explicit
''''''''

In ``explicit``, an example of a dynamic solution with an explicit time integration is shown.
The explicit scheme is selected using the ``_explicit_lumped_mass`` constant::

model.initFull(_analysis_method = _explicit_lumped_mass);

Note that it is also the default value, hence using ``model.initFull();`` is equivalent.

This example models the propagation of a wave in a steel beam. The beam and the applied displacement in the :math:`x` direction are shown in :numref:`fig-ex-explicit`.

.. _fig-ex-explicit:
.. figure:: examples/c++/solid_mechanics_model/explicit/images/explicit.svg
:align: center
:width: 90%

Numerical setup.

The length and height of the beam are :math:`L={10}\textrm{m}` and :math:`h =
{1}\textrm{m}`, respectively. The material is linear elastic, homogeneous and
isotropic (density: :math:`7800\mathrm{kg/m}^3`, Young's modulus:
:math:`210\mathrm{GPa}` and Poisson's ratio: :math:`0.3`). The imposed
displacement follow a Gaussian function with a maximum amplitude of :math:`A =
{0.01}\textrm{m}`. The potential, kinetic and total energies are computed. The
safety factor is equal to :math:`0.8`.

The dynamic solution is depicted in :numref:`fig-ex-explicit_disp`.

.. _fig-ex-explicit_disp:
.. figure:: examples/c++/solid_mechanics_model/explicit/images/bar_pulse.gif
:align: center
:width: 90%

Dynamic solution: lateral displacement.



.. math::

u_x = A \mathrm{sin}(\frac{2 \pi k}{L} X_x) e^{- \frac{\frac{2 \pi k}{L} X_x}/{L}}^2

with :math:`u_x` and :math:`X_x` being the displacement and position in the
:math:`x` direction.