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


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

It is a modeling in plane constraints.

Y, V

D

B

C1

X, U

O

C

A

B1

Decoupage: :math:`4\mathrm{\times }4` elements

Boundary conditions:


1. in :math:`O`, :math:`u\mathrm{=}v\mathrm{=}0`


2. in :math:`B`, :math:`u\mathrm{=}0`


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

Number of knots: 65

Number of meshes and type: 16 QUAD8

Node name


.. csv-table::

    ":math:`O=\mathrm{N38}` "," :math:`A=\mathrm{N1}` "," :math:`B\mathrm{=}\mathit{N23}` "," :math:`C=\mathrm{N16}` "," "," :math:`D=\mathrm{N3}` "," :math:`\mathrm{B1}=\mathrm{N9}` "," :math:`\mathrm{C1}=\mathrm{N30}`"



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


.. csv-table::

    "**Location**", "**Value type**", "**Reference**"
    "Point :math:`A` "," :math:`T` ", "75."
    "Point :math:`B` "," :math:`T` ", "25."
    "Point :math:`C` "," :math:`T` ", "20."
    "Point :math:`D` "," :math:`T` ", "5."
    "Point :math:`\mathrm{B1}` "," :math:`T` ", "55."
    "Point :math:`\mathrm{C1}` "," :math:`T` ", "60."
    "Point :math:`O` "," :math:`T` ", "40."
    "Point :math:`A` "," :math:`u` ", "2.68975"
    "", ":math:`v` ", "2.55"
    "Point :math:`B` "," :math:`u` ", "0."
    "", ":math:`v` ", "-2.65125"
    "Point :math:`C` "," :math:`u` ", "-2.695"
    "Point :math:`D` "," :math:`u` ", "-2.7002"
    "", ":math:`v` ", "-2.695"
    "Point :math:`\mathrm{B1}` "," :math:`u` ", "0.0700"
    "", ":math:`v` ", "2.59875"
    "Point :math:`\mathrm{C1}` "," :math:`u` ", "2.625"



notes
---------

It is necessary to finely discretize function :math:`E(t)` in order to obtain satisfactory results. For this test, 160 discretization points were taken, for the temperature range [:ref:`5., 75. <5., 75.>`].