:orphan:

Elements
========

Per-element living documentation — one sub-gallery per registered
element.  Each script is a runnable companion to the corresponding
theory page under
:doc:`/user-guide/pre-processing/elements/index`, exercising the same
shape functions, quadrature rule, and formulation options on a tiny
self-contained problem.

These examples run on every docs build, so the theory pages stay
grounded in code that actually works.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

.. thumbnail-parent-div-close

.. raw:: html

    </div>

BEAM188 gallery
===============

Runnable BEAM188 (3D 2-node beam) 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="Slender steel cantilever modelled with a line of BEAM188 elements. Two validations:">

.. only:: html

  .. image:: /gallery/elements/beam188/images/thumb/sphx_glr_example_beam188_thumb.png
    :alt:

  :doc:`/gallery/elements/beam188/example_beam188`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">BEAM188 — cantilever tip deflection and first mode</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

COMBIN14 gallery
================

Runnable COMBIN14 (3D 2-node spring) 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="Three co-linear nodes joined by two COMBIN14 springs of stiffness k1 and k2. With the far end fixed and a tip load F the free-end displacement is F / k_eq where k_eq = k1 · k2 / (k1 + k2).">

.. only:: html

  .. image:: /gallery/elements/combin14/images/thumb/sphx_glr_example_combin14_thumb.png
    :alt:

  :doc:`/gallery/elements/combin14/example_combin14`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">COMBIN14 — two springs in series</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

LINK180 gallery
===============

Gallery of runnable LINK180 (3D 2-node truss) examples.
See ``examples/link180/README.md`` in the repository for the element
theory write-up.


.. 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="Single LINK180 spar fixed at node 1 and pulled along the x-axis at node 2. The tip displacement is compared to the closed-form rod solution u = P L / (E A) and the axial stress is plotted on the deformed mesh.">

.. only:: html

  .. image:: /gallery/elements/link180/images/thumb/sphx_glr_example_link180_thumb.png
    :alt:

  :doc:`/gallery/elements/link180/example_link180`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">LINK180 — axial truss under end load</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

MASS21 gallery
==============

Runnable MASS21 (1-node lumped mass) 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="Two nodes connected by a COMBIN14 spring. A MASS21 element sits on the free node. The first modal frequency is compared to the textbook SDOF result ω = √(k / m).">

.. only:: html

  .. image:: /gallery/elements/mass21/images/thumb/sphx_glr_example_mass21_thumb.png
    :alt:

  :doc:`/gallery/elements/mass21/example_mass21`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MASS21 — single-DOF spring-mass oscillator</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

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="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">PLANE182 — plane-stress uniaxial tension</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

SHELL181 gallery
================

Runnable SHELL181 (4-node shell) 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="Single SHELL181 element (a 1 m × 1 m flat plate of thickness t) in pure in-plane tension. Out-of-plane DOFs are suppressed so the problem reduces to plane-stress membrane behaviour: u_x = σ L / E and the Poisson contraction u_y = −ν u_x.">

.. only:: html

  .. image:: /gallery/elements/shell181/images/thumb/sphx_glr_example_shell181_thumb.png
    :alt:

  :doc:`/gallery/elements/shell181/example_shell181`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SHELL181 — uniaxial stretch of a flat square plate</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

SOLID185 gallery
================

Runnable SOLID185 (8-node hex) 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="Single SOLID185 element (a 1 m unit cube) with one face clamped in the pulling direction and the opposite face loaded. The displacement field is uniform — u_x = σ L / E on the loaded face — which gives a clean check on the full 24 × 24 stiffness plus the boundary/load handling.">

.. only:: html

  .. image:: /gallery/elements/solid185/images/thumb/sphx_glr_example_solid185_thumb.png
    :alt:

  :doc:`/gallery/elements/solid185/example_solid185`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SOLID185 — uniaxial tension of a unit cube</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

SOLID186 gallery
================

Runnable SOLID186 (20-node serendipity hex) 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="Single SOLID186 brick (a unit cube, 20 nodes including the mid-edge nodes of the serendipity family) loaded in uniaxial tension.  The consistent-load vector for a serendipity 8-node face has corner weight -1/12 and mid-edge weight +1/3; applying these produces a uniform σxx field, so εxx = σ/E and εyy = εzz = −ν·εxx exactly at every node.">

.. only:: html

  .. image:: /gallery/elements/solid186/images/thumb/sphx_glr_example_solid186_thumb.png
    :alt:

  :doc:`/gallery/elements/solid186/example_solid186`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SOLID186 — uniaxial tension on a 20-node hex</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>

SOLID187 gallery
================

Runnable SOLID187 (10-node quadratic tetrahedron) 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="Single SOLID187 (10-node quadratic tet) driven by a fully-prescribed displacement field that matches a uniform strain state. Under all-Dirichlet BCs the solve has a unique solution equal to the prescribed field, so the recovered strain tensor matches the analytical one to machine precision. Useful as a self-contained smoke test that SOLID187 + femorph_solver.Model.eel are in lockstep.">

.. only:: html

  .. image:: /gallery/elements/solid187/images/thumb/sphx_glr_example_solid187_thumb.png
    :alt:

  :doc:`/gallery/elements/solid187/example_solid187`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">SOLID187 — prescribed uniform strain on a 10-node tet</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /gallery/elements/beam188/index.rst
   /gallery/elements/combin14/index.rst
   /gallery/elements/link180/index.rst
   /gallery/elements/mass21/index.rst
   /gallery/elements/plane182/index.rst
   /gallery/elements/shell181/index.rst
   /gallery/elements/solid185/index.rst
   /gallery/elements/solid186/index.rst
   /gallery/elements/solid187/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: elements_python.zip </gallery/elements/elements_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: elements_jupyter.zip </gallery/elements/elements_jupyter.zip>`


.. only:: html

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

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