3. Modeling A

3.1. Characteristics of modeling

2 elements POU_D_E \({k}_{y}={k}_{z}=1\) \(\phi =0\) by section type

\(\mathrm{S1}\): Rectangular section modelled by SECTION: “GENERALE”

\(\begin{array}{}\begin{array}{cccc}A=0.02& \mathrm{Iy}=0.1666E-4& \mathrm{Iz}=0.6666E-4& {J}_{x}=0.45776E-4\\ & \mathrm{Ry}=0.1& \mathrm{Rz}=0.05& {R}_{T}=0.0892632\end{array}\\ \mathrm{Point}\mathrm{de}\mathrm{calcul}\mathrm{des}\mathrm{contraintes}\end{array}\)

\(\mathrm{S2}\): Corner section

\(\begin{array}{ccc}A=1.856E-3& {I}_{y}=4.167339E-4& {I}_{z}=1.045547E-4\\ {J}_{x}=03.9595E-8& {e}_{y}=41.012E-3& {e}_{z}=0.0\end{array}\)

\(\mathrm{S3}\): Rectangular section modelled by 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. Characteristics of the mesh

\(4\times 2\) mesh SEG_2. The beam is oriented according to the vector \((\mathrm{1,}\mathrm{1,}1)\).

3.3. Tested sizes and results

Load case	Beam	Identification	Reference
\({F}_{x}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({u}_{x}(B)\)	2.887E-10
		\({\theta }_{\mathrm{xx}}(0)\)
	\(\mathrm{S2}\)	\({u}_{x}(B)\)	3.11E-9
	\(\mathrm{S4}\)	\({u}_{x}(B)\)	1.838E-10
		\({\sigma }_{\mathrm{xx}}\)	31.83
\({F}_{y}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({u}_{y}(B)\)	+1.414E-7
		\({\theta }_{z}(B)\)	1.225E-7
		\({\sigma }_{\mathrm{xx}}(0)\)	3000
	\(\mathrm{S2}\)	\({u}_{y}(B)\)	9.017E-8
	\(\mathrm{S4}\)	\({\sigma }_{\mathrm{xx}}(0)\)	2546.479
\({F}_{z}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({u}_{z}(B)\)	6.532E-7
		\({\theta }_{y}(B)\)	-4.243E-7
		\({\sigma }_{\mathrm{xx}}(0)\)	6000
		\({\sigma }_{\mathrm{xz}}(0)\)	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
		\({\sigma }_{\mathrm{xx}}(0)\)	2546.479
		\({\sigma }_{\mathrm{xz}}(0)\)	31.831
\({M}_{x}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({\theta }_{x}(B)\)	3.279E-7
		\({\sigma }_{\mathrm{xy}}={\sigma }_{\mathrm{xz}}(0)\)	1950.0
	\(\mathrm{S2}\)	\({\theta }_{x}(B)\)	3.791E-4
		\({u}_{z}(B)\)	2.199E-5
	\(\mathrm{S4}\)	\({\theta }_{x}(B)\)	9.556E-8
		\({\sigma }_{\mathrm{xy}}={\sigma }_{\mathrm{xz}}(0)\)	636.62
\({M}_{y}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({u}_{z}(B)\)	-4.899E-7
		\({\theta }_{y}(B)\)	4.243E-7
		\({\sigma }_{\mathrm{xx}}(0)\)	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
		\({\sigma }_{\mathrm{xx}}(0)\)	1273.2395
\({M}_{z}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({u}_{y}(B)\)	1.061E-7
		\({\theta }_{z}(B)\)	1.225E-7
		\({\sigma }_{\mathrm{xx}}(0)\)	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
		\({\sigma }_{\mathrm{xx}}(0)\)	1273.2395
\({M}_{y}=1\)	\(\mathrm{S1}=\mathrm{S3}\)	\({\sigma }_{\mathrm{xx}}\mathrm{max}(0)\)	4550.0
\({M}_{z}=1\) \({F}_{x}=1\)		\({\sigma }_{\mathrm{xx}}(\frac{a}{\mathrm{2,}}\frac{b}{2})\)	1550.0
	\(\mathrm{S4}\)	\({\sigma }_{\mathrm{xx}}\mathrm{max}(0)\)	1832.4636
\({F}_{y}=1\)	\(\mathit{S1},\mathit{S3}\)	\({\sigma }_{\mathit{xy}}(0)\)	2000.0
\({F}_{z}=1\)		\({\sigma }_{\mathit{xz}}(0)\)	2000.0
\({M}_{x}=1\)		\({\sigma }_{\mathit{xx}}\mathit{max}(0)\)	9000.0
	\(\mathit{S1},\mathit{S3}\)	\({\sigma }_{\mathit{xx}}\left(\frac{a}{\mathrm{2,}}\frac{b}{2}\right)\)	-9000.0
	\(\mathit{S4}\)	\({\sigma }_{\mathit{xx}}\mathit{max}(0)\)	3601.27
		\({\sigma }_{\mathit{xy}}(0)\)	668.451