B, C, D, E models
========================

Boundary conditions and loads
-------------------------------------

The acceleration condition is a function of time:

:math:`{A}_{0}.\mathrm{sin}(2\pi .\mathit{f.t})` with :math:`f=5\mathit{Hz};{A}_{0}=1.0m/{s}^{2}` for 4 periods i.e. :math:`t\in [0,\mathrm{0.8sec}]`

then

:math:`0` for :math:`t\in [\mathrm{0.8sec},\mathrm{3.2sec}]`


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    :width: 6.3374in
    :height: 2.0772in


.. _RefImage_10000000000003100000010156AF4181B1770E5F.png:

In command DYNA_NON_LINE the time diagram is: for modeling B type NEWMARK (average acceleration).

In command DYNA_VIBRA the time diagram is: for C modeling type EULER, for modeling D type RK54, for modeling E type RK32.


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

The quantities tested are displacement and effort.

The displacement and force functions are extracted from the results and subtracted from the displacement and force functions obtained by a method of integrating the problem external to *Code_Aster*. These new functions are normalized by the maximum value of either movements or efforts. The quantity tested is the maximum deviation.

This gives for the trip:

:math:`\mathit{Grandeur}\mathit{testée}=\frac{\mathit{Max}[{\mathit{Depl}}_{\mathit{Externe}}(\mathit{Temps})–{\mathit{Depl}}_{\text{Code\_Aster}}(\mathit{Temps})]}{\mathit{Max}[{\mathit{Depl}}_{\mathit{Externe}}(\mathit{Temps})]}`

Tolerances are by default.


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    :width: 5.9055in
    :height: 4.1693in


.. _RefImage_100000000000034A000002532AF3C9A301BBD858.png:

**Figure** 4.2-a **: Responses (displacement over time) calculated by an external method** **and by** **Code_Aster** **with the commands** **DYNA_NON_LINEet** **** DYNA_VIBRA. **


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    :width: 5.9055in
    :height: 4.1693in


.. _RefImage_100000000000034A0000025389EB9C358CAD79E6.png:

**Figure** 4.2-b **: Responses (strength as a function of time), calculated by an external method and** **by** **Code_Aster** **with the commands** **DYNA_NON_LINEet** **DYNA_VIBRA.**


.. image:: images/100000000000034A0000025393659EB07FE4CBE0.png
    :width: 5.9055in
    :height: 4.1693in


.. _RefImage_100000000000034A0000025393659EB07FE4CBE0.png:

**Figure** 4.2-c **: Responses (Force as a function of displacement), calculated by an external method and** **by** **Code_Aster** **with the commands** **DYNA_NON_LINEet** **DYNA_VIBRA.**