B and C models
====================


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

B and C models are the same except that B modeling uses DIS_TR elements while C modeling uses 2D_ DIS_TR elements.

This modeling allows, in addition to a new use of modal recombination, the validation of direct integration at adaptive steps.

**Discrete element of stiffness in translation and rotation**


.. image:: images/10000DF000001FF0000006345695854C605BA72A.svg
    :width: 412
    :height: 80


.. _RefImage_10000DF000001FF0000006345695854C605BA72A.svg:

Characteristics of the elements:


.. csv-table::

    "DISCRET:", "with nodal masses", "M_ TR_D_N ", "M_ TR_N"
    "", "and stiffness matrices", "K_ TR_D_L ", "K_ TR_L"
    "", "and damping matrices", "A_ TR_D_L ", "A_ TR_L"


Boundary conditions and blocked directions:


.. csv-table::

    "in all nodes", "DDL_IMPO:", "(TOUT: 'OUI' DY: 0., DZ: 0.)
    (TOUT: 'OUI' DRX: 0. DRY: 0 DRZ: 0)"
    "at the end nodes", "", "(GROUP_NO: AB DX: 0.)"


Integration schemes tested in this release:


* Integration by modal recombination with the Euler schema.


* Integration by direct integration with algorithm ADAPT_ORDRE2, no maximum time :math:`{10}^{-3}s`.


* Integration by modal recombination with schema RUNGE_KUTTA_32, with a relative error tolerance of :math:`{10}^{-3}s` and a maximum time step of :math:`{10}^{-3}s`.


* Integration by modal recombination with schema RUNGE_KUTTA_54, with a relative error tolerance of :math:`{10}^{-3}s` and a maximum time step of :math:`{10}^{-3}s`.


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

Number of knots: 10

Number of meshes and types: 9 SEG2


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

**Transient by modal recombination with algorithm EULER**


.. csv-table::

    "**Time**", "**Reference**"
    "0.09", "4.02 E—5"
    "0.18", "4.22 E—6"
    "0.27", "3.89 E—5"
    "0.37", "5.98 E—6"
    "0.46", "3.73 E—5"
    "0.54", "7.14 E—6"
    "0.63", "3.64 E—5"
    "0.72", "8.07 E—6"
    "0.81", "3.58 E—5"
    "0.9", "8.76 E—6"
    "0.99", "3.52 E—5"
    "1.08", "—3.08 E—5"
    "1.18", "3.02 E—5"
    "1.27", "—2.88 E—5"
    "1.36", "2.80 E—5"
    "1.45", "—2.65 E—5"


Transient by direct integration with algorithm ADAPT_ORDRE2


.. csv-table::

    "**Time**", "**Reference**"
    "0.09", "4.02 E—5"
    "0.18", "4.22 E—6"
    "0.27", "3.89 E—5"
    "0.37", "5.98 E—6"
    "0.46", "3.73 E—5"
    "0.54", "7.14 E—6"
    "0.63", "3.64 E—5"
    "0.72", "8.07 E—6"
    "0.81", "3.58 E—5"
    "0.9", "8.76 E—6"
    "0.99", "3.52 E—5"
    "1.08", "—3.08 E—5"
    "1.18", "3.02 E—5"
    "1.27", "—2.88 E—5"
    "1.36", "2.80 E—5"
    "1.45", "—2.65 E—5"


**Transient by modal recombination** with algorithm RUNGE_KUTTA_32


.. csv-table::

    "**Time**", "**Reference**"
    "0.09", "4.02 E—5"
    "0.18", "4.22 E—6"
    "0.27", "3.89 E—5"
    "0.37", "5.98 E—6"
    "0.46", "3.73 E—5"
    "0.54", "7.14 E—6"
    "0.63", "3.64 E—5"
    "0.72", "8.07 E—6"
    "0.81", "3.58 E—5"
    "0.9", "8.76 E—6"
    "0.99", "3.52 E—5"
    "1.08", "—3.08 E—5"
    "1.18", "3.02 E—5"
    "1.27", "—2.88 E—5"
    "1.36", "2.80 E—5"
    "1.45", "—2.65 E—5"


**Transient by modal recombination** with algorithm RUNGE_KUTTA_54


.. csv-table::

    "**Time**", "**Reference**"
    "0.09", "4.02 E—5"
    "0.18", "4.22 E—6"
    "0.27", "3.89 E—5"
    "0.37", "5.98 E—6"
    "0.46", "3.73 E—5"
    "0.54", "7.14 E—6"
    "0.63", "3.64 E—5"
    "0.72", "8.07 E—6"
    "0.81", "3.58 E—5"
    "0.9", "8.76 E—6"
    "0.99", "3.52 E—5"
    "1.08", "—3.08 E—5"
    "1.18", "3.02 E—5"
    "1.27", "—2.88 E—5"
    "1.36", "2.80 E—5"
    "1.45", "—2.65 E—5"



notes
---------

The A and B models lead to the same results.

The relative minima (:math:`t=0.18,0.54,\dots`) do not have very good precision during the excitation phase with a :math:`\Delta t=0.001` step.