4. B modeling

4.1. Characteristics of modeling

The initial mesh \(\mathrm{ma}\) (substructuring level \(-2\)) only contains the 12 QUAD4 of \(\mathrm{IJBA}\) and \(\mathrm{ABCD}\).

The macr_elem_stat \(({S}_{1})\) is set based on the elements in \(\mathrm{ABCD}\). This macr_elem_stat is condensed on the nodes of \(\mathrm{AB}\) and \(\mathrm{CD}\) (level \(-2\)).

The \(-1\) level \(\text{ma\_123}\) mesh is defined by rotating \(\text{S\_1}\) twice to represent crown \(\mathrm{ABCEGHFDA}\).

The macr_elem_stat \(\text{S\_123}\) is defined using substructures \(\mathrm{ABCD}\), \(\mathrm{DCEF}\), and \(\mathrm{FEGH}\). This macr_elem_stat is condensed on the nodes of \(\mathrm{AB}\) and \(\mathrm{GH}\).

The \(\mathrm{mag0}\) mesh is defined by the macr_elem_stat \(\text{S\_123}\).

The final mesh \(\mathrm{mag}\) (level \(0\)) is defined by the mesh \(\mathrm{mag0}\) that is assembled (ASSE_MAILLAGE) with the initial mesh \(\mathrm{ma}\) to recover the meshes of \(\mathrm{IJBA}\).

The resolution is then done on this final mesh, then the displacements within the macr_elem_stat are calculated using the operator DEPL_INTERNE.

4.2. Characteristics of the mesh

Number of knots: 20

Number of meshes and types: 12 QUAD4

4.3. Tested sizes and results

Identification	Reference
\(\mathrm{P1}\) \(u\)	1.88327
\(\mathrm{P1}\) \(v\)	2.59224 10—2
\(\mathrm{P2}\) \(u\)	—8.27372 10—2
\(\mathrm{P2}\) \(v\)	8.27372 10—2
\(\mathrm{P3}\) \(u\)	2.70375 10—1
\(\mathrm{P3}\) \(v\)	5.69552 10—1
\(\mathrm{P4}\) \(u\)	5.17703 10—1
\(\mathrm{P4}\) \(v\)	5.43387 10—1
\(\mathrm{P1}\) \(u\)	1.71883
\(\mathrm{P1}\) \(v\)	—6.04367
\(\mathrm{P2}\) \(u\)	—4.60196 10—2
\(\mathrm{P2}\) \(v\)	4.60196 10—2
\(\mathrm{P3}\) \(u\)	2.26903 10—1
\(\mathrm{P3}\) \(v\)	—6.14296 10—1
\(\mathrm{P4}\) \(u\)	—9.57110 10—1
\(\mathrm{P4}\) \(v\)	—2.53878