8. F modeling#

8.1. Characteristics of modeling#

1 elements TUYAU_3M with 4 nodes, calculation with STAT_NON_LINE.

8.2. Characteristics of the mesh#

1 SEG4 mesh. The beam is oriented according to the vector (4, 3, 0).

8.3. Note on the content of the fields#

The stress fields at the Gauss points for element TUYAU, SIEF_ELGA, in the element’s local coordinate system, are organized as follows:

We store the values:

for each Gauss point in the length, \((n=\mathrm{1,}3)\)

for each integration point in the thickness, \((n=\mathrm{1,}{\mathrm{2N}}_{\mathrm{COU}}+1)\)

for each integration point on the circumference, \((n=\mathrm{1,}{\mathrm{2N}}_{\mathrm{SECT}}+1)\)

6 deformation or stress components:

EPXX EPYY EPZZ EPXY EPXZ EPYZ or

SIXX SIYY SIZZ SIXY SIXZ SIYZ

where \(X\) refers to the direction given by the element’s two vertex nodes, \(Y\) represents the angle \(\phi\) describing the circumference, and \(Z\) represents the radius. EPZZ and EPYZ corresponding to \({\epsilon }_{\mathrm{rr}}\), \({\epsilon }_{r\phi }\) in the case of deformations and SIZZ and SIYZ corresponding to \({\sigma }_{\mathrm{rr}}\), \({\sigma }_{r\phi }\) in the case of constraints are taken equal to zero.

In STAT_NON_LINE, the number of layers is variable, as is the number of sectors. Here, 3 layers and 16 sectors are used by analogy with modeling A.

8.4. Quantities tested and results of the F modeling#

Load case	Size	Reference	% difference
1	XX	5.53E—06	—0.04
1	DY	4.14E—06	—0.04
2	DRZ	2.63E—02	—0.04
2	XX	—5.27E—02	—0.02
2	DY	7.02E—02	—0.02
3	DRX	1.58E—02	—0.04
3	DRY	—2.11E—02	—0.02
3	DZ	8.78E—02	—0.04
4	DRX	1.10E—02	0
4	DRY	8.21E—03	0
5	DRX	—6.32E—03	—0.04
5	DRY	8.42E—03	—0.04
5	DZ	—2.63E—02	—0.04
6	DRZ	1.05E—02	—0.04
6	XX	—1.58E—02	—0.04
6	DY	2.11E—02	—0.04
7	WO	7.38E—06	—3.3

Case of load	Field	Mesh	Point	Component	Reference	% difference
1	SIEF_ELGA	M18	z	z	SIXX	2.76E+05	—1.159
1	EFGE_ELNO	M18	1	1	N	5.00E+02	0.136
4	SIEF_ELGA	M18	1	1	SIXY	—6.75E+06	—0.159
4	SIEF_ELGA	M18	693	693	SIXY	—8.42E+06	0.049
4	EFGE_ELNO	M18	1	1	MT	5.00E+02	0
5	SIEF_ELGA	M18	479	479	SIXX	1.35E+07	—1.288
5	EFGE_ELNO	M18	1	1	MFY	5.00E+02	0.123
6	SIEF_ELGA	M18	471	471	SIXX	1.35E+07	—1.288
6	EFGE_ELNO	M18	1	1	MFZ	5.00E+02	0.123
7	SIEF_ELGA	M18	1	1	SIYY	4.56E+07	—0.641
7	SIEF_ELGA	M18	693	693	SIYY	3.56E+07	—0.371

Generalized deformations DEGE_ELNO:

Load case	Loads	Size	Reference	% difference
1	\({F}_{X}={4.10}^{2}\)	\(\mathrm{EPXX}\)	1.38155E-06	—0.04
	\({F}_{Y}={3.10}^{2}\)
2	\({F}_{X}=–{3.10}^{2}\)	\(\mathrm{GAXY}\)	3.5920E-06	21
	\({F}_{Y}={4.10}^{2}\)	\(\mathrm{KZ}\)	1.0530E—02	—0.04
3	\({F}_{Z}={5.10}^{2}\)	\(\mathrm{GAXZ}\)	3.5920E-06	21
		\(\mathrm{KY}\)	—1.0530E—02	—0.04
4	\({M}_{X}={4.10}^{2}\)	\(\mathrm{GAT}\)	2.73783E-03	0
	\({M}_{Y}={3.10}^{2}\)
5	\({M}_{X}=–{3.10}^{2}\)	\(\mathrm{KY}\)	2.1060E-03	—0.04
	\({M}_{Y}={4.10}^{2}\)
6	\({M}_{Z}=5{10}^{2}\)	\(\mathrm{KZ}\)	2.1060E-03	—0.04

8.5. notes#

The shear values corresponding to the shear force are not accurate for this modeling. This is due to the low discretization for this modeling (only one element).