M modeling
==============




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

Flexion-shear coupling in the plane.


.. image:: images/1000020000000131000000F1568056C23582F307.png
    :width: 2.7638in
    :height: 2.2819in


.. _RefImage_1000020000000131000000F1568056C23582F307.png:

Figure 15.1-a: mesh

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

Boundary conditions (see figure below):


.. image:: images/10000200000002A9000001237C4BFB344F7F3898.png
    :width: 5.9043in
    :height: 2.4035in


.. _RefImage_10000200000002A9000001237C4BFB344F7F3898.png:

Figure 15.1-b: Boundary conditions


* we impose an embedding in :math:`{A}_{1}`, and::


* :math:`{u}_{x}={D}_{0}\cdot y,{u}_{y}=0` on edge :math:`{A}_{1}-{A}_{3}`, :math:`{u}_{x}=0,{u}_{y}={D}_{0}\cdot x` and :math:`\mathrm{DRY}=0.0` on edge :math:`{A}_{1}-{A}_{2}`


* :math:`{u}_{x}={D}_{0}\cdot y,{u}_{y}={D}_{0}\cdot L` and DRY = :math:`{R}_{0}` × :math:`f(t)` on edge :math:`{A}_{2}-{A}_{4}`, :math:`{u}_{x}={D}_{0}\cdot L,{u}_{y}={D}_{0}\cdot x` on edge :math:`{A}_{3}-{A}_{4}`,

where :math:`{D}_{0}=3.3{10}^{-3}\cdot f(t)`, :math:`{R}_{0}=3.0{10}^{-2}`, 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: 4.7252in
    :height: 2.5945in


.. _RefImage_10000000000001F8000001201AA96929C8D1ABF2.png:




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

Number of knots: 121.

Number of stitches: 200 TRIA3; 40 SEG2.




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

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


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**", "**tolerance**"
    "At t=1,0", "", "", ""
    "*Movement* :math:`\mathrm{DX}` *in* :math:`\mathrm{A2}` "," NON_REGRESSION ", "0", "1 10-6"
    "*Move* :math:`\mathrm{DZ}` *en* :math:`\mathrm{A2}` "," NON_REGRESSION "," ", "-0.0150132720825", "1 10-4"
    "*Effort* :math:`{N}_{\mathrm{yy}}` *in* :math:`\mathrm{A2}` "," NON_REGRESSION "," ", "336025.268865", "1 10-4"
    "Damage variable :math:`\mathrm{d1}` in :math:`\mathrm{A1}` "," NON_REGRESSION "," ", "56.9559592676", "1 10-4"
    "Damage variable :math:`\mathrm{d2}` in :math:`\mathrm{A1}` "," NON_REGRESSION "," ", "59.5462291219", "1 10-4"
    "To :math:`t=\mathrm{2,8}` ", "", "", ""
    "*Movement* :math:`\mathrm{DX}` *in* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "-0.00264", "1 10-4"
    "*Movement* :math:`\mathrm{DZ}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION ", "0.010135582881", "1 10-4"
    "*Effort* :math:`{N}_{\mathrm{yy}}` *in* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "-268829.505848", "1 10-4"
    "Damage variable :math:`\mathrm{d1}` in :math:`\mathit{A1}` "," NON_REGRESSION "," ", "56.9559592676", "1 10-4"
    "Damage variable :math:`\mathit{d2}` in :math:`\mathit{A1}` "," NON_REGRESSION "," ", "59.5462291219", "1 10-4"
    "To :math:`t=\mathrm{3,0}` ", "", "", ""
    "Damage variable :math:`\mathit{d1}` in :math:`\mathit{A1}` "," NON_REGRESSION "," ", "59.4924066054", "1 10-4"
    "Damage variable :math:`\mathit{d2}` in :math:`\mathit{A1}` "," NON_REGRESSION "," ", "59.5462291219", "1 10-4"


**Comparative diagrams multilayer model-modell** **** GLRC_DM - model**** DHRC ****of the shear force bending moment**:math:`{N}_{\mathit{xy}}`**as a function of the distortion: **


.. image:: images/10000000000001F800000120AC7034389DF73B98.png
    :width: 5.2508in
    :height: 3.0008in


.. _RefImage_10000000000001F800000120AC7034389DF73B98.png:

Comparative diagrams multi-layer model GLRC_DM **- model**- model** DHRC of the bending moment :math:`{M}_{\mathit{yy}}` as a function of rotation:


.. image:: images/100000000000020100000120910198B14934C1B7.png
    :width: 5.3445in
    :height: 3.0008in


.. _RefImage_100000000000020100000120910198B14934C1B7.png:




.. _refnumpara__30394215: