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150 | import eqsig
from eqsig import duhamels
import matplotlib.pyplot as plt
import numpy as np
import openseespy.opensees as op
import opensees_constants as opc #opensees_constants.py should be close to main file or use sys.path... to its directory
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:
"""
op.wipe()
op.model('basic', '-ndm', 2, '-ndf', 3) # 2 dimensions, 3 dof per node
# Establish nodes
bot_node = 1
top_node = 2
op.node(bot_node, 0., 0.)
op.node(top_node, 0., 0.)
# Fix bottom node
op.fix(top_node, opc.FREE, opc.FIXED, opc.FIXED)
op.fix(bot_node, opc.FIXED, opc.FIXED, opc.FIXED)
# Set out-of-plane DOFs to be slaved
op.equalDOF(1, 2, *[2, 3])
# nodal mass (weight / g):
op.mass(top_node, mass, 0., 0.)
# Define material
bilinear_mat_tag = 1
mat_type = "Steel01"
mat_props = [f_yield, k_spring, r_post]
op.uniaxialMaterial(mat_type, bilinear_mat_tag, *mat_props)
# Assign zero length element
beam_tag = 1
op.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
op.timeSeries('Path', load_tag_dynamic, '-dt', dt, '-values', *values)
op.pattern('UniformExcitation', pattern_tag_dynamic, opc.X, '-accel', load_tag_dynamic)
# set damping based on first eigen mode
angular_freq = op.eigen('-fullGenLapack', 1) ** 0.5
alpha_m = 0.0
beta_k = 2 * xi / angular_freq
beta_k_comm = 0.0
beta_k_init = 0.0
op.rayleigh(alpha_m, beta_k, beta_k_init, beta_k_comm)
# Run the dynamic analysis
op.wipeAnalysis()
op.algorithm('Newton')
op.system('SparseGeneral')
op.numberer('RCM')
op.constraints('Transformation')
op.integrator('Newmark', 0.5, 0.25)
op.analysis('Transient')
tol = 1.0e-10
iterations = 10
op.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 op.getTime() < analysis_time:
curr_time = op.getTime()
op.analyze(1, analysis_dt)
outputs["time"].append(curr_time)
outputs["rel_disp"].append(op.nodeDisp(top_node, 1))
outputs["rel_vel"].append(op.nodeVel(top_node, 1))
outputs["rel_accel"].append(op.nodeAccel(top_node, 1))
op.reactions()
outputs["force"].append(-op.nodeReaction(bot_node, 1)) # Negative since diff node
op.wipe()
for item in outputs:
outputs[item] = np.array(outputs[item])
return outputs
def show_single_comparison():
"""
Create a plot of an elastic analysis, nonlinear analysis and closed form elastic
:return:
"""
record_filename = 'test_motion_dt0p01.txt'
motion_step = 0.01
rec = np.loadtxt(record_filename)
acc_signal = eqsig.AccSignal(rec, motion_step)
period = 1.0
xi = 0.05
mass = 1.0
f_yield = 1.5 # Reduce this to make it nonlinear
r_post = 0.0
periods = np.array([period])
resp_u, resp_v, resp_a = duhamels.response_series(motion=rec, dt=motion_step, periods=periods, xi=xi)
k_spring = 4 * np.pi ** 2 * mass / period ** 2
outputs = get_inelastic_response(mass, k_spring, f_yield, rec, motion_step, xi=xi, r_post=r_post)
outputs_elastic = get_inelastic_response(mass, k_spring, f_yield * 100, rec, motion_step, xi=xi, r_post=r_post)
ux_opensees = outputs["rel_disp"]
ux_opensees_elastic = outputs_elastic["rel_disp"]
bf, sps = plt.subplots(nrows=2)
sps[0].plot(acc_signal.time, resp_u[0], label="Eqsig")
sps[0].plot(outputs["time"], ux_opensees, label="Opensees fy=%.3gN" % f_yield, ls="--")
sps[0].plot(outputs["time"], ux_opensees_elastic, label="Opensees fy=%.3gN" % (f_yield * 100), ls="--")
sps[1].plot(acc_signal.time, resp_a[0], label="Eqsig") # Elastic solution
time = acc_signal.time
acc_opensees_elastic = np.interp(time, outputs_elastic["time"], outputs_elastic["rel_accel"]) - rec
print("diff", sum(acc_opensees_elastic - resp_a[0]))
sps[1].plot(time, acc_opensees_elastic, label="Opensees fy=%.2gN" % (f_yield * 100), ls="--")
sps[0].legend()
sps[1].legend()
plt.show()
if __name__ == '__main__':
show_single_comparison()
|
