Element library
===============

femorph-solver ships a library of structural finite elements.  Each
element is built from published FEM theory (textbook / journal
citations on its theory page).  Element names are **topology-first
and vendor-neutral** — ``HEX8``, ``HEX20``, ``TET10``, ``BEAM2``,
``QUAD4_SHELL``, etc.  The MAPDL catalogue names (``SOLID185``,
``SOLID186``, ``BEAM188``, …) are retained as **compatibility
aliases** so existing ``.cdb`` decks load unchanged.

Correctness is verified against two independent evidence sources:
analytical / textbook closed-form solutions (``tests/analytical/``)
*and* agreement with MAPDL on shared benchmarks for migration
safety.  MAPDL is a yardstick, not a source of implementation
detail.

Pick an element by dimension and kinematics:

.. list-table::
    :widths: 22 18 15 55
    :header-rows: 1

    * - Element (canonical)
      - MAPDL alias
      - Kind
      - Notes
    * - :doc:`TRUSS2 <link180>`
      - ``LINK180``
      - 3D 2-node truss
      - Axial only; 3 DOF/node.
    * - :doc:`SPRING <combin14>`
      - ``COMBIN14``
      - 3D 2-node spring
      - Longitudinal KEYOPT(2)=0; 3 DOF/node.
    * - :doc:`POINT_MASS <mass21>`
      - ``MASS21``
      - 1-node point mass
      - KEYOPT(3)=2; 3 DOF/node.
    * - :doc:`BEAM2 <beam188>`
      - ``BEAM188``
      - 3D 2-node Euler–Bernoulli beam
      - 6 DOF/node; axial + torsion + two bending planes.
    * - :doc:`QUAD4_PLANE <plane182>`
      - ``PLANE182``
      - 2D 4-node quad
      - 2 DOF/node; plane stress / plane strain.
    * - :doc:`QUAD4_SHELL <shell181>`
      - ``SHELL181``
      - 4-node Mindlin shell
      - Selective reduced integration; drilling stabilisation.
    * - :doc:`HEX8 <solid185>`
      - ``SOLID185``
      - 3D 8-node hex
      - 2×2×2 Gauss; B-bar / enhanced-strain options.
    * - :doc:`HEX20 <solid186>`
      - ``SOLID186``
      - 3D 20-node serendipity hex
      - Bedrosian 2×2×2 stiffness, Irons 14-point mass; degenerate
        ``WEDGE15`` and ``PYR13`` auto-dispatched.
    * - :doc:`TET10 <solid187>`
      - ``SOLID187``
      - 3D 10-node tet
      - 4-point Keast Gauss (both K and M).

Registry and dispatch
---------------------

Element classes register into :mod:`femorph_solver.elements` and are
discovered by string name.  Both the neutral name and the MAPDL
alias resolve to the same kernel::

    from femorph_solver.elements import get, registered

    registered()
    # ['BEAM188', 'COMBIN14', 'LINK180', 'MASS21', 'PLANE182', 'SHELL181',
    #  'SOLID185', 'SOLID186', 'SOLID186P', 'SOLID186W', 'SOLID187']

    hex_kernel = get("SOLID185")  # same class, MAPDL-alias lookup

On an :class:`femorph_solver.Model`, the registry is queried through
:meth:`~femorph_solver.Model.et`::

    m = femorph_solver.Model()
    m.et(185, "HEX8")              # canonical neutral name
    m.et(185, "SOLID185")          # MAPDL-compat alias — identical behaviour

Every element class implements the :class:`~femorph_solver.elements.ElementBase`
interface — :meth:`ke` for stiffness, :meth:`me` for mass, optional
:meth:`ke_batch` / :meth:`me_batch` for vectorised assembly.

.. toctree::
    :hidden:
    :maxdepth: 1

    link180
    combin14
    mass21
    beam188
    plane182
    shell181
    solid185
    solid186
    solid187