E modeling
==============


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

A D_ PLAN modeling is used with the element type QUAD4 and the contact processing method LAC.


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

A convergence study is carried out with the fineness of the mesh from the calculated solution to the analytical solution. A series of meshes obtained by uniform refinement using the MACR_ADAP_MAIL command is used:


* mesh 0:6 SEG2, 4 QUAD4


* mesh 1:12 SEG2, 10 QUAD4


* mesh 2:24 SEG2, 28 QUAD4


* mesh 3:48 SEG2, 88 QUAD4


* mesh 4:96 SEG2, 304 QUAD4


* mesh 5:192 SEG2, 1120 QUAD4

The curved :math:`\text{MAITRE}` surface is represented by a single SEG3.


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

The convergence speed is tested with the fineness of the mesh from the calculated solution to the analytical solution in standard :math:`{L}_{2}`:


* the largest real :math:`{\alpha }_{U}>0` such as :math:`{\parallel {\underline{U}}^{\text{calc}}-{\underline{U}}^{\text{ref}}\parallel }_{\mathrm{0,}\Omega }<{C}_{U}\times {h}^{{\alpha }_{U}}` where :math:`{C}_{U}` is independent of :math:`h` for displacement;


* the largest real :math:`{\alpha }_{p}>0` such as :math:`{\parallel {p}^{\text{calc}}-{p}^{\text{ref}}\parallel }_{\mathrm{0,}{\Gamma }_{C}}<{C}_{p}\times {h}^{{\alpha }_{p}}` where :math:`{C}_{p}` is independent of :math:`h` for contact pressure.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**"
    ":math:`{\alpha }_{U}` ", "'ANALYTIQUE'", "2.0"
    ":math:`{\alpha }_{p}` ", "'ANALYTIQUE'", "0.5"