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


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

**Elements D_ PLAN** MEDPQU8

Mesh comprising 2 elements depending on the width, 50 elements according to the length.

100 items in total

In 2D, the movements of the beam are written as:

:math:`\begin{array}{}\\ \begin{array}{}{U}_{x}(X,Y)=\frac{\rho {\omega }^{2}}{2\sqrt{2}E}(r{L}^{2}-\frac{{r}^{3}}{3})\\ {U}_{y}(X,Y)=\frac{\rho {\omega }^{2}}{2\sqrt{2}E}(r{L}^{2}-\frac{{r}^{3}}{3})\\ \end{array}\end{array}`

with :math:`r=\sqrt{{X}^{2}+{Y}^{2}}`


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

Number of knots: 405

Number of meshes and types: 100 QUAD8


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


.. csv-table::

    "**Identification**", "**Reference**"
    ":math:`\mathrm{DX}` in :math:`L` ", "10.341 10—3"
    ":math:`\mathrm{DY}` in :math:`L` ", "10.341 10—3"