6. D modeling

6.1. Characteristics of modeling

10 elements TUYAU_6M, calculation with STAT_NON_LINE.

6.2. Characteristics of the mesh

10 SEG3 stitches. The beam is oriented according to the vector (4, 3, 0).

6.3. Note on field content

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.

6.4. Quantities tested and results of modeling D

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	—0.056
2	DY	7.02E—02	—0.056
3	DRX	1.58E—02	—0.04
3	DRY	—2.11E—02	—0.039
3	DZ	8.78E—02	—0.056
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	—0.039
6	XX	—1.58E—02	—0.04
6	DY	2.11E—02	—0.039
7	WO	7.38E—06	—2.946

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	FX= 4.102	EPXX		1.38155E-06	—0.04
	FY= 3.102
2	FX= —3.102	GAXY	3.5920E-06	32
	FY= 4.102	KZ	1.0530E—02	—1.2
3	FZ= 5.102	GAXZ	3.5920E-06	32
		KY	-1.0530E—02	—1.2
4	MX= 4.102	GAT	2.73783E-03	0
	MY= 3.102
5	MX= —3.102	KY	2.1060E-03	—0.04
	MY= 4.102
6	MZ= 5 102	KZ	2.1060E-03	—0.04

6.5. notes

The shear values corresponding to the shear force are not accurate for this modeling. This is due to the second-order interpolation functions of this element, for beam movements and girder rotations. Since transverse beam shears are obtained by: \({\gamma }_{\mathrm{xy}}={\theta }_{z}-\frac{{\mathrm{du}}_{y}}{\mathrm{dx}}\), and because for simple bending, the rotations vary like polynomials of order 2, but the displacements, like polynomials of order 3, which is poorly approximated by the interpolation functions. The derivative of the displacements is therefore not precise.