From fbe41983c2b6c323efb0b4eec11ab72e8687f5a3 Mon Sep 17 00:00:00 2001 From: jjaramillod93 Date: Fri, 8 Nov 2024 22:14:00 -0500 Subject: [PATCH 1/6] add NonlinearMDOF.rst --- src/NonlinearMDOF.rst | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 src/NonlinearMDOF.rst diff --git a/src/NonlinearMDOF.rst b/src/NonlinearMDOF.rst new file mode 100644 index 0000000..0f27874 --- /dev/null +++ b/src/NonlinearMDOF.rst @@ -0,0 +1,31 @@ +.. include:: sub.txt + +============== +Nonlinear MDOF +============== + +#. The source code is developed by `Joseph Jaramillo `_ from National University of Engineering. +#. The source code is shown below, which can be downloaded :download:`here `. +#. The ground motion file :download:`here `. +#. And also the python plotting script :download:`here `. +#. Make sure the `numpy`_ and `matplotlib`_ packages are installed in your Python distribution. +#. Run the source code in your favorite Python program and should see: + +:: + + Natural periods: Natural frequencies: + T1 = 0.628 [s] | f1 = 1.592 [Hz] + T2 = 0.257 [s] | f2 = 3.898 [Hz] + T3 = 0.162 [s] | f3 = 6.164 [Hz] + +.. image:: /_static/nonlinear_mdof_abs_accel.jpg + +.. image:: /_static/nonlinear_mdof_rel_accel.jpg + +.. image:: /_static/nonlinear_mdof_rel_disp.jpg + +.. image:: /_static/nonlinear_mdof_hysteresis.jpg + +.. literalinclude:: /pyExamples/nonlinear_mdof.py + :linenos: + From 26232791d7df7e8e1c14639f98ee12285f9d107b Mon Sep 17 00:00:00 2001 From: jjaramillod93 Date: Fri, 8 Nov 2024 22:15:03 -0500 Subject: [PATCH 2/6] add nonlinear_mdof.py --- pyExamples/nonlinear_mdof.py | 130 +++++++++++++++++++++++++++++++++++ 1 file changed, 130 insertions(+) create mode 100644 pyExamples/nonlinear_mdof.py diff --git a/pyExamples/nonlinear_mdof.py b/pyExamples/nonlinear_mdof.py new file mode 100644 index 0000000..5e248d1 --- /dev/null +++ b/pyExamples/nonlinear_mdof.py @@ -0,0 +1,130 @@ +''' +========================================================================================================================= +================================================== NonLinear MDOF ======================================================= +========================================================================================================================= + +By M. Eng. Joseph Jaramillo, National University of Engineering +e-mail: jjaramillod@uni.edu.pe +Date - 22/10/2024 + +This example models a multi-degree-of-freedom (MDOF) damped system commonly used in earthquake engineering of a three-story +building. It conducts a nonlinear dynamic (time history) analysis using the El Centro 1940 earthquake as the input ground +motion. +''' + +import openseespy.opensees as ops +import numpy as np +import plot_nonlinear_mdof_graphs +# Base units +m = 1 # Meters +s = 1 # Seconds +kN = 1 # Kilo Newtons + +# Derivated units +g = 9.81*m/s**2 # Gravity +cm = 1e-2*m # Centimeter +mm = 1e-3*m # Milimeter +Ton = kN*s**2/m # Ton + +# Parameters - data +N = 3 # N° DOF +h = 0.05 # Damping ratio +dt = 0.02 # Time step +dt_out = 0.001 # Output time step +tFinal = 35 # Analysis stop time +m1 = 0.1*Ton # Mass / floor +m2 = 0.1*Ton +m3 = 0.1*Ton +Py1 = 0.55*kN # Yielding strength / floor +Py2 = 0.45*kN +Py3 = 0.30*kN +K1 = 60*kN/m # Stiffness / floor +K2 = 50*kN/m +K3 = 30*kN/m +b = 0.01 # Strain-hardening ratio + +######## Model ############### +ops.wipe() # clear memory of all past model definitions +ops.model('basic', '-ndm', 1, '-ndf', 1) # Define the model builder, ndm=#dimension, ndf=#dofs + +# Create nodes +ops.node(0, 0) +ops.node(1, 0, '-mass', m1) +ops.node(2, 0, '-mass', m2) +ops.node(3, 0, '-mass', m3) + +# Define boundary condition +ops.fix(0, 1) + +# Material definition +ops.uniaxialMaterial('Steel01', 1, Py1, K1, b) +ops.uniaxialMaterial('Steel01', 2, Py2, K2, b) +ops.uniaxialMaterial('Steel01', 3, Py3, K3, b) + +# Element definition +ops.element('zeroLength', 1, 0, 1, '-mat', 1 , '-dir', 1, '-doRayleigh', 1) +ops.element('zeroLength', 2, 1, 2, '-mat', 2 , '-dir', 1, '-doRayleigh', 1) +ops.element('zeroLength', 3, 2, 3, '-mat', 3 , '-dir', 1, '-doRayleigh', 1) + +# Set Rayleigh damping +w1, w2, w3 = np.array(ops.eigen('-fullGenLapack', 3))**0.5 +a0 = 2*h*w1*w2/(w1+w2) +a1 = 2*h/(w1+w2) +ops.rayleigh(a0, .0, .0, a1) # RAYLEIGH damping + +# Natural periods +print('\nNatural periods: Natural frequencies:') +print(f'T1 = {2*np.pi/w1:.3f} [s] | f1 = {w1/(2*np.pi):.3f} [Hz]') +print(f'T2 = {2*np.pi/w2:.3f} [s] | f2 = {w2/(2*np.pi):.3f} [Hz]') +print(f'T3 = {2*np.pi/w3:.3f} [s] | f3 = {w3/(2*np.pi):.3f} [Hz]') + +# Define the dynamic analysis +load_tag = 1 +patter_tag = 1 +direc = 1 +ops.timeSeries('Path', load_tag, '-dt', dt, '-filePath', r'./el_centro.th', '-factor', g) # Reading ground motion +ops.pattern('UniformExcitation', patter_tag, direc, '-accel', load_tag) + +# Define output data files +rD_path = r'./Relative_disp.out' +ops.recorder('Node', '-file', r'./Relative_disp.out', '-time', '-dT', dt_out, '-node', 1, 2, 3, '-dof', 1, 'disp') # Relative displacements with respect to the ground + +rA_path = r'./Relative_accel.out' +ops.recorder('Node', '-file', rA_path, '-time', '-dT', dt_out, '-node', 1, 2, 3, '-dof', 1, 'accel') # Relative accelerations with respect to the ground + +aA_path = r'./Absolute_accel.out' +ops.recorder('Node', '-file', aA_path, '-timeSeries', load_tag, '-time', '-dT', dt_out, '-node', 0, 1, 2, 3, '-dof', 1, 'accel') # Absolute accelerations + +eF_path = r'./Element_force.out' +ops.recorder('Element', '-file', eF_path, '-time', '-dT', dt_out, '-ele', 1, 2, 3, 'localForce') # Local spring force + +# Run the dynamic analysis +Gamma = 0.5 +Beta = 0.25 +tol = 1.0e-12 +itrs = 100 +ops.wipeAnalysis() +ops.algorithm('Newton') +ops.system('BandGen') +ops.numberer('Plain') +ops.constraints('Plain') +ops.integrator('Newmark', Gamma, Beta) +ops.analysis('Transient') +ops.test('NormUnbalance', tol, itrs) +num_steps = int(tFinal/dt_out+1) +ops.analyze(num_steps, dt_out) +ops.wipe() + +rD = np.genfromtxt(rD_path, usecols=[1, 2, 3]).T + +rA = np.genfromtxt(rA_path, usecols=[1, 2, 3]).T +aA = np.genfromtxt(aA_path, usecols=[1, 2, 3, 4]).T + +eF = np.genfromtxt(eF_path, usecols=[1, 2, 3]).T + + +# Matplotlib plots +rD /= mm +K = [K1, K2, K3] +Py = [Py1, Py2, Py3] +plot_nonlinear_mdof_graphs.plot(N, rD, rA, aA, eF, dt_out, num_steps, tFinal, K, Py) From 3487585a92a74d1f1e5aaad47f21b8a3e9b7a551 Mon Sep 17 00:00:00 2001 From: jjaramillod93 Date: Fri, 8 Nov 2024 22:16:24 -0500 Subject: [PATCH 3/6] add figures --- 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+-2.4700000e-03 +-2.4100000e-03 +-2.3500000e-03 +-2.2800000e-03 +-2.2200000e-03 +-2.1600000e-03 +-2.0900000e-03 +-2.0300000e-03 +-1.9700000e-03 +-1.9000000e-03 +-1.8400000e-03 +-1.7800000e-03 +-1.7100000e-03 +-1.6500000e-03 +-1.5800000e-03 +-1.5200000e-03 +-1.4600000e-03 +-1.3900000e-03 +-1.3300000e-03 +-1.2700000e-03 +-1.2000000e-03 +-1.1400000e-03 +-1.0800000e-03 +-1.0100000e-03 +-9.5000000e-04 +-8.9000000e-04 +-8.2000000e-04 +-7.6000000e-04 +-7.0000000e-04 +-6.3000000e-04 +-5.7000000e-04 +-5.1000000e-04 +-4.4000000e-04 +-3.8000000e-04 +-3.2000000e-04 +-2.5000000e-04 +-1.9000000e-04 +-1.3000000e-04 +-6.0000000e-05 +0.0000000e+00 +0.0000000e+00 From cb0a627f4d47baf02d0700f27eb414f1f0a89d06 Mon Sep 17 00:00:00 2001 From: jjaramillod93 Date: Fri, 8 Nov 2024 22:27:07 -0500 Subject: [PATCH 5/6] add earthquake.rst --- src/earthquake.rst | 44 +++++++++++++++++++++++--------------------- 1 file changed, 23 insertions(+), 21 deletions(-) diff --git a/src/earthquake.rst b/src/earthquake.rst index a5d8166..1b60dd6 100644 --- a/src/earthquake.rst +++ b/src/earthquake.rst @@ -1,21 +1,23 @@ -===================== - Earthquake Examples -===================== - - -#. :doc:`Canti2DEQ` -#. :doc:`RCFrameEarthquake` -#. :doc:`exampleNamedSpacedNonlinearSDOF` -#. :doc:`exampleRotDSpectra` - - - -.. toctree:: - :maxdepth: 1 - :hidden: - - Canti2DEQ - RCFrameEarthquake - exampleNamedSpacedNonlinearSDOF - exampleRotDSpectra - +===================== + Earthquake Examples +===================== + + +#. :doc:`Canti2DEQ` +#. :doc:`RCFrameEarthquake` +#. :doc:`exampleNamedSpacedNonlinearSDOF` +#. :doc:`exampleRotDSpectra` +#. :doc:`NonlinearMDOF` + + + +.. toctree:: + :maxdepth: 1 + :hidden: + + Canti2DEQ + RCFrameEarthquake + exampleNamedSpacedNonlinearSDOF + exampleRotDSpectra + NonlinearMDOF + From 78da9018078c8bbcfc9af1320441149e36fc89f2 Mon Sep 17 00:00:00 2001 From: jjaramillod93 Date: Fri, 8 Nov 2024 22:36:21 -0500 Subject: [PATCH 6/6] plot_nonlinear_mdof_graphs.py --- pyExamples/plot_nonlinear_mdof_graphs.py | 124 +++++++++++++++++++++++ 1 file changed, 124 insertions(+) create mode 100644 pyExamples/plot_nonlinear_mdof_graphs.py diff --git a/pyExamples/plot_nonlinear_mdof_graphs.py b/pyExamples/plot_nonlinear_mdof_graphs.py new file mode 100644 index 0000000..21126b7 --- /dev/null +++ b/pyExamples/plot_nonlinear_mdof_graphs.py @@ -0,0 +1,124 @@ +import numpy as np +import matplotlib.pyplot as plt +from matplotlib.ticker import MultipleLocator +from matplotlib import rcParams + +rcParams['font.family'] = 'Times New Roman' +rcParams['font.size'] = 10 +rcParams['lines.linewidth'] = 0.8 +rcParams['lines.color'] = 'C0' +rcParams['legend.frameon'] = False +rcParams['axes.linewidth'] = 0.5 +rcParams['xtick.major.width'] = 0.9 +rcParams['xtick.minor.width'] = 0.9 +rcParams['ytick.major.width'] = 0.9 +rcParams['ytick.minor.width'] = 0.9 +rcParams["savefig.format"] = 'jpg' +rcParams["savefig.transparent"] = False +rcParams["grid.alpha"] = 0.35 +rcParams["grid.color"] = 'k' +rcParams["grid.linewidth"] = 0.5 +rcParams['figure.titleweight'] = 'bold' +rcParams['savefig.dpi'] = 600 + + +def