D modeling
==============


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

Modeling DKT. We mesh only half of the cylinder (symmetry with respect to plane :math:`y=0`) 30 mesh QUAD4 in the height and 60 on the half-circumference.


.. image:: images/100000000000021A0000038E7D3C7A498A4E3653.png
    :width: 2.6902in
    :height: 4.55in


.. _RefImage_100000000000021A0000038E7D3C7A498A4E3653.png:


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

Number of knots: 1894

Number of meshes and types: 1800 QUAD4

Note:

To obtain a precise solution to this problem, it is necessary to use a fairly refined mesh (here 1800 QUAD4).

The following errors are observed as a function of discretization:


.. csv-table::

    "Number of items", "Maximum displacement error"
    "450 QUAD4 "," 0.5%"
    "1800 QUAD4 "," 0.2%"
    "900 TRIA3 "," 17%"
    "3600 TRIA3 "," 1.4%"


It can be seen that for this problem, meshing in quadrangles is preferable.


Tested values
---------------

Isotropic material


.. csv-table::

    "**Value**", "**Identification**", "**Reference**"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DY}(\mathrm{PM})` ", "5.8018E—05"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DX}(\mathrm{A1})` ", "5.8018E—05"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DX}(\mathrm{A2})` ", "—5.8018E—05"
    ":math:`\mathrm{Uz}(z=L)` "," :math:`\mathrm{DZ}(\mathrm{A3})` ", "—2.4429E—05"
    ":math:`\mathrm{Uz}(z=L)` "," :math:`\mathrm{DZ}(\mathrm{A4})` ", "—2.4429E—05"
    ":math:`\mathrm{SigmaTT}(z=0)` "," :math:`\mathrm{SIZZ}(\mathrm{PM})` ", "2.1375E+06"


Orthotropic material


.. csv-table::

    "**Value**", "**Identification**", "**Reference**"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DY}(\mathrm{PM})` ", "5.8018E—05"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DX}(\mathrm{A1})` ", "5.8018E—05"
    ":math:`\mathrm{Ur}(z=0)` "," :math:`\mathrm{DX}(\mathrm{A2})` ", "—5.8018E—05"
    ":math:`\mathrm{Uz}(z=L)` "," :math:`\mathrm{DZ}(\mathrm{A3})` ", "—6.10714E—06"
    ":math:`\mathrm{Uz}(z=L)` "," :math:`\mathrm{DZ}(\mathrm{A4})` ", "—6.10714E—06"
    ":math:`\mathrm{SigmaTT}(z=0)` "," :math:`\mathrm{SIZZ}(\mathrm{PM})` ", "2.1375E+06"