3. Modeling A

3.1. Characteristics of modeling

We place ourselves in a massive 3D frame. We will impose successively:

• a translation of vector \((2.5;3.9;\mathrm{-}12.3)\),

• a rotation of an angle of 33 degrees and an axis passing through the points \((10;0.5;3.8)\) and \((0;10;0)\),

• a second rotation with an angle \(\mathrm{-}161\) degrees and an axis passing through \((\mathrm{-}3.;0.5;3.8)\) and with a direction \((0;1;0)\),

• a scaling by a factor \(5\).

We thus test all the scenarios authorized by the syntax of the keywords TRANSLATION, ROTATION and ECHELLE.

Then, we start again from the initial mesh and we impose on it successively:

• a change in the base of vectors \((1.23;0.23;0)\) and \((-2.3;12.3;0)\),

• a scaling by a factor \(5\).

In this way, we test the keywords MODI_BASE and ECHELLE together.

3.2. Characteristics of the mesh

The mesh has a single element of type HEXA8.

3.3. Tested sizes and results

For the first part, with TRANSLATION, ROTATION, and ECHELLE:

Points observed	Coordinates	Reference
\(\mathit{P1}\)	\(X\)	5.2501368890123E+00
	\(Y\)	—2.1551486020681E+00
	\(Z\)	7.8600118786924E+01
\(\mathit{P7}\)	\(X\)	—1.3714414455621E+01
	\(Y\)	1.9199906921638E+01
	\(Z\)	7.0898989267417E+01
\(\mathit{P8}\)	\(X\)	—9.9168576521849E+00
	\(Y\)	2.0297577804345E+01
	\(Z\)	6.783734242495183E+01

For the second part, with MODI_BASE and ECHELLE:

Points observed	Coordinates	Reference
\(P2\)	\(X\)	4.9148126952461E+00
	\(Y\)	—9.1903001618423E-01
	\(Z\)	0.0000000000000E+00
\(P7\)	\(X\)	7.6719027437988E+00
	\(Y\)	1.3825408069554E+01
	\(Z\)	2.5000000000000E+01
\(\mathit{P8}\)	\(X\)	2.7570900485527E+00
	\(Y\)	1.4744438085738E+01
	\(Z\)	2.5000000000000E+01