B modeling
==============

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


.. image:: images/100002010000022600000162FA671B697B1B65A3.tif
    :width: 3.1665in
    :height: 1.6583in


.. _RefImage_100002010000022600000162FA671B697B1B65A3.tif:

GEOA

GEOB

P1

P4

P3

A

PMB: concrete medium (0.5; 0.5; 0.)

PMA: steel medium (0.5; 0.5; -0.1)

**Modeling**:

**3D** linear elements (GEOB) and **GRILLE_MEMBRANE** elements ** (GEOA) supported on the nodes on the underside.

**Boundary conditions**:

Face :math:`A`: blocked by :math:`\mathit{DX}=0`

Line :math:`\mathit{P1}-\mathit{P4}`: blocked by :math:`\mathit{DZ}=0`

Point :math:`\mathit{P1}`: blocked by :math:`\mathit{DY}=0`

**Thermal load:**

The concrete remains at :math:`20°C`.

Steel goes from :math:`20°C` to :math:`120°C` between the moments :math:`0` and :math:`1`,

In both cases, the reference temperature is :math:`20°C`.

**Note:**

*Compared to other models, a non-linear calculation with the behavior* GRILLE_ISOT_LINE *is added to validate the option* EPSP_ELGA *.*

*The material parameters* ECRO_LINE *used are as follows:* D_ SIGM_EPSI *=* *=* :math:`1E7` *:math:`0.5E11` .*


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

Knots: 243

Meshes: 104 CUB8pour concrete and 52 QUAD4 for steel


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


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Displacement DXau point PMB ", "'ANALYTIQUE'", "7.19892100E-05"," 1.00%"
    "Displacement DZau point PMB ", "'ANALYTIQUE'", "''", "5.35714274E-04"," 1.05%"
    "Stress SIXXdans steel at point PMA ", "'ANALYTIQUE'", "''", "-8.571429E+07"," 1.00%"
    "Stress SIXXdans the concrete at point PMB ", "'ANALYTIQUE'", "''", "4.52857145E+06"," 1.00%"


**Note:**

*The displacement and stress values are evaluated at the center of the plate because in modelling* :math:`\mathrm{3D}` *there are free edge effects at the end, not considered by the analytical solution.*

Validation of EPVC_ELGA, EPME_ELGA and EPSP_ELGA on elastic calculation (the tests on EPSI_ELGA and SIEF_ELGA are used to obtain reference values):


.. csv-table::

    "**Instant**", "**Mesh/Point**", "**Field/Component**", "**Reference Type**", "**Reference Value**", "**Tolerance (%)**"
    "1.0", "M107/1"," EPSI/EXX ","/", "'NON_REGRESSION'", ""
    "1.0", "M107/1"," EPVC/EPTHER_L ","/", "'ANALYTIQUE'", "1.0E-03", "0.1"
    "1.0", "M107/1"," EPME/EXX ","/", "'NON_REGRESSION'", "-"
    "1.0", "M107/1"," EPSP/EXX ","/", "'ANALYTIQUE'", "0. ", "-"


Complementary validation of EPME_ELGA and EPSP_ELGA on an anelastic calculation:


.. csv-table::

    "**Instant**", "**Mesh/Point**", "**Field/Component**", "**Reference Type**", "**Reference Value**", "**Tolerance (%)**"
    "1.0", "M107/1"," SIEF/SIXX ","/", "'NON_REGRESSION'", "-"
    "1.0", "M107/1"," EPME/EPXX ","/", "'NON_REGRESSION'", "-"
    "1.0", "M107/1"," EPSP/EPXX ","/", "'NON_REGRESSION'", "-"