5. C modeling

5.1. Characteristics of modeling

5.2. Characteristics of the mesh

Number of knots: 224

Number of meshes and type: 384 TRIA3

5.3. Tested values

Identification	Numeric reference [bib1]	Experimental reference [bib2]	Aster	% difference
Move \(w\) to point \(F\)	\(1.325{10}^{\mathrm{-}3}m\)		\(1.35{10}^{\mathrm{-}3}m\)		\(1.327{10}^{\mathrm{-}3}m\)	0.154 [bib1] —1.701 [bib2]
Move \(w\) to point \(C\)	\(–2.45{10}^{\mathrm{-}3}m\)		\(–2.46{10}^{\mathrm{-}3}m\)	\(–2.379{10}^{\mathrm{-}3}m\)	—2.881 [bib1] —3.275 [bib2]
Move \(w\) to point \(D\)	\(–0.51{10}^{\mathrm{-}3}m\)		\(–0.35{10}^{\mathrm{-}3}m\)		\(–0.529{10}^{\mathrm{-}3}m\)	3.859 [bib1] 51.337 [bib2]
Constraint \(\mathit{SIXX}\) at point \(F\)	\(1.68\mathit{MPa}\)		\(1.9\mathit{MPa}\)	\(1.643\mathit{MPa}\)	—2.155 [bib1] —13.484 [bib2]
Constraint \(\mathit{SIYY}\) at point \(F\)	\(1.8\mathit{MPa}\)		\(1.55\mathit{MPa}\)	\(1.782\mathit{MPa}\)	—0.986 [bib1] —14.984 [bib2]

5.4. 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.

5.5. Value of normal 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].

5.6. Stress value along CD

The stress profiles calculated by the code are generally in agreement with the work of Batoz.