6. D modeling#

6.1. Characteristics of modeling#

_images/Object_8.svg

6.2. Characteristics of the mesh#

Number of knots: 224

Number of meshes and type: 192 QUAD4

6.3. Tested values#

Identification	Reference [bib1]	Reference [bib2]	Aster	% difference
Displacement \(w\) at point \(F\)	\(1.325{10}^{-3}m\)	\(1.35{10}^{-3}m\)		\(1.329{10}^{\mathrm{-}3}m\)	0.365 [bib1] —1.494 [bib2]
Displacement \(w\) at point \(C\)	\(–2.45{10}^{-3}m\)	\(–2.46{10}^{-3}m\)		\(–2.369{10}^{-3}m\)	—3.274 [bib1] —3.667 [bib2]
Displacement \(w\) at point \(D\)	\(–0.51{10}^{-3}m\)	\(–0.35{10}^{-3}m\)		\(–0.528{10}^{-3}m\)	3.634 [bib1] 51.009 [bib2]

Constraint \(\mathit{SIXX}\) at point \(F\)	\(1.68\mathrm{MPa}\)	\(1.9\mathrm{MPa}\)		\(1.79\mathrm{MPa}\)	6.616 [bib1] —5.729 [bib2]
Constraint \(\mathrm{SIYY}\) at point \(F\)	\(1.8\mathrm{MPa}\)	\(1.55\mathrm{MPa}\)		\(1.84\mathrm{MPa}\)	2.465 [bib1] 18.991 [bib2]

6.4. notes#

The values of the coefficients CISA_L and CISA_T are not available. As the structure is thin (\(h/R=0.045\)), it is assumed that the effects of transverse shear are negligible, so we imposed CISA_L = CISA_T = \({10}^{10}\).
The normal \(w\) displacement is expressed in the local cylindrical coordinate \((R,\theta ,z)\), it is the displacement normal to the shell element. The displacement \(w\) tested is that of the global coordinate system (displacement following \(z\)).

6.5. Value of the displacement along CD#

It can be noted that beyond the difference observed in the experimental value at point \(D\), the normal displacement calculated along \(\mathrm{CD}\) is very close to the theoretically « deep shells » solution adopted by Batoz [bib1].

6.6. Stress values along CD#