B modeling
==============

Characteristics of modeling
-----------------------------------

For this modeling, two mobile hardware points are considered according to the following diagram:


.. image:: images/Object_31.png
    :width: 1.8134in
    :height: 0.6917in


.. _RefSchema_Object_31.png:

The system is perfectly symmetric. The same formulation as modeling A is obtained if normal shock rigidities equal to half of the rigidities chosen for modeling A.

Indeed, if we note: :math:`{x}_{2}=-{x}_{3}=x`

The reaction force :math:`{F}_{\mathrm{ext}}` is in the following form:

During the first phase: :math:`{F}_{\mathrm{ext}}=-{K}_{1}({x}_{2}-{x}_{3})=-2{K}_{1}x`

During the second phase: :math:`{F}_{\mathrm{ext}}=-{F}_{\mathrm{seuil}}`

During the third phase: :math:`{F}_{\mathrm{ext}}=-{K}_{2}({x}_{2}-{x}_{3}-2{d}_{p})=-2{K}_{2}(x-{d}_{p})`

During the fourth phase: :math:`{F}_{\mathrm{ext}}=0`

We model the problem with an obstacle like BI_PLAN_Y.

At the initial instant, the two hardware points are in contact with an initial speed equal to :math:`2m\mathrm{/}s`.

The quantities obtained following buckling due to shock are evaluated using the keyword FLAMBAGE of the DYNA_VIBRA operator, with the time diagrams EULER and ADAPT_ORDRE2.

With the adaptive time diagram ADAPT_ORDRE2, we define (in seconds):


* the initial time step: PAS = 0.001,


* the maximum value of the time step: PAS_MAXI = 0.005.


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

Number of knots: 4

Number of stitches: 2 SEG2


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

The values of the quantities related to buckling behavior during the shock are tested.


.. csv-table::

    "**Identification**", "**Reference**", "**T** reference type", "**Precision**"
    ":math:`{t}_{\mathrm{fl}}` "," :math:`\frac{\pi }{6}s` ", "'ANALYTIQUE'", "0.01%"
    ":math:`{d}_{p}` ", "3 m", "'ANALYTIQUE'", "0.01%"
    ":math:`x({t}_{0})=x(\frac{\pi }{6}+2\sqrt{3}+\frac{\pi +6}{\sqrt{2}})` ", "0m", "'ANALYTIQUE'", "1.e-4m"