Modeling A
==============


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

A single element based on a QUAD4 mesh, in D_ PLAN.


.. image:: images/100003E6000016040000138942F2B161FB87F9EC.svg
    :width: 213
    :height: 187


.. _RefImage_100003E6000016040000138942F2B161FB87F9EC.svg:

Loading and boundary conditions are modelled by:

DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)

DDL_IMPO: (NOEUD: N03, DX: 0.)

FORCE_NODALE: (NOEUD; (N01 N02), FX: :math:`-\frac{1}{2}{\sigma }_{d}(t)`, FY: :math:`-\frac{1}{2}{\tau }_{d}(t)`)

FORCE_NODALE: (NOEUD; (N01 N04), FX: :math:`-\frac{1}{2}{\tau }_{d}(t)`)

FORCE_NODALE: (NOEUD; (N03 N04), FY: :math:`\frac{1}{2}{\tau }_{d}(t)`)

FORCE_NODALE: (NOEUD; (N02 N03), FX: :math:`\frac{1}{2}{\tau }_{d}(t)`)

where :math:`{\sigma }_{d}(t)` and :math:`{\tau }_{d}(t)` are the positive functions defined above [:ref:`§1.3 <§1.3>`].


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

Behavior LEMAITRE (THETA =0.5)


.. csv-table::

    "**Variables**", "**Moment (s)**", "**Reference**", "**Tolerance**"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xx}}}` ", "30", "1.7620 10—4"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xy}}}` ", "30", "1.81585 10—4"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xx}}}` ", "3630", "1.9030 10—3"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xy}}}` ", "3630", "2.0789 10—3"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xx}}}` ", "3660", "1.9130 10—3"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xy}}}` ", "3660", "2.1906 10—3"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xx}}}` ", "3720", "1.8740 10—3"," 0.5%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xy}}}` ", "3720", "3.1813 10—3"," 0.5%"


Behavior VISC_ENDO_LEMA (with 10 times finer temporal discretization)


.. csv-table::

    "**Variables**", "**Moment (s)**", "**Reference**", "**Tolerance**"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xx}}}` ", "30", "1.762 10—4"," 0.7%"
    ":math:`{\varepsilon }_{{\nu }_{\mathrm{xy}}}` ", "30", "1.816 10—4"," 0.7%"