.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/01-simple/simpleBeamElementExample.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_01-simple_simpleBeamElementExample.py>`
        to download the full example code.

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

.. _sphx_glr_examples_01-simple_simpleBeamElementExample.py:


Beam Element Canteleaver Beam
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Simple canteleaver beam example using different kind of elements

.. GENERATED FROM PYTHON SOURCE LINES 7-94




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

 .. code-block:: none

    Reaction RX at the clamped extermity: 0.0
    Reaction RY at the clamped extermity: 1.9999999999999822
    Reaction RZ at the clamped extermity: 0.0
    Moment MX at the clamped extermity: 0.0
    Moment MY at the clamped extermity: 0.0
    Moment MZ at the clamped extermity: 20.0
    RX at the free extremity: 0.0
    RZ at the free extremity: 0.0
    Analytical deflection:  -0.008695165057587216
    [ 0.         -0.00869517  0.        ]






|

.. code-block:: Python


    import fedoo as fd
    import numpy as np

    E = 1e5
    nu = 0.3

    fd.ModelingSpace("3D")
    fd.constitutivelaw.ElasticIsotrop(E, nu, name="ElasticLaw")

    # circular section
    R = 1
    Section = np.pi * R**2
    Jx = np.pi * R**4 / 2
    Iyy = np.pi * R**4 / 4
    Izz = np.pi * R**4 / 4
    k = 0.8  # reduce section for shear (k=0 -> no shear effect)

    L = 10  # beam lenght
    F = -2  # Force applied on right section

    # Build a straight beam mesh
    Nb_elm = 10  # Number of elements
    crd = np.linspace(0, L, Nb_elm + 1).reshape(-1, 1) * np.array([[1, 0, 0]])
    # crd = np.linspace(0,L,Nb_elm+1).reshape(-1,1)* np.array([[0,0,1]]) #beam oriented in the Z axis
    elm = np.c_[np.arange(0, Nb_elm), np.arange(1, Nb_elm + 1)]

    fd.Mesh(crd, elm, "lin2", name="beam")
    nodes_left = [0]
    nodes_right = [Nb_elm]

    # computeShear = 0: no shear strain are considered. Bernoulli element is used ("i.e "bernoulliBeam" element)
    # computeShear = 1: shear strain using the "beam" element (shape functions depend on the beam parameter) ->  Friedman, Z. and Kosmatka, J. B. (1993).  An improved two-node Timoshenkobeam finite element.Computers & Structures, 47(3):473–481
    # computeShear = 2: shear strain using the "beamFCQ" element (using internal variables) -> Caillerie, D., Kotronis, P., and Cybulski, R. (2015). A new Timoshenko finite element beamwith internal degrees of freedom.International Journal of Numerical and Analytical Methods in Geomechanics
    computeShear = 1

    if computeShear == 0:
        fd.weakform.BeamEquilibrium(
            "ElasticLaw", Section, Jx, Iyy, Izz, name="WFbeam"
        )  # by default k=0 i.e. no shear effect
        fd.Assembly.create("WFbeam", "beam", "bernoulliBeam", name="beam")
    elif computeShear == 1:
        fd.weakform.BeamEquilibrium("ElasticLaw", Section, Jx, Iyy, Izz, k=k, name="WFbeam")
        fd.Assembly.create("WFbeam", "beam", "beam", name="beam")
    else:  # computeShear = 2
        fd.Mesh["beam"].add_internal_nodes(
            1
        )  # adding one internal nodes per element (this node has no geometrical sense)
        fd.weakform.Beam("ElasticLaw", Section, Jx, Iyy, Izz, k=k, name="WFbeam")
        fd.Assembly.create("WFbeam", "beam", "beamFCQ", name="beam")

    pb = fd.problem.Linear("beam")

    pb.bc.add("Dirichlet", nodes_left, ["Disp", "Rot"], 0)
    pb.bc.add("Neumann", nodes_right, "DispY", F)

    pb.solve()

    # Post treatment
    results = pb.get_results(fd.Assembly["beam"], ["Fext"])["Fext"]

    print("Reaction RX at the clamped extermity: " + str(results[0][0]))
    print("Reaction RY at the clamped extermity: " + str(results[1][0]))
    print("Reaction RZ at the clamped extermity: " + str(results[2][0]))
    print("Moment MX at the clamped extermity: " + str(results[3][0]))
    print("Moment MY at the clamped extermity: " + str(results[4][0]))
    print("Moment MZ at the clamped extermity: " + str(results[5][0]))

    print("RX at the free extremity: " + str(results[0][nodes_right[0]]))
    print("RZ at the free extremity: " + str(results[2][nodes_right[0]]))

    results = pb.get_results("beam", "BeamStress")["BeamStress"]
    IntMoment = np.array(results[3:])
    IntForce = np.array(results[:3])

    U = np.reshape(pb.get_dof_solution("all"), (6, -1)).T
    Theta = U[: nodes_right[0] + 1, 3:]
    U = U[: nodes_right[0] + 1, 0:3]

    sol = F * L**3 / (3 * E * Izz)
    if computeShear != 0 and k != 0:
        G = E / (1 + nu) / 2
        sol += F * L / (k * G * Section)
    print("Analytical deflection: ", sol)
    print(U[-1])

    M = fd.Assembly["beam"].global_matrix.todense()


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

   **Total running time of the script:** (0 minutes 0.014 seconds)


.. _sphx_glr_download_examples_01-simple_simpleBeamElementExample.py:

.. only:: html

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

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

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

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

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

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

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


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

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