.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02-constraints/rigid_tie.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_02-constraints_rigid_tie.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02-constraints_rigid_tie.py:


Rigid tie constraint
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Example of a 2D rigid tie.
The bottom face of a square is clamped. A rigid body
rotation is imposed on the top face.

.. GENERATED FROM PYTHON SOURCE LINES 8-64




.. image-sg:: /examples/02-constraints/images/sphx_glr_rigid_tie_001.png
   :alt: rigid tie
   :srcset: /examples/02-constraints/images/sphx_glr_rigid_tie_001.png
   :class: sphx-glr-single-img




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

 .. code-block:: none

    Iter 1 - Time: 0.20000 - dt 0.20000 - NR iter: 3 - Err: 0.00208
    Iter 2 - Time: 0.40000 - dt 0.20000 - NR iter: 3 - Err: 0.00382
    Iter 3 - Time: 0.60000 - dt 0.20000 - NR iter: 3 - Err: 0.00522
    Iter 4 - Time: 0.80000 - dt 0.20000 - NR iter: 3 - Err: 0.00634
    Iter 5 - Time: 1.00000 - dt 0.20000 - NR iter: 3 - Err: 0.00838






|

.. code-block:: Python


    import fedoo as fd
    import numpy as np

    fd.ModelingSpace("2D")  # plane strain assumption

    NLGEOM = True
    E = 200e3
    nu = 0.3

    mesh = fd.mesh.rectangle_mesh()
    material = fd.constitutivelaw.ElasticIsotrop(E, nu, name="ConstitutiveLaw")

    wf = fd.weakform.StressEquilibrium(material, nlgeom=NLGEOM, name="wf")

    assembly = fd.Assembly.create("wf", mesh)

    # node set for boundary conditions
    bottom = mesh.find_nodes("Y", mesh.bounding_box.ymin)
    top = mesh.find_nodes("Y", mesh.bounding_box.ymax)

    # add CD nodes
    ref_node = mesh.add_virtual_nodes(2)  # reference node for rigid body motion
    node_cd = [ref_node[0], ref_node[0], ref_node[1]]
    var_cd = ["DispX", "DispY", "DispX"]

    pb = fd.problem.NonLinear(assembly)
    pb.set_nr_criterion("Displacement", err0=1, tol=1e-2, max_subiter=5)

    results = pb.add_output(
        "rigid_tie_example", assembly, ["Disp", "Stress", "Strain", "Fext"]
    )

    pb.bc.add(fd.constraint.RigidTie2D(top, node_cd, var_cd))

    pb.bc.add("Dirichlet", bottom, "Disp", 0)
    pb.bc.add("Dirichlet", ref_node[1], "DispY", 0)  # to block the non used virtual dof
    pb.bc.add(
        "Dirichlet", ref_node[1], "DispX", -np.pi / 4
    )  # Rigid rotation of the right end

    pb.nlsolve(dt=0.2, tmax=1, update_dt=True, print_info=1, interval_output=0.2)

    # =============================================================
    # Example of plots with pyvista - uncomment the desired plot
    # =============================================================

    # ------------------------------------
    # Simple plot with default options
    # ------------------------------------
    results.plot("Stress", component="YY", data_type="Node", show=True)

    # ------------------------------------
    # Write movie with default options
    # ------------------------------------
    # results.write_movie('rigid_tie_example', 'Stress', 'vm', 'Node', framerate = 12, quality = 5)


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

   **Total running time of the script:** (0 minutes 0.564 seconds)


.. _sphx_glr_download_examples_02-constraints_rigid_tie.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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