plot(N, rD, rA, aA, eF, dt_out, num_steps, tFinal, K, Py): + + z = lambda x: np.min(x) if abs(np.min(x)) > abs(np.max(x)) else np.max(x) + t = np.arange(0, num_steps) * dt_out + + # Plotting absolute accelerations + fig, axs = plt.subplots(N+1, figsize=(8, 5), sharex=True, sharey=True) + fig.suptitle('Absolute Accelerations') + + gm = aA[0] + peak = z(gm) + axs[0].plot(t, gm, f'k', label=f'Ground peak: {peak:.2f} [m/s2]') + + for i, ax in enumerate(axs[1:]): + x = aA[i+1] + peak = z(x) + ax.plot(t, x, f'C{i+1}', label=f'Floor {i+1} peak: {peak:.2f} [m/s2]') + + for ax in axs: + ax.set_xlim(.0, tFinal) + ax.set_ylim(-8, 8) + ax.grid() + ax.legend(loc=(0.72, 1.0)) + ax.label_outer() + ax.xaxis.set_major_locator(MultipleLocator(5)) + ax.yaxis.set_major_locator(MultipleLocator(4)) + + axs[1].set_ylabel('Acceleration [m/s2]', loc='top') + axs[1].yaxis.set_label_coords(-0.05, .5) + axs[3].set_xlabel('Time [s]') + + plt.subplots_adjust(0.08, 0.1, 0.97, 0.9, 0.1, 0.4) + plt.savefig(r'./nonlinear_mdof_abs_accel.jpg') + + + # Plotting relative accelerations + fig, axs = plt.subplots(N, figsize=(8, 3.8)) + fig.suptitle('Relative Accelerations') + + for i, ax in enumerate(axs): + peak = z(rA[i]) + ax.plot(t, rA[i], f'C{i+1}', label=f'Floor {i+1} peak: {peak:.2f} [m/s2]') + ax.set_xlim(.0, tFinal) + ax.set_ylim(-8, 8) + ax.xaxis.set_major_locator(MultipleLocator(5)) + ax.yaxis.set_major_locator(MultipleLocator(4)) + ax.grid() + ax.legend(loc=(0.72, 1.0)) + ax.label_outer() + axs[1].set_ylabel('Acceleration [m/s2]') + axs[2].set_xlabel('Time [s]') + plt.subplots_adjust(0.08, 0.12, 0.97, 0.9, 0.1, 0.4) + plt.savefig(r'./nonlinear_mdof_rel_accel.jpg') + + # Plotting relative displacements + fig, axs = plt.subplots(N, figsize=(8, 3.8)) + fig.suptitle('Relative Displacements') + + for i, ax in enumerate(axs): + peak = z(rD[i]) + ax.plot(t, rD[i], f'C{i+1}', label=f'Floor {i+1} peak: {peak:.2f} [mm]') + ax.set_xlim(.0, tFinal) + ax.set_ylim(-80, 80) + ax.xaxis.set_major_locator(MultipleLocator(5)) + ax.yaxis.set_major_locator(MultipleLocator(40)) + ax.grid() + ax.legend(loc=(0.72, 1.0)) + ax.label_outer() + axs[1].set_ylabel('Displacement [mm]') + axs[2].set_xlabel('Time [s]') + plt.subplots_adjust(0.08, 0.12, 0.97, 0.9, 0.1, 0.4) + plt.savefig(r'./nonlinear_mdof_rel_disp.jpg') + + + # Plotting Hysteresis by floor + fig, axs = plt.subplots(1, N, figsize=(10, 3.5)) + fig.suptitle('Floor Hysteresis') + + axs[0].plot(rD[0,:], eF[0,:], 'C1', label=f'Floor 1 (K={K[0]} [kN/m]; Py={Py[0]:.2f} [kN])') + axs[1].plot(rD[1,:] - rD[0,:], eF[1,:], 'C2', label=f'Floor 2 (K={K[1]} [kN/m]; Py={Py[1]:.2f} [kN])') + axs[2].plot(rD[2,:] - rD[1,:], eF[2,:], 'C3', label=f'Floor 3 (K={K[2]} [kN/m]; Py={Py[2]:.2f} [kN])') + + for ax in axs: + # ax.set_xlim(.0, tFinal) + ax.set_ylim(-0.6, 0.6) + ax.set_xlim(-30, 30) + ax.grid() + ax.legend(loc=(0.06, 1.0)) + ax.label_outer() + ax.set_xlabel('Displacement [mm]') + ax.xaxis.set_major_locator(MultipleLocator(10)) + ax.yaxis.set_major_locator(MultipleLocator(0.2)) + + axs[0].set_ylabel('Force [kN]') + plt.subplots_adjust(0.06, 0.13, 0.97, 0.86, 0.1) + plt.savefig(r'./nonlinear_mdof_hysteresis.jpg') + + plt.show() + +

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