Routines AFRELA and AFLRCH
=============================




The AFRELA routine
-----------------


.. code-block:: text

    SUBROUTINE AFRELA (COEFR, COEFC, DDL, NOEUD, NDIM, DIRECT,

    + NBTERM, BETAR, BETAC, BETAF,, TYPCOE,, TYPVAL, LISREL)

    C-------------------------------------------------------

    C BUT: AFFECTATION D'UNE RELATION ENTRE DDLS A UNE SD LISTE_RELA

    C (IF L' OBJET LISREL N' EXISTE PAS, IT EST CREE)

    C

    C-------------------------------------------------------

    C COEFR (NBTERM) - IN - R -: TABLEAU DES COEFFICIENTS FROM THE RELATION

    C LES COEFFICIENTS SONT REELS

    C-------------------------------------------------------

    C COEFC (NBTERM) - IN - C -: TABLEAU DES COEFFICIENTS FROM THE RELATION

    C LES COEFFICIENTS SONT COMPLEXES

    C-------------------------------------------------------

    C DDL (NBTERM) - IN - K8 -: TABLEAU DES DDL FROM THE RELATION

    C-------------------------------------------------------

    C NOEUD (NBTERM) - IN - K8 -: TABLEAU DES NOEUDS FROM THE RELATION

    C-----------------------------------------------------------------------

    C NDIM (NBTERM) - IN - I -: DIMENSION OF PROBLEME (0, 2 OR 3)

    C SI = 0 PAS OF CHANGEMENT OF REPERE

    C THE RELATION EST DONNEE DANS THE BASE

    C GLOBALE

    C-------------------------------------------------------

    C DIRECT (3, NBTERM) - IN - R -: TABLEAU DES VECTEURS RELATIFS A CHAQUE

    C TERME DEFINISSANT THE DIRECTION OF THE

    C COMPOSANTE QUE L'ON VEUT CONTRAINDRE

    C-------------------------------------------------------

    C NBTERM - IN - I -: NOMBRE OF TERMES OF THE RELATION

    C-------------------------------------------------------

    C BETAR - IN - R -: VALEUR REELLE FROM SECOND MEMBRE

    C-------------------------------------------------------

    C BETAC - IN - C -: VALEUR COMPLEXE FROM SECOND MEMBRE

    C-------------------------------------------------------

    C BETAF - IN - K8 -: VALEUR FONCTION FROM SECOND MEMBRE

    C-------------------------------------------------------

    C TYPCOE - IN - K4 -: TYPE DES COEFFICIENTS FROM THE RELATION:

    C = 'REEL' OR 'COMP'

    C-------------------------------------------------------

    C TYPVAL - IN - K4 -: TYPE FROM SECOND MEMBRE

    C = 'REEL' OR 'COMP' OR 'FONC'

    C-------------------------------------------------------

    C LISREL - IN - K19 -: NOM FROM SD LISTE_RELA

    C - JXVAR -

    C-------------------------------------------------------

Two scenarios should be considered:


* the degrees of freedom to be linked are given in the absolute coordinate system: DX, DY,...


* some degrees of freedom to be linked are given in a local coordinate system.

**Case A** (all within the absolute coordinate system):


* NBTERMest the number of degrees of freedom linked by the relationship.


* NDIMest a vector filled with 0s


* DIRECTest useless.

Example 1:

we want to impose: :math:`3.\mathrm{\times }\mathit{DX}(\mathit{N1})+2.\mathrm{\times }\mathit{DY}(\mathit{N2})\mathrm{-}\mathrm{4.DRZ}(\mathit{N1})\mathrm{=}F` (function)


.. code-block:: text
 NBTERM = 3
TYPCOE = 'REEL'
TYPVAL = 'FONC'
COEFR = (3., 2., -4.)
NDIM = (0, 0, 0)
DDL = ('DX', 'DY', 'DRZ')
NOEUD = ('N1', 'N2', 'N1')
BETAF = 'F'

**Case B** (local reference):

For each node involved in the relationship, we can give a local coordinate system in which the relationship is simpler (the normal to a surface for example).

Example 2:

let :math:`n` be a unit vector with :math:`(\mathit{nx},\mathit{ny},\mathit{nz})` components.

We want the next move :math:`n` to node :math:`\mathit{N3}` to be zero.


.. code-block:: text
 NBTERM = 1
TYPCOE = 'REEL'
TYPVAL = 'REEL'
COEFR = (1.)
NDIM = (3)
DIRECT = (nx, ny, nz)
DDL = ('DEPL')
NOEUD = ('N1')
BETAR = 0.

Notes:

*NBTERMn is not the number of terms in the final relationship (here:**3) . *

*When using (for a "term") the possibility of a local reference* * *NDIM /= 0the name of the degree of freedom must be conventionally* *' DEPL '* *or* **or* *' ROTA '*

Example 3:

RC


.. csv-table::

    "let", "n1: a unit vector of components (n1x, n1y, n1z)"
    "", "n2: a unit vector of components (n2x, n2y, n2z)"


the following data:


.. code-block:: text
 NBTERM = 3
TYPCOE = 'REEL'
TYPVAL = 'REEL'
COEFR = (4.,2., -3.)
NDIM = (3,0,3)
DIRECT = (n1x, n1y, n1z, rbid, rbid, rbid, rbid, n2x, n2y, n2z)
DDL = ('DEPL', 'DX', 'ROTA')
NOEUD = ('N1', 'N3', 'N2')
BETAR = 5.

describe the relationship in 7 terms:


.. code-block:: text
 4. *(N1x*Dx (N1) +N1y*dy (N1) +N1z*DZ (N1))
+ 2. *XX (N3)
+ -3. *(N2x*Dx (N2) +N2y*dy (N2) +N2z*DZ (N2)) = 5.




The AFLRCH routine
-----------------


.. code-block:: text

    SUBROUTINE AFLRCH (LISREL, CHARGE)

    C --------------------------------------------------------

    C AJOUT D'UNE LISTE_RELA DANS UNE CHARGE

    C

    C LES RELATIONS IDENTIQUES TO SEIN OF LISTE_RELA SONT

    C ELIMINEES. THE PRINCIPE OF SURCHARGE EST APPLIQUE:

    C C' EST THE DERNIER SECOND MEMBRE QUI EST CONSERVE.

    C --------------------------------------------------------

    C LISREL IN/ JXVAR - K19 -: NOