code/9.py

# Parameters configuration
import openseespy.opensees as ops  # Import OpenSeesPy for structural analysis
import opsvis as opsv  # Import opsvis for visualization
import matplotlib.pyplot as plt  # Import Matplotlib for plotting
ops.wipe()  # Clear any existing model
ops.model('basic', '-ndm', 2, '-ndf', 3)  # Define a 2D model with 3 degrees of freedom per node (DOF)
# Column and girder lengths
colL, girL = 4., 6.
# Section properties: cross-sectional area (A) and moment of inertia (Iz)
Acol, Agir = 2.e-3, 6.e-3
IzCol, IzGir = 1.6e-5, 5.4e-5
# Young's modulus (E)
E = 200.e9
# Define the material property dictionary for columns and girders
Ep = {
    1: [2e11, 2e-3, 1.6e-5], # Columns
    2: [2e11, 6e-3, 5.4e-5]  # Girders
}

# Define the node coordinates
ops.node(1, 0.0, 0.0)
ops.node(2, 6.0, 0.0)
ops.node(3, 12.0, 0.0)
ops.node(4, 18.0, 0.0)
ops.node(5, 0.0, 4.0)
ops.node(6, 6.0, 4.0)
ops.node(7, 12.0, 4.0)
ops.node(8, 18.0, 4.0)
ops.node(9, 0.0, 8.0)
ops.node(10, 6.0, 8.0)
ops.node(11, 12.0, 8.0)
ops.node(12, 18.0, 8.0)

# Define boundary conditions (supports)
ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
ops.fix(3, 1, 1, 1)
ops.fix(4, 1, 1, 1)

# Plot the model before defining elements
opsv.plot_model()
# Add title
plt.title('plot_model before defining elements')

# Define transformation type for elements (Linear)
ops.geomTransf('Linear', 1)

# Define column and girder elements (elastic beam-column elements)
ops.element('elasticBeamColumn', 1, 1, 5, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 2, 2, 6, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 3, 3, 7, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 4, 4, 8, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 5, 5, 9, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 6, 6, 10, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 7, 7, 11, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 8, 8, 12, 2e-3, 2e11, 1.6e-5, 1)
ops.element('elasticBeamColumn', 9, 5, 6, 6e-3, 2e11, 5.4e-5, 1)
ops.element('elasticBeamColumn', 10, 6, 7, 6e-3, 2e11, 5.4e-5, 1)
ops.element('elasticBeamColumn', 11, 7, 8, 6e-3, 2e11, 5.4e-5, 1)
ops.element('elasticBeamColumn', 12, 9, 10, 6e-3, 2e11, 5.4e-5, 1)
ops.element('elasticBeamColumn', 13, 10, 11, 6e-3, 2e11, 5.4e-5, 1)
ops.element('elasticBeamColumn', 14, 11, 12, 6e-3, 2e11, 5.4e-5, 1)

# Define external loads
Px = 2e3

# Create a dictionary to store element loads
Ew = {
    9: ['-beamUniform', 0.0, 0.0],
    10: ['-beamUniform', 0.0, 0.0],
    11: ['-beamUniform', 0.0, 0.0],
    12: ['-beamUniform', 0.0, 0.0],
    13: ['-beamUniform', 0.0, 0.0],
    14: ['-beamUniform', 0.0, 0.0],
}

# Define time series for constant loads
ops.timeSeries('Constant', 1)
ops.pattern('Plain', 1, 1)

# Applying point loads
ops.load(5, Px, 0.0, 0.0)
ops.load(9, Px, 0.0, 0.0)

# Applying distributed loads
for etag in Ew:
    ops.eleLoad('-ele', etag, '-type', Ew[etag][0], Ew[etag][1], Ew[etag][2])
# Analysis settings
ops.constraints('Transformation')  # Apply transformation constraints
ops.numberer('RCM')  # Renumber the nodes using Reverse Cuthill-McKee (RCM)
ops.system('BandGeneral')  # Define the solution algorithm
ops.test('NormDispIncr', 1.0e-6, 6, 2)  # Convergence test criteria
ops.algorithm('Linear')  # Use linear algorithm for solving
ops.integrator('LoadControl', 1)  # Control load increments
ops.analysis('Static')  # Define a static analysis
ops.analyze(1)  # Perform the analysis

# Print the model data
ops.printModel()

# Plot the model after defining elements
opsv.plot_model()
plt.title('plot_model after defining elements')

# Plot the applied loads on the model in 2D
opsv.plot_loads_2d(nep=10,  # Number of points along each element
                   sfac=1,  # Scale factor for loads
                   fig_wi_he=(10, 5),  # Width and height of the figure
                   fig_lbrt=(0.1, 0.1, 0.9, 0.9),  # Left, bottom, right, top margins
                   fmt_model_loads={'color': 'red', 'linewidth': 1.5},  # Formatting for load arrows
                   node_supports=True,  # Display node supports
                   truss_node_offset=0.05,  # Offset for truss elements
                   ax=None)  # Matplotlib axis, None to use current axis

# Plot deformations (scaled) after analysis
opsv.plot_defo()

# Plot internal force diagrams: N (axial), V (shear), M (moment)
sfacN, sfacV, sfacM = 5.e-5, 5.e-5, 5.e-5  # Scale factors for internal force diagrams
# Plot axial force distribution
opsv.section_force_diagram_2d('N', sfacN)
plt.title('Axial force distribution')
# Plot shear force distribution
opsv.section_force_diagram_2d('T', sfacV)
plt.title('Shear force distribution')
# Plot bending moment distribution
opsv.section_force_diagram_2d('M', sfacM)
plt.title('Bending moment distribution')

# Show all plots
plt.show()

# Exit the program
exit()