Solid dynamics example gallery
==============================

The figures on this page are generated from the example implementations during
the documentation build.  The setup schematics are drawn programmatically and
the response figures and animation use trajectories produced by the actual
solid-dynamics solver.

Cantilever beam
---------------

The cantilever example clamps the left boundary and applies a smooth transient
transverse resultant on the right boundary.

.. image:: ../_static/solid_dynamics/cantilever_setup.png
   :alt: Cantilever beam problem setup
   :width: 90%
   :align: center

The vertical displacement history at the midpoint of the free end is computed
with the default Neo-Hookean model and velocity-primary implicit Newmark solver.
No artificial damping is enabled in the default example.

.. image:: ../_static/solid_dynamics/cantilever_response.png
   :alt: Cantilever beam tip-displacement response
   :width: 75%
   :align: center

The full displacement snapshots can also be viewed as a deformed-mesh
animation.  The displayed deformation is magnified when needed for visibility;
the magnification factor is shown in the animation.

.. image:: ../_static/solid_dynamics/cantilever_deformation.gif
   :alt: Animated cantilever beam deformation
   :width: 90%
   :align: center

Doubly clamped Gaussian perturbation
------------------------------------

The second example fixes both ends and initializes a centered transverse
Gaussian displacement.  It is unforced after release.

.. image:: ../_static/solid_dynamics/clamped_gaussian_setup.png
   :alt: Doubly clamped Gaussian perturbation setup
   :width: 90%
   :align: center

The following curve is the center-point vertical displacement produced by the
Neo-Hookean solver.  Because the example has no Rayleigh damping, changes in
the center-point amplitude reflect nonlinear and multimode dynamics rather than
an imposed damping model.

.. image:: ../_static/solid_dynamics/clamped_gaussian_response.png
   :alt: Doubly clamped Gaussian response
   :width: 75%
   :align: center

Longitudinal two-way wave
-------------------------

For the linear-wave verification problem, all transverse degrees of freedom are
constrained and an axial Gaussian displacement is released from rest.  Before
boundary reflections, the solution reduces to the scalar two-way wave equation.

.. image:: ../_static/solid_dynamics/linear_wave_setup.png
   :alt: Longitudinal two-way wave setup
   :width: 90%
   :align: center

The finite-element solution is compared directly with the analytic D'Alembert
solution at the same time.

.. image:: ../_static/solid_dynamics/linear_wave_solution.png
   :alt: Finite-element and analytic two-way wave solutions
   :width: 75%
   :align: center

A coupled spatial/temporal refinement study with :math:`\Delta t\propto\Delta x`
shows the expected near-second-order convergence.

.. image:: ../_static/solid_dynamics/linear_wave_convergence.png
   :alt: Two-way wave convergence study
   :width: 70%
   :align: center

Generation
----------

All media on this page are regenerated by
``examples/nonlinear_solid_dynamics/generate_docs_media.py`` during the
Sphinx build.  This keeps the visualizations tied to the current solver rather
than maintaining hand-generated result images.