.. _V2.01.031:

**v2.01.031** SDLD31 - Elementary validation of time diagrams in dynamics
===============================================================================

**Summary:**

This test case makes it possible to validate the programming of integration diagrams in time in DYNA_NON_LINE and DYNA_VIBRA.

More specifically, for DYNA_NON_LINE we test the following implicit schemes:


1. average acceleration (keyword NEWMARK) with resolution when moving and accelerating;


2. modified average acceleration (keyword HHT with MODI_EQUI =' NON ');


3. HHT complete (HHT keyword with MODI_EQUI =' OUI ');

With the complete HHT diagram, we also test the pursuits because this schema requires a particular initialization. Likewise, we also validate the pursuits for average acceleration with acceleration resolution because it is not tested in other test cases.

As for DYNA_VIBRA, the schemes with constant time steps are tested, i.e.:


1. explicit order 1 diagram says EULER;


2. implicit schema NEWMARK of order 2;


3. Explicit order 4 diagram says DEVOGELAERE

The aim being to study the behavior of the patterns over time, the problem chosen is deliberately very simple: it is a linear system with 1 degree of freedom mass-spring which is subjected to a sinusoidal force.

The reference solution is obtained by re-programming the integration diagrams in Matlab and by calculating the analytical solution.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_mes_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A_-_DYNA_NON_LINE
    Mod_lisations_B_et_C_-_DYNA_VIBRA
    Synth_se_des_r_sultats