.. _r5.05.05:

**r5.05.05** Dynamic nonlinear algorithm
===============================================

**Summary:**

The operator DYNA_NON_LINE [:ref:`DYNA_NON_LINE <U4.53.01>`] is used for the nonlinear dynamic analysis of structures by direct integration in time. Nonlinearities can come from the behavior of the material, from the connections (touch-friction), or from large geometric transformations (large displacements and large rotations).

The organization of DYNA_NON_LINE is very similar to that of the quasistatic nonlinear operator STAT_NON_LINE [:ref:`R5.03.01 <R5.03.01>`]. *Prioritily*, all behavioral relationships developed in the context of STAT_NON_LINE work in that of DYNA_NON_LINE.

The general formulation of the nonlinear dynamic problem is presented here in order to specify the joints between purely dynamic aspects and those already treated in other operators or formulations available in *Code_Aster*: management of boundary conditions, fluid-structure couplings, damping, damping, damping, calculation in relative coordinate systems, then the properties of the temporal numerical integration scheme, which is developed independently of any behavioral relationship. We explain how this one is articulated with Newton's algorithm to deal with material and geometric nonlinearities.

We have three complementary and effective implicit time schemes:


* the Newmark family,


* the modified average acceleration ("HHT" in DYNA_NON_LINE, with the option MODI_EQUI =' NON '),


* the complete HHT diagram ("HHT" in DYNA_NON_LINE, with the option MODI_EQUI =' OUI '), as well as its "without overshooting" version proposed in [:ref:`bib35 <bib35>`] (' NOHHT 'in DYNA_NON_LINE).


The operator also proposes two explicit diagrams:

* the central differences,

* the Tchamwa-Wielgosz dissipative diagram.

We give some tips for good use that the documentation [:ref:`Conseils généraux d’utilisation de l’opérateur DYNA_NON_LINE <U2.06.13>`] complements.


.. toctree::
    :hidden:

    self

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

    Notations
    Dynamique_non_lin_aire___discr_tisation_spatiale_du_probl_me_continu
    Sch_ma_d_int_gration_temporelle___sch_ma_de_NEWMARK_et_m_thode_de_NEWTON
    Qualit_s_et_d_fauts_du_sch_ma_de_NEWMARK
    Une_variante_du_sch_ma_de_NEWMARK___les_sch_mas_HHT_et_d_acc_l_ration_moyenne_modifi_e
    Les_sch_mas_explicites
    Shift_de_masse
    Exemple
    Conclusion
    Bibliographie