1. Modeling A

1.1. Geometry and modeling

The mesh is composed of:

• 9 SEG2 cells on which the 6 types of beams and the 2 types of discrete elements with two nodes are modelled (there are two elements in POU_D_T).

• 2 SEG3 meshes on which the 2 types of 3-knot pipes are modelled.

• 1 SEG4 mesh on which a 4-knot pipe is modelled.

• 2 POI1sur meshes which model the 2 types of discrete elements at a node.

All cells that have a length are oriented according to the vector \((\mathrm{1,}\mathrm{1,}0)\).

1.2. Orientation of the local coordinate system

In order to define the local coordinate system for these elements, we use the keywords ANGL_VRIL for beams and discrete elements with two nodes, GENE_TUYAU for pipes and ANGL_NAUT for discrete elements at one node of the keyword factor ORIENTATION of the AFFE_CARA_ELEM operator (see U4.42.01).

The table above gives the orientations chosen for each element:

Beams	ANGL_VRIL	\(90\)
Discreet with two knots	ANGL_VRIL	\(\mathrm{-}90\)
Discreet to a knot	ANGL_NAUT	\((\mathrm{90,}\mathrm{-}90.0\mathrm{,90}.0)\)
Pipes	GENE_TUYAU	\((0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\)

1.3. Calculation of local landmarks

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

1.3.1. Beams

The vector \(x\) is defined by geometry and is therefore equal to \(\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2},0\right)\). The \(90\) value of ANGL_VRIL rotates the default coordinate system of \(90°\), which results in \(y\mathrm{=}(\mathrm{0,0}\mathrm{,1})\) and \(z=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2},0\right)\).

1.3.2. Discreet with two knots

As for the \(x=\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2},0\right)\) beams, but this time we pivot in the other direction which gives \(y\mathrm{=}(\mathrm{0,0},\mathrm{-}1)\) and \(z=\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2},0\right)\).

1.3.3. pipes

No change for \(x\). We gave the value \((0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\) to GENE_TUYAU, the vector \(y\) is then the projection of \((0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\) on the plane orthogonal to \(x\), that is to say \((0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\) itself.

So we have \(z=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2},0\right)\).

But a different treatment of angle GAMMA1 in Code_Aster induces an additional rotation of 90° around \(x\) which finally gives:

\(y=\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2},0\right)\) and \(z\mathrm{=}(0.\mathrm{,0}\mathrm{.},\mathrm{-}1.)\)

Note:

Pipes carried with SEG4 links are not compatible with those carried by SEG3 links. They are therefore treated separately.

1.3.4. Discreet at a knot

In this case the local coordinate system is only defined by the values of ANGL_NAUT. The second component of the given vector gives \(x\mathrm{=}(0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\). From the three components we determine that \(y\mathrm{=}(0.,\mathrm{-}1.\mathrm{,0}\mathrm{.})\) and \(z\mathrm{=}(1.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})\).

1.4. Tested sizes

The tested results are shown in the following table:

MAILLE	Vector	Component	Reference Value	Tolerance
POU1	\(x\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
POU3	\(x\)	Y	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
POU5	\(x\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
POU7	\(x\)	Y	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
DISL1	\(x\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY32	\(x\)	Y	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
DISN2	\(x\)	Z	\(1.0\)	\(1.E\mathrm{-}8\)
POU2	\(y\)	Z	\(1.0\)	\(1.E\mathrm{-}8\)
POU4	\(y\)	Z	\(1.0\)	\(1.E\mathrm{-}8\)
POU6	\(y\)	Z	\(1.0\)	\(1.E\mathrm{-}8\)
DISL2	\(y\)	Z	\(-1.0\)	\(1.E\mathrm{-}8\)
DISN1	\(y\)	Y	\(-1.0\)	\(1.E\mathrm{-}8\)
TUY31	\(y\)	Y	\(-0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY41	\(x\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY41	\(x\)	Y	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY41	\(y\)	X	\(0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY41	\(y\)	Y	\(-0.707106781186E0\)	\(1.E\mathrm{-}8\)
TUY41	\(z\)	Z	\(-1.0\)	\(1.E\mathrm{-}8\)