.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/Beam/Beam1.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_Beam_Beam1.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_Beam_Beam1.py:


Beam1
=====

Beam subjected to pure tensile loading.

.. GENERATED FROM PYTHON SOURCE LINES 12-125



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam1_001.png
         :alt: SEG2: Ne = 10, Nn = 11
         :srcset: /examples/Beam/images/sphx_glr_Beam1_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam1_002.png
         :alt: Boundary conditions
         :srcset: /examples/Beam/images/sphx_glr_Beam1_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam1_003.png
         :alt: $ux^{e}$
         :srcset: /examples/Beam/images/sphx_glr_Beam1_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam1_004.png
         :alt: $u_x(x)$
         :srcset: /examples/Beam/images/sphx_glr_Beam1_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam1_005.png
         :alt: $N(x)$
         :srcset: /examples/Beam/images/sphx_glr_Beam1_005.png
         :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    
    err ux: 1.52e-14%
    err N: 4.40e-14%

    ==================== Mesh ====================

    Element type: SEG2
    Ne = 10, Nn = 11

    ==================== Model ====================

    <EasyFEA.Models.Beam._beam.BeamStructure object at 0x74a3ab3b9910>

    solver:scipy

    ============= Boundary Conditions =============

    Unspecified.

    =================== Results ===================



    Ux max = 4.45e-05
    Ux min = 0.00e+00

    =================== TicTac ===================

    Mesh: 12.259 ms
    Boundary Conditions: 36.955 µs
    Matrix: 18.818 ms
    Solver: 2.685 ms
    Display: 39.283 ms






|

.. code-block:: Python
   :lineno-start: 13


    import matplotlib.pyplot as plt
    import numpy as np

    from EasyFEA import Display, Models, Mesher, ElemType, Simulations
    from EasyFEA.Geoms import Domain, Line

    if __name__ == "__main__":
        Display.Clear()

        # ----------------------------------------------
        # Configuration
        # ----------------------------------------------

        # geom
        L = 10
        nL = 10
        h = 0.1
        b = 0.1

        # model
        E = 200000e6
        v = 0.3
        rho = 7800
        beamDim = 1

        # load
        g = 10
        q = rho * g * (h * b)
        F = 5000

        # ----------------------------------------------
        # Mesh
        # ----------------------------------------------

        # Create a section for the beam
        mesher = Mesher()
        section = mesher.Mesh_2D(Domain((0, 0), (b, h)))

        p1 = (0, 0)
        p2 = (L, 0)
        line = Line(p1, p2, L / nL)
        beam = Models.Beam.Isotropic(beamDim, line, section, E, v)

        mesh = mesher.Mesh_Beams([beam], elemType=ElemType.SEG2)

        # ----------------------------------------------
        # Simulation
        # ----------------------------------------------

        # Initialize the beam structure with the defined beam segments
        beamStructure = Models.Beam.BeamStructure([beam])

        # Create the beam simulation
        simu = Simulations.Beam(mesh, beamStructure)
        dof_n = simu.Get_dof_n()

        # Apply boundary conditions
        simu.add_dirichlet(mesh.Nodes_Point(p1), [0] * dof_n, simu.Get_unknowns())
        simu.add_lineLoad(mesh.nodes, [q], ["x"])
        simu.add_neumann(mesh.Nodes_Point(p2), [F], ["x"])

        # Solve the beam problem and get displacement results
        sol = simu.Solve()
        simu.Save_Iter()

        # ----------------------------------------------
        # Results
        # ----------------------------------------------

        Display.Plot_Mesh(simu, deformFactor=L / 10 / sol.max())
        Display.Plot_BoundaryConditions(simu)
        Display.Plot_Result(simu, "ux")

        # ------------------------
        # ux
        # ------------------------

        A = section.area
        x = np.linspace(0, L, 100)
        ux_x = lambda x: (F * x / (E * A)) + (rho * g * x / 2 / E * (2 * L - x))

        ux = simu.Result("ux")
        x_n = mesh.coord[:, 0]
        err_ux = np.abs(ux_x(x_n) - ux).max() / np.abs(ux_x(L))
        Display.MyPrint(f"\nerr ux: {err_ux * 100:.2e}%")

        axUx = Display.Init_Axes()
        axUx.plot(x, ux_x(x), label="Analytical", c="blue")
        axUx.scatter(x_n, ux, label="FE", c="red", marker="x", zorder=2)
        axUx.set_title("$u_x(x)$")
        axUx.legend()

        # ------------------------
        # N
        # ------------------------

        N_x = lambda x: F + q * (L - x)

        x_e = x_n[mesh.connect].mean(1)  # element centroid x-coords
        N = simu.Result("N", nodeValues=False)
        err_N = np.abs(N_x(x_e) - N).max() / np.abs(N_x(x_e)).max()
        Display.MyPrint(f"\nerr N: {err_N * 100:.2e}%")

        axN = Display.Init_Axes()
        axN.plot(x, N_x(x), label="Analytical", c="blue")
        axN.scatter(x_e, N, label="FE", c="red", marker="x", zorder=2)
        axN.set_title("$N(x)$")
        axN.legend()

        print(simu)

        plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.347 seconds)


.. _sphx_glr_download_examples_Beam_Beam1.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: Beam1.ipynb <Beam1.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: Beam1.py <Beam1.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: Beam1.zip <Beam1.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_