14.2.3. Example name spaced nonlinear SDOFΒΆ

  1. The source code is developed by Maxim Millen from University of Porto.
  2. The source code is shown below, which can be downloaded here.
  3. Also download the constants file here, and the ground motion file
  4. Make sure the numpy, matplotlib and eqsig packages are installed in your Python distribution.
  5. Run the source code in your favorite Python program and should see
../_images/example_name_spaced_nonlinear_SDOF.png
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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()