3. Modeling A

3.1. Characteristics of modeling A

Figure 3.1- 3.1-a

Only a quarter of a plate is modelled. Symmetry conditions are introduced on the two faces shown above.

In addition, all the edge nodes located halfway through are fixed at \(x,y,z\).

In order to represent the thin shell hypotheses as accurately as possible, linear constraints are introduced on the degrees of freedom of the edge nodes. These are written:

for two nodes \(i\) and \(j\) located on either side of the middle sheet:

\({u}_{i}+{u}_{j}=0\)

\({v}_{i}+{v}_{j}=0\)

where u and v designate the movements along the axes \(x\) and \(y\).

The follower pressure is applied linearly using 6 increments.

3.2. Characteristics of the mesh

Number of nodes:	2091
Number of meshes and types:	368 HEXA20, 28 PENTA15
	92 QUAD8, 7 TRIA6

3.3. Tested values

Identification	Reference
Arrow \(\mathrm{w0}\) \((\mathrm{mm})\)	—1.441838E—3
SIXX \((\mathrm{MPa})\) center, half—thickness	3850.9
SIYY \((\mathrm{MPa})\) center, half—thickness	3850.9
SIXX \((\mathrm{MPa})\) center, lower skin	8133.6
SIYY \((\mathrm{MPa})\) center, lower skin	8133.6
SIXX \((\mathrm{MPa})\) \(r=R/2\), half—thickness	3512.8
SIYY \((\mathrm{MPa})\) \(r=R/2\), half—thickness	2947.5
SIXX \((\mathrm{MPa})\) \(r=R/2\), lower skin	7815.7
SIYY \((\mathrm{MPa})\) \(r=R/2\), lower skin	7307.0

3.4. notes

The same precision on the results is obtained using a single loading increment.