FEmethods/run_examples.py at master · JJCoding01/FEmethods · GitHub

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"""
Examples for FEMethods showing how to use the module

"""

import numpy as np

from femethods.elements import Beam
from femethods.loads import MomentLoad, PointLoad
from femethods.reactions import FixedReaction, PinnedReaction


def intro_demo():
    """
    Simply supported beam with a single centered point load

    This is the example shown in the intro docs
    """
    print("=" * 79)
    print("Intro Demo")
    print("Show an example of a simply supported beam with centered load")

    # Note that both the reaction and load are both lists. They must always be
    # given to Beam as a list,
    r = [PinnedReaction(x) for x in [0, 30]]  # define reactions as list
    p = [PointLoad(magnitude=-100, location=15)]  # define loads as list

    b = Beam(30, loads=p, reactions=r)

    # an explicit solve is required to calculate the reaction values
    b.solve()

    print(b)

    b.plot(
        diagrams=("shear", "moment", "deflection"),
        # plot_kwargs={"label": "approx solution"},
    )
    b.show()


def example_1():
    """
    Cantilevered Beam with Fixed Support and End Loading
    """
    print("=" * 79)
    print("Example 1")
    print(
        "Show an example with a cantilevered beam with a fixed support and "
        "point load at the end\n"
    )

    beam_len = 10
    P = -200
    E = 29e6
    I = 125
    # Note that both the reaction and load are both lists. They must always be
    # given to Beam as a list,
    r = [FixedReaction(beam_len)]  # define reactions as list
    p = [PointLoad(magnitude=P, location=0)]  # define loads as list

    b = Beam(beam_len, loads=p, reactions=r, mesh=None, E=E, Ixx=I)

    # an explicit solve is required to calculate the reaction values
    b.solve()
    print(b)

    fig, axes = b.plot(
        diagrams=("shear", "moment", "deflection"),
        plot_kwargs={"label": "approx solution"},
    )
    x = np.linspace(0, beam_len, 100)
    Mx = -P * x
    Vx = -P * np.ones(np.size(x))
    dx = (P / (6 * E * I)) * (2 * beam_len**3 - 3 * beam_len**2 * x + x**3)
    axes[0].plot(x, Vx, "--", label="exact solution")
    axes[1].plot(x, Mx, "--", label="exact solution")
    axes[-1].plot(x, dx, "--", label="exact solution")
    axes[-1].legend()
    b.show()


def example_2():
    """
    Cantilevered Beam with 3 Pinned Supports and End Loading
    """
    print("=" * 79)
    print("Example 2")
    print("Show an example with 3 Pinned Supports and End Loading\n")
    beam_len = 10

    # Note that both the reaction and load are both lists. They must always be
    # given to Beam as a list,
    r = [PinnedReaction(0), PinnedReaction(2), PinnedReaction(6)]  # define reactions
    p = [PointLoad(magnitude=-2, location=beam_len)]  # define loads

    b = Beam(beam_len, loads=p, reactions=r, E=29e6, Ixx=125)

    # an explicit solve is required to calculate the reaction values
    b.solve()
    print(b)

    b.plot()
    b.show()


def example_3():
    """
    Cantilevered Beam with Fixed Support and Force and Moment at end
    """
    print("=" * 79)
    print("Example 3")
    print(
        "Show an example with a cantilevered beam with a fixed support and "
        "point load and moment load at the end\n"
    )

    beam_len = 10
    # Note that both the reaction and load are both lists. They must always be
    # given to Beam as a list,
    r = [FixedReaction(0)]  # define reactions as list

    p = [PointLoad(-2, beam_len), MomentLoad(-2, beam_len)]  # define loads as list

    # since the force and moment are acting at the same location, it can also be applied
    # using the base Load and defining the fm_factor, as shown below. Defining the loads
    # this way will give the same results
    # from femethods.loads import Load
    # p = [Load(magnitude=1, location=beam_len, fm_factor=(-2, -2))]

    b = Beam(beam_len, loads=p, reactions=r, E=29e6, Ixx=125)
    print(b)

    b.plot()
    b.show()


if __name__ == "__main__":
    np.set_printoptions(
        precision=None,
        linewidth=300,
        suppress=True,
        formatter={"float": "{:0,.5f}".format, "int": "{:0,.0f}".format},
    )
    # intro_demo()
    # example_1()
    example_2()
    # example_3()