.. _sphx_glr_gallery_elements_plane182:

PLANE182 gallery
================

Runnable PLANE182 (2D 4-node quad) examples.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The 4-node bilinear plane element maps to the natural coordinates (\xi, \eta) \in [-1, 1]^2.  Two translational DOFs per node; 8 DOFs per element.">

.. only:: html

  .. image:: /gallery/elements/plane182/images/thumb/sphx_glr_example_quad4_plane_reference_geometry_thumb.png
    :alt:

  :doc:`/gallery/elements/plane182/example_quad4_plane_reference_geometry`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">QUAD4 plane reference geometry — bilinear shape functions + 2×2 Gauss</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Renders the four bilinear (4-node) shape functions N_i(\xi, \eta) on the reference quadrilateral \hat\Omega = [-1, +1]^2:">

.. only:: html

  .. image:: /gallery/elements/plane182/images/thumb/sphx_glr_example_quad4_shape_functions_thumb.png
    :alt:

  :doc:`/gallery/elements/plane182/example_quad4_shape_functions`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">QUAD4 bilinear shape functions on the reference square</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A square piece of plate is fixed on its left edge and pulled on its right edge. We check the tip displacement against Hooke&#x27;s law u_x = σ L / E and the Poisson contraction u_y = −ν u_x in plane stress, then render the deformed mesh.">

.. only:: html

  .. image:: /gallery/elements/plane182/images/thumb/sphx_glr_example_plane182_thumb.png
    :alt:

  :doc:`/gallery/elements/plane182/example_plane182`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">QUAD4_PLANE — plane-stress uniaxial tension</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /gallery/elements/plane182/example_quad4_plane_reference_geometry
   /gallery/elements/plane182/example_quad4_shape_functions
   /gallery/elements/plane182/example_plane182