3. Modélisation A#
3.1. Caractéristiques de la modélisation#
2 éléments POU_D_E \({k}_{y}={k}_{z}=1\) \(\phi =0\) par type de section
\(\mathrm{S1}\) : Section rectangulaire modélisée par SECTION : “GENERALE”
\(\begin{array}{}\begin{array}{cccc}A=0.02& \mathrm{Iy}=0.1666E-4& \mathrm{Iz}=0.6666E-4& {J}_{x}=0.45776E-4\\ & \mathrm{Ry}=0.1& \mathrm{Rz}=0.05& {R}_{T}=0.0892632\end{array}\\ \mathrm{Point}\mathrm{de}\mathrm{calcul}\mathrm{des}\mathrm{contraintes}\end{array}\)
\(\mathrm{S2}\) : Section cornière
\(\begin{array}{ccc}A=1.856E-3& {I}_{y}=4.167339E-4& {I}_{z}=1.045547E-4\\ {J}_{x}=03.9595E-8& {e}_{y}=41.012E-3& {e}_{z}=0.0\end{array}\)
\(\mathrm{S3}\) : Section rectangulaire modélisée par SECTION : RECTANGLE
\(\mathrm{Hy}=0.2\) \(\mathrm{Hz}=0.1\)
\(\mathrm{S4}\) : Section CERCLE \(R=0.1\)
\({I}_{Y}={I}_{Z}=\frac{\pi {R}^{4}}{4}=\frac{\pi}{4}{10}^{-4}\)
3.2. Caractéristiques du maillage#
\(4\times 2\) maillesSEG_2. La poutre est orientée selon le vecteur \((1,1,1)\) .
3.3. Grandeurs testées et résultats#
Cas de charge |
Poutre |
Identification |
Référence |
\({F}_{x}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({u}_{x}(B)\) |
2.887E-10 |
\({\theta}_{xx}(0)\) |
|||
\(\mathrm{S2}\) |
\({u}_{x}(B)\) |
3.11E-9 |
|
\(\mathrm{S4}\) |
\({u}_{x}(B)\) |
1.838E-10 |
|
\({\sigma}_{xx}\) |
31.83 |
||
\({F}_{y}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({u}_{y}(B)\) |
+1.414E-7 |
\({\theta}_{z}(B)\) |
1.225E-7 |
||
\({\sigma}_{xx}(0)\) |
3000 |
||
\(\mathrm{S2}\) |
\({u}_{y}(B)\) |
9.017E-8 |
|
\(\mathrm{S4}\) |
\({\sigma}_{xx}(0)\) |
2546.479 |
|
\({F}_{z}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({u}_{z}(B)\) |
6.532E-7 |
\({\theta}_{y}(B)\) |
-4.243E-7 |
||
\({\sigma}_{xx}(0)\) |
6000 |
||
\({\sigma}_{xz}(0)\) |
50 |
||
\(\mathrm{S2}\) |
\({u}_{z}(B)\) |
9.279E-7 |
|
\({\theta}_{y}(B)\) |
1.553E-5 |
||
\({\theta}_{x}(B)\) |
1.555E-5 |
||
\(\mathrm{S4}\) |
\({u}_{z}(B)\) |
1.386E-7 |
|
\({\theta}_{y}(B)\) |
-9E-8 |
||
\({\sigma}_{xx}(0)\) |
2546.479 |
||
\({\sigma}_{xz}(0)\) |
31.831 |
||
\({M}_{x}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({\theta}_{x}(B)\) |
3.279E-7 |
\({\sigma}_{xy}={\sigma}_{xz}(0)\) |
1950.0 |
||
\(\mathrm{S2}\) |
\({\theta}_{x}(B)\) |
3.791E-4 |
|
\({u}_{z}(B)\) |
2.199E-5 |
||
\(\mathrm{S4}\) |
\({\theta}_{x}(B)\) |
9.556E-8 |
|
\({\sigma}_{xy}={\sigma}_{xz}(0)\) |
636.62 |
||
\({M}_{y}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({u}_{z}(B)\) |
-4.899E-7 |
\({\theta}_{y}(B)\) |
4.243E-7 |
||
\({\sigma}_{xx}(0)\) |
3000 |
||
\(\mathrm{S2}\) |
\({u}_{z}(B)\) |
-1.959E-8 |
|
\({\theta}_{y}(B)\) |
1.697E-8 |
||
\(\mathrm{S4}\) |
\({u}_{z}(B)\) |
-1.04E-7 |
|
\({\theta}_{y}(B)\) |
9.0E-8 |
||
\({\sigma}_{xx}(0)\) |
1273.2395 |
||
\({M}_{z}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({u}_{y}(B)\) |
1.061E-7 |
\({\theta}_{z}(B)\) |
1.225E-7 |
||
\({\sigma}_{xx}(0)\) |
1500.0 |
||
\(\mathrm{S2}\) |
\({u}_{y}(B)\) |
6.763E-8 |
|
\({\theta}_{z}(B)\) |
7.809E-8 |
||
\(\mathrm{S4}\) |
\({u}_{y}(B)\) |
9.0E-7 |
|
\({\sigma}_{z}(B)\) |
1.04E-7 |
||
\({\sigma}_{xx}(0)\) |
1273.2395 |
||
\({M}_{y}=1\) |
\(\mathrm{S1}=\mathrm{S3}\) |
\({\sigma}_{xx}\max(0)\) |
4550.0 |
\({M}_{z}=1\) \({F}_{x}=1\) |
\({\sigma}_{xx}(\frac{a}{2,}\frac{b}{2})\) |
1550.0 |
|
\(\mathrm{S4}\) |
\({\sigma}_{xx}\max(0)\) |
1832.4636 |
|
\({F}_{y}=1\) |
\(\mathit{S1},\mathit{S3}\) |
\({\sigma}_{xy}(0)\) |
2000.0 |
\({F}_{z}=1\) |
\({\sigma}_{xz}(0)\) |
2000.0 |
|
\({M}_{x}=1\) |
\({\sigma}_{xx}max(0)\) |
9000.0 |
|
\(\mathit{S1},\mathit{S3}\) |
\({\sigma}_{xx}\left(\frac{a}{2,}\frac{b}{2}\right)\) |
-9000.0 |
|
\(\mathit{S4}\) |
\({\sigma}_{xx}max(0)\) |
3601.27 |
|
\({\sigma}_{xy}(0)\) |
668.451 |