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

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


.. image:: images/100000000000011C000000D7038EF5011D44D4C8.png
    :width: 2.3571in
    :height: 1.7709in


.. _RefImage_100000000000011C000000D7038EF5011D44D4C8.png:

The arch is meshed using POU_D_E straight beam elements.

Boundary conditions:

• At point :math:`A` such as :math:`X\mathrm{=}R`, :math:`Y\mathrm{=}0`: :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0`, and :math:`\mathit{RY}\mathrm{=}0`

• At point :math:`B` such as :math:`X\mathrm{=}0`, :math:`Y\mathrm{=}R`: :math:`\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0`, and :math:`\mathit{RX}\mathrm{=}0`

For static analysis, unit moments around :math:`Z` are defined at nodes 1 and 19.


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

Number of knots: 19

Number of stitches: 18 POU_D_E


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

Critical load


CALC_MODES with SOLVEUR_MODAL =_F (METHODE = 'SORENSEN')
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. csv-table::

    "**Identification**
    **Critical load number**", "**Reference**", "**Code_Aster**", ":math:`\text{\%}` **difference**"
    "1", "2.86074", "2.75137", "3.823"
    "2", "8.63207", "8.30613", "3.776"
    "3", "-8.78382", "-8.39554", "4.420"
    "4", "14.4147", "13.93216", "3.348"
    "5", "-14.5551", "-14.01104", "3.738"



CALC_MODES with OPTION = 'PROCHE'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. csv-table::

    "**Identification**
    **Critical load number**", "**Reference**", "**Code_Aster**", ":math:`\text{\%}` **difference**"
    "1", "2.86074", "2.75137", "3.823"
    "2", "8.63207", "8.30613", "3.776"
    "3", "-8.78382", "-8.39554", "4.420"
    "4", "14.4147", "13.93216", "3.348"
    "5", "-14.5551", "-14.01104", "3.738"



CALC_MODES with OPTION = 'SEPARE'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. csv-table::

    "**Identification**
    **Critical load number**", "**Reference**", "**Code_Aster**", ":math:`\text{\%}` **difference**"
    "1", "2.86074", "2.75137", "3.823"
    "2", "8.63207", "8.30613", "3.776"
    "3", "-8.78382", "-8.39554", "4.420"
    "4", "14.4147", "13.93216", "3.348"
    "5", "-14.5551", "-14.01104", "3.738"



CALC_MODES with OPTION = 'AJUSTE'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. csv-table::

    "**Identification**
    **Critical load number**", "**Reference**", "**Code_Aster**", ":math:`\text{\%}` **difference**"
    "1", "2.86074", "2.75137", "3.823"
    "2", "8.63207", "8.30613", "3.776"
    "3", "-8.78382", "-8.39554", "4.420"
    "4", "14.4147", "13.93216", "3.348"
    "5", "-14.5551", "-14.01104", "3.738"