.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/Beam/Beam3.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_Beam3.py>`
        to download the full example code.

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

.. _sphx_glr_examples_Beam_Beam3.py:


Beam3
=====

A bi-fixed beam undergoing bending deformation.

.. GENERATED FROM PYTHON SOURCE LINES 11-113



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


    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam3_001.png
         :alt: SEG2: Ne = 10, Nn = 11
         :srcset: /examples/Beam/images/sphx_glr_Beam3_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam3_002.png
         :alt: Section
         :srcset: /examples/Beam/images/sphx_glr_Beam3_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam3_003.png
         :alt: Boundary conditions
         :srcset: /examples/Beam/images/sphx_glr_Beam3_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/Beam/images/sphx_glr_Beam3_004.png
         :alt: $uy^{e}$
         :srcset: /examples/Beam/images/sphx_glr_Beam3_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    err uy : 0.00 %

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

    Element type: SEG2
    Ne = 10, Nn = 11

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

    <EasyFEA.models._beam.BeamStructure object at 0x78ce3f1c1110>

    solver : scipy

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

    Unspecified.

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



    Ux max = 0.00e+00
    Ux min = 0.00e+00

    Uy max = 0.00e+00
    Uy min = -6.71e-03

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

    Mesh : 80.150 ms
    Boundary Conditions : 65.804 µs
    Matrix : 27.260 ms
    Solver : 13.510 ms
    Display : 223.311 ms
    PostProcessing : 184.298 µs






|

.. code-block:: Python
   :lineno-start: 12


    from EasyFEA import Display, Models, plt, np, Mesher, ElemType, Simulations
    from EasyFEA.Geoms import Line, Point, Points

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

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

        # geom
        L = 120
        h = 20
        b = 13
        e = 2

        # model
        E = 210000
        v = 0.3

        # load
        load = 800

        # ----------------------------------------------
        # Section
        # ----------------------------------------------

        def DoSym(p: Point, n: np.ndarray) -> Point:
            pc = p.copy()
            pc.Symmetry(n=n)
            return pc

        p1 = Point(-b / 2, -h / 2)
        p2 = Point(b / 2, -h / 2)
        p3 = Point(b / 2, -h / 2 + e)
        p4 = Point(e / 2, -h / 2 + e, r=e)
        p5 = DoSym(p4, (0, 1))
        p6 = DoSym(p3, (0, 1))
        p7 = DoSym(p2, (0, 1))
        p8 = DoSym(p1, (0, 1))
        p9 = DoSym(p6, (1, 0))
        p10 = DoSym(p5, (1, 0))
        p11 = DoSym(p4, (1, 0))
        p12 = DoSym(p3, (1, 0))
        contour = Points([p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12], e / 6)
        section = Mesher().Mesh_2D(contour)

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

        elemType = ElemType.SEG2
        beamDim = 2  # must be >= 2

        p1 = Point()
        pL = Point(x=L / 2)
        p2 = Point(x=L)
        line = Line(p1, p2, L / 9)
        beam = Models.BeamElasIsot(beamDim, line, section, E, v)

        mesh = Mesher().Mesh_Beams([beam], additionalPoints=[pL], elemType=elemType)

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

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

        # Create the beam simulation
        simu = Simulations.BeamSimu(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_dirichlet(mesh.Nodes_Point(p2), [0] * dof_n, simu.Get_unknowns())
        simu.add_neumann(mesh.Nodes_Point(pL), [-load], ["y"])

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

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

        u_an = load * L**3 / (192 * E * beam.Iz)

        uy_1d = np.abs(simu.Result("uy").min())

        Display.MyPrint(f"err uy : {np.abs(u_an - uy_1d) / u_an * 100:.2f} %")

        Display.Plot_Mesh(simu, L / 20 / sol.min())
        ax = Display.Plot_Mesh(section)
        ax.set_title("Section")
        Display.Plot_BoundaryConditions(simu)
        Display.Plot_Result(simu, "uy", L / 20 / sol.min())

        print(simu)

        plt.show()


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

   **Total running time of the script:** (0 minutes 0.295 seconds)


.. _sphx_glr_download_examples_Beam_Beam3.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: Beam3.ipynb <Beam3.ipynb>`

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

      :download:`Download Python source code: Beam3.py <Beam3.py>`

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

      :download:`Download zipped: Beam3.zip <Beam3.zip>`


.. only:: html

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

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