3. C modeling#

3.1. Geometry and modeling#

The mesh is composed of:

1 QUAD9sur mesh to which we assign the COQUE_3D modeling
1 QUAD8sur mesh to which models GRILLE_MEMBRANE and MEMBRANE are affected
1 TRIA7sur mesh to which we assign the COQUE_3D modeling
1 TRIA6sur mesh to which we assign the GRILLE_MEMBRANE modeling

3.2. Orientation of the local coordinate system#

In order to define the local coordinate system for these elements, the ANGL_REP keyword from the AFFE_CARA_ELEM operator is used (see U4.42.01).

The table above gives the orientations chosen for each element:

Cases	ANGL_REP	\((45.0,\mathrm{-}45.0)\)
Grids	ANGL_REP	\((\mathrm{45.0,}-45.0)\)
Membranes	ANGL_REP	\((45.0,\mathrm{-}45.0)\)

3.3. Calculation of local landmarks#

Local landmarks are formed by the vectors \(x\), \(y\), and \(z\).

For shells and grids the vector \(z\) is defined by the normal exiting to the shell. In our example we will have \(z=\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2},0\right)\).

The value given to ANGL_REP defines a vector whose projection on the tangential plane to the element gives the vector \(x\). So the values in the example are \(x=\left(\mathrm{0.5,0}\mathrm{.5,}\frac{\sqrt{2}}{2}\right)\) and \(y=\left(-\mathrm{0.5,}-\mathrm{0.5,}\frac{\sqrt{2}}{2}\right)\).

3.4. Tested sizes#

The tested results are shown in the following table:

MAILLE	Vector	Component	Reference Value	Tolerance
CQ3D4	\(x\)	X	\(0.5\)	\(1.E\mathrm{-}8\)
CQ3D3	\(x\)	Y	\(0.5\)	\(1.E\mathrm{-}8\)
CQ3D4	\(x\)	Z	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
GRME4	\(x\)	X	\(0.5\)	\(1.E\mathrm{-}8\)
GRME3	\(x\)	Y	\(0.5\)	\(1.E\mathrm{-}8\)
GRME4	\(x\)	Z	\(0.707106781186E0\)	\(1.E-8\)
MEMB4	\(x\)	Z	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
CQ3D4	\(z\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
CQ3D3	\(z\)	Y	\(\mathrm{-}0.707106781186E0\)	\(1.E\mathrm{-}8\)
GRME4	\(z\)	X	\(0.707106781186E0\)	\(1.E-8\)
GRME3	\(z\)	Y	\(\mathrm{-}0.707106781186E0\)	\(1.E\mathrm{-}8\)
MEMB4	\(z\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)