1, fb.n_bays + 1):
ele_i = bb * 10000 + ss
md["B%i-S%i" % (bb, ss)] = ele_i
sd["B%i-S%i" % (bb, ss)] = ele_i
ed["B%i-S%i" % (bb, ss)] = ele_i
mat_props = elastic_bilin(ei_beams[ss][bb - 1],
0.05 * ei_beams[ss][bb - 1],
phi_y_beam[ss][bb - 1])
opy.uniaxialMaterial(opc.ELASTIC_BILIN, ele_i, *mat_props)
# opy.uniaxialMaterial("Elastic", ele_i, ei_beams[ss][bb - 1])
node_numbers = [
nd["C%i-S%i" % (bb, ss + 1)], nd["C%i-S%i" % (bb + 1, ss + 1)]
]
print((opc.BEAM_WITH_HINGES, ele_i, *node_numbers,
sd["B%i-S%i" % (bb, ss)], l_hinge, sd["B%i-S%i" % (bb, ss)],
l_hinge, sd["B%i-S%i" % (bb, ss)], geo_tag))
# Old definition
# opy.element(opc.BEAM_WITH_HINGES, ele_i,
# *[nd["C%i-S%i" % (bb, ss - 1)], nd["C%i-S%i" % (bb + 1, ss)]],
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# e_conc,
# a_beams[ss - 1][bb - 1],
# i_beams[ss - 1][bb - 1], geo_tag
# )
# New definition
# opy.element(opc.BEAM_WITH_HINGES, ele_i,
# *node_numbers,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], l_hinge,
# sd["B%i-S%i" % (bb, ss)], geo_tag # TODO: make this elastic
#
# )
# Elastic definition
opy.element(opc.ELASTIC_BEAM_COLUMN, ele_i, *node_numbers,
a_beams[ss - 1][bb - 1], e_conc,
i_beams[ss - 1][bb - 1], geo_tag)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * asig.values) # should be negative
opy.timeSeries('Path', load_tag_dynamic, '-dt', asig.dt, '-values',
*values)
opy.pattern('UniformExcitation', pattern_tag_dynamic, opc.X, '-accel',
load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = opy.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2**0.5
if isinstance(angular_freq, complex):
raise ValueError(
"Angular frequency is complex, issue with stiffness or mass")
alpha_m = 0.0
beta_k = 2 * xi / angular_freq
beta_k_comm = 0.0
beta_k_init = 0.0
period = angular_freq / 2 / np.pi
print("period: ", period)
opy.rayleigh(alpha_m, beta_k, beta_k_init, beta_k_comm)
# Run the dynamic analysis
opy.wipeAnalysis()
opy.algorithm('Newton')
opy.system('SparseGeneral')
opy.numberer('RCM')
opy.constraints('Transformation')
opy.integrator('Newmark', 0.5, 0.25)
opy.analysis('Transient')
#opy.test("NormDispIncr", 1.0e-1, 2, 0)
tol = 1.0e-10
iter = 10
opy.test('EnergyIncr', tol, iter, 0, 2) # TODO: make this test work
analysis_time = (len(values) - 1) * asig.dt + extra_time
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
print("Analysis starting")
while opy.getTime() < analysis_time:
curr_time = opy.getTime()
opy.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(
opy.nodeDisp(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
outputs["rel_vel"].append(
opy.nodeVel(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
outputs["rel_accel"].append(
opy.nodeAccel(nd["C%i-S%i" % (1, fb.n_storeys)], opc.X))
opy.reactions()
react = 0
for cc in range(1, fb.n_cols):
react += -opy.nodeReaction(nd["C%i-S%i" % (cc, 0)], opc.X)
outputs["force"].append(react) # Should be negative since diff node
opy.wipe()
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:
"""
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
# Establish nodes
bot_node = 1
top_node = 2
opy.node(bot_node, 0., 0.)
opy.node(top_node, 0., 0.)
# Fix bottom node
opy.fix(top_node, opc.FREE, opc.FIXED, opc.FIXED)
opy.fix(bot_node, opc.FIXED, opc.FIXED, opc.FIXED)
# Set out-of-plane DOFs to be slaved
opy.equalDOF(1, 2, *[2, 3])
# nodal mass (weight / g):
opy.mass(top_node, mass, 0., 0.)
# Define material
bilinear_mat_tag = 1
mat_type = "Steel01"
mat_props = [f_yield, k_spring, r_post]
opy.uniaxialMaterial(mat_type, bilinear_mat_tag, *mat_props)
# Assign zero length element
beam_tag = 1
opy.element('zeroLength', beam_tag, bot_node, top_node, "-mat", bilinear_mat_tag, "-dir", 1, '-doRayleigh', 1)
# Define the dynamic analysis
load_tag_dynamic = 1
pattern_tag_dynamic = 1
values = list(-1 * motion) # should be negative
opy.timeSeries('Path', load_tag_dynamic, '-dt', dt, '-values', *values)
opy.pattern('UniformExcitation', pattern_tag_dynamic, opc.DOF_X, '-accel', load_tag_dynamic)
# set damping based on first eigen mode
angular_freq2 = opy.eigen('-fullGenLapack', 1)
if hasattr(angular_freq2, '__len__'):
angular_freq2 = angular_freq2[0]
angular_freq = angular_freq2 ** 0.5
alpha_m = 0.0
beta_k = 2 * xi / angular_freq
beta_k_comm = 0.0
beta_k_init = 0.0
opy.rayleigh(alpha_m, beta_k, beta_k_init, beta_k_comm)
# Run the dynamic analysis
opy.wipeAnalysis()
opy.algorithm('Newton')
opy.system('SparseGeneral')
opy.numberer('RCM')
opy.constraints('Transformation')
opy.integrator('Newmark', 0.5, 0.25)
opy.analysis('Transient')
tol = 1.0e-10
iterations = 10
opy.test('EnergyIncr', tol, iterations, 0, 2)
analysis_time = (len(values) - 1) * dt
analysis_dt = 0.001
outputs = {
"time": [],
"rel_disp": [],
"rel_accel": [],
"rel_vel": [],
"force": []
}
while opy.getTime() < analysis_time:
curr_time = opy.getTime()
opy.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(opy.nodeDisp(top_node, 1))
outputs["rel_vel"].append(opy.nodeVel(top_node, 1))
outputs["rel_accel"].append(opy.nodeAccel(top_node, 1))
opy.reactions()
outputs["force"].append(-opy.nodeReaction(bot_node, 1)) # Negative since diff node
opy.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def test_define_uniaxial_steel101_section():
opy.wipe()
opy.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
section1_id = 1
uniaxial_steel01_section(section1_id)