N modeling
==============




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

Anticlastic flexure

Modeling: DKTG. :math:`L=1.0m`.


.. image:: images/1000020000000131000000F1568056C23582F307.png
    :width: 2.6346in
    :height: 1.9193in


.. _RefImage_1000020000000131000000F1568056C23582F307.png:

Figure 16.1-a: mesh

Boundary conditions (see figure below):


.. image:: images/Cadre32.gif


.. _RefSchema_Cadre32.gif:

DX=0

DZ= XYD0

**Figure** 16.1-b **: Boundary Conditions**


* we impose an embedding in :math:`{A}_{1}`, and we block the point :math:`B` in its movement according to :math:`\mathrm{Ox}`.


* :math:`{u}_{z}={D}_{0}\cdot y\cdot x` on all four edges :math:`{A}_{1}-{A}_{3}`, :math:`{A}_{1}-{A}_{2}`,, :math:`{A}_{2}-{A}_{4}`, and :math:`{A}_{3}-{A}_{4}`

where :math:`{D}_{0}=3.0{10}^{-2}\cdot f(t)`, and :math:`f(t)` represent the magnitude of cyclic loading as a function of the (pseudo-time) parameter :math:`t`, defined as:


.. image:: images/10000000000001F8000001201AA96929C8D1ABF2.png
    :width: 5.2508in
    :height: 3.0008in


.. _RefImage_10000000000001F8000001201AA96929C8D1ABF2.png:

The deformation of such an anticlastic flexure test is of the horse saddle type as presented below:


.. image:: images/10000000000004580000019DAA29D50C3D084587.jpg
    :width: 3.4736in
    :height: 1.811in


.. _RefImage_10000000000004580000019DAA29D50C3D084587.jpg:




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

Number of knots: 121.

Number of stitches: 200 TRIA3; 40 SEG2.




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

The results obtained by modeling DHRC are evaluated by non-regression tests at various times:


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**", "**tolerance**"
    "To :math:`t=\mathrm{0,05}` ", "", "", ""
    "*Moment* :math:`\mathit{MXY}` *en* :math:`B` "," NON_REGRESSION "," ", "4282.65341065", "1 10-6"
    "To :math:`t=\mathrm{0,5}` ", "", "", ""
    "*Moment* :math:`\mathit{MXY}` *en* :math:`B` "," NON_REGRESSION "," ", "30025.5726844", "1 10-6"
    "To :math:`t=\mathrm{1,5}` ", "", "", ""
    "*Moment* :math:`\mathit{MXY}` *en* :math:`B` "," NON_REGRESSION "," ", "27953.608413", "1 10-6"
    "To :math:`t=\mathrm{3,0}` ", "", "", ""
    "*Moment* :math:`\mathit{MXY}` *en* :math:`B` "," NON_REGRESSION "," ", "-55907.216826", "1 10-6"
    "To :math:`t=\mathrm{3,5}` ", "", "", ""
    "*Moment* :math:`\mathit{MXY}` *en* :math:`B` "," NON_REGRESSION "," ", "-27953.608413", "1 10-6"



.. _RefNumPara__30394423:


.. _refnumpara__30394423: