6. D modeling

6.1. 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:

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

with \(r=\sqrt{{X}^{2}+{Y}^{2}}\)

6.2. Characteristics of the mesh

Number of knots: 405

Number of meshes and types: 100 QUAD8

6.3. Tested sizes and results

Identification	Reference
\(\mathrm{DX}\) in \(L\)	10.341 10—3
\(\mathrm{DY}\) in \(L\)	10.341 10—3