B, D models
==================

Characteristics of the models
----------------------------------

The plate is modelled in :math:`\mathrm{2D}` in plane deformations, by QUAD4 elements. The springs are modeled by seg2 assigned a 2D_dis_T modeling whose characteristics are k_t_d_l. They are translational discretes having a diagonal matrix, see the documentation for affe_cara_elem.

Modeling B uses behavior DIS_CHOC, modeling D uses behavior DIS_CONTACT.


Characteristics of the mesh
----------------------------

The plate is cut with :math:`\mathrm{ny}=16`. The length of the plate is :math:`b=2m`.


Tested sizes and results
------------------------------

For time step No. 1, the movements of the ends of the springs, which are not connected to the plate, are imposed at zero. The results of*Code_Aster* are compared with the discrete solution, which corresponds to the solution of the modelled problem. The equilibrium solution is obtained for :math:`n=12`, equation.


.. csv-table::

    "**Nature of results**", ":math:`{U}_{A}` "," :math:`{U}_{B}`"
    "Ongoing solution", ":math:`\frac{-4}{1125}` "," :math:`\frac{4}{3375}`"
    "Discreet solution (:math:`n=12`)", ":math:`\frac{-208}{58875}` "," :math:`\frac{176}{153075}`"
    "Tolerance", ":math:`1.0E-04` "," :math:`1.0E-04`"


For time step No. 2, the movements of the ends of the springs, not connected to the plate, are moved by :math:`+5.0E-03m`. The results of*Code_Aster* are compared with the discrete solution, which corresponds to the solution of the modelled problem.


.. csv-table::

    "**Nature of results**", ":math:`{U}_{A}` "," :math:`{U}_{B}`"
    "Ongoing solution", ":math:`\frac{-4}{1125}+\frac{5}{1000}` "," :math:`\frac{4}{3375}+\frac{5}{1000}`"
    "Discreet solution (:math:`n=12`)", ":math:`\frac{-208}{58875}+\frac{5}{1000}` "," :math:`\frac{176}{153075}+\frac{5}{1000}`"
    "Tolerance", ":math:`1.0E-04` "," :math:`1.0E-04`"