3. Modeling A#

3.1. Characteristics of modeling#

3.2. Characteristics of the mesh#

Number of knots: 224

Number of meshes and type: 192 QUAD4

3.3. Tested values#

Identification	Numerical reference [bib1]	Experimental reference [bib2]	Aster	% differences
Move \(w\) to point \(F\)	\(0.35{10}^{\mathrm{-}4}m\)		\(0.6{10}^{\mathrm{-}4}m\)		\(0.373{10}^{\mathrm{-}4}m\)	6.703 [bib1] —37.757 [bib2]
Move \(w\) to point \(C\)	\(–0.7{10}^{\mathrm{-}3}m\)		\(–0.6{10}^{\mathrm{-}3}m\)	\(–0.721{10}^{\mathrm{-}3}\)	3.033 [bib1] 20.205 [bib2]
Move \(w\) to point \(D\)	\(0.25{10}^{\mathrm{-}4}m\)		\(0.1{10}^{\mathrm{-}3}m\)		\(0.369{10}^{\mathrm{-}4}\)	47.689 [bib1] -63.078 [bib2]

Constraint \(\mathit{SIXX}\) at point \(F\)	\(–0.350\mathit{MPa}\)		\(–0.325\mathit{MPa}\)	\(–0.480\mathit{MPa}\)	37.339 [bib1] 47.904 [bib2]
Constraint \(\mathit{SIYY}\) at point \(F\)	\(0.500\mathit{MPa}\)		\(0.600\mathit{MPa}\)	\(0.490\mathit{MPa}\)	-1.901 [bib1] -18.259 [bib2]

3.4. Value of the normal displacement W along CD#

It can be noted that beyond the differences observed on the tested points \(C\), \(F\), \(D\), the normal displacement calculated along \(\mathit{CD}\) is close to the theoretically « deep shells » solution adopted by Batoz [bib1]. The errors relating to points \(F\) and \(D\) can be attributed to the low value of the displacement (of the order of \({10}^{\mathrm{-}5}m\)).

3.5. Stress value along CD#

It can be noted that the constraints calculated along \(\mathrm{CD}\) are generally in agreement with the theoretically « deep shells » solution adopted by Batoz [bib1].

3.6. notes#

Values for the CISA_L and CISA_T coefficients are not available. As the structure is thin (\(h\mathrm{/}R\mathrm{=}0.045\)), it is assumed that the effects of transverse shear are negligible, so we imposed CISA_L = CISA_T = \({10}^{10}\).
The normal displacement \(w\) (figure of [§4.2]) is expressed in the local cylindrical coordinate system \((R,\theta ,z)\), it is the displacement normal to the shell element. The displacement \(w\) tested in [§4.1] is for its part expressed in the global coordinate system (displacement following \(z\)).