.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/LinearizedElasticity/Elas1.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_LinearizedElasticity_Elas1.py>`
        to download the full example code.

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

.. _sphx_glr_examples_LinearizedElasticity_Elas1.py:


Elas1
=====

A cantilever beam undergoing bending deformation.

.. GENERATED FROM PYTHON SOURCE LINES 11-92



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


    *

      .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas1_001.png
         :alt: QUAD9: Ne = 81, Nn = 385
         :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas1_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas1_002.png
         :alt: Boundary conditions
         :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas1_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas1_003.png
         :alt: $uy$
         :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas1_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas1_004.png
         :alt: $\sigma_{vm}$
         :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas1_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none



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

    Element type: QUAD9
    Ne = 81, Nn = 385

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

    ElasIsot:
    E = 2.10e+05, v = 0.3
    planeStress = True
    thickness = 1.30e+01

    solver : pypardiso

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

    Unspecified.

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


    W def = 371.24

    Svm max = 165.59

    Evm max = 0.09 %

    Ux max = 7.49e-02
    Ux min = -7.49e-02

    Uy max = 0.00e+00
    Uy min = -9.28e-01

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

    Mesh : 260.262 ms
    Boundary Conditions : 776.768 µs
    Matrix : 2.017 s
    Solver : 5.083 s
    Display : 376.061 ms
    PostProcessing : 237.486 ms
    Resolution hyperelastic : 6.573 s
    PyVista_Interface : 17.072 s
    

    =================== Result ===================
    err W : 0.24 %
    err uy : 0.68 %






|

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


    from EasyFEA import Display, Models, plt, np, ElemType, Simulations
    from EasyFEA.Geoms import Domain

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

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

        # geom
        dim = 2
        L = 120  # mm
        h = 13
        I = h**4 / 12  # mm4

        # model
        E = 210000  # MPa (Young's modulus)
        v = 0.3  # Poisson's ratio
        coef = 1

        # load
        load = 800  # N

        # expected results
        W_an = 2 * load**2 * L / E / h**2 * (L**2 / h**2 + (1 + v) * 3 / 5)  # mJ
        uy_an = load * L**3 / (3 * E * I)

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

        N = 3
        meshSize = h / N

        domain = Domain((0, 0), (L, h), meshSize)

        if dim == 2:
            mesh = domain.Mesh_2D([], ElemType.QUAD9, isOrganised=True)
        else:
            mesh = domain.Mesh_Extrude(
                [], [0, 0, -h], [N], ElemType.HEXA27, isOrganised=True
            )

        nodes_x0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
        nodes_xL = mesh.Nodes_Conditions(lambda x, y, z: x == L)

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

        material = Models.ElasIsot(dim, E, v, planeStress=True, thickness=h)
        simu = Simulations.ElasticSimu(mesh, material)

        simu.add_dirichlet(nodes_x0, [0] * dim, simu.Get_unknowns())
        simu.add_surfLoad(nodes_xL, [-load / h**2], ["y"])

        sol = simu.Solve()
        simu.Save_Iter()

        uy_num = -simu.Result("uy").min()
        W_num = simu._Calc_Psi_Elas()

        # ----------------------------------------------
        # Results
        # ----------------------------------------------
        print(simu)

        Display.Section("Result")

        print(f"err W : {np.abs(W_an - W_num) / W_an * 100:.2f} %")

        print(f"err uy : {np.abs(uy_an - uy_num) / uy_an * 100:.2f} %")

        Display.Plot_Mesh(simu, h / 2 / np.abs(sol).max())
        Display.Plot_BoundaryConditions(simu)
        Display.Plot_Result(simu, "uy", nodeValues=True, coef=1 / coef, ncolors=20)
        Display.Plot_Result(simu, "Svm", plotMesh=True, ncolors=11)

        plt.show()


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

   **Total running time of the script:** (0 minutes 0.261 seconds)


.. _sphx_glr_download_examples_LinearizedElasticity_Elas1.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: Elas1.ipynb <Elas1.ipynb>`

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

      :download:`Download Python source code: Elas1.py <Elas1.py>`

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

      :download:`Download zipped: Elas1.zip <Elas1.zip>`


.. only:: html

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

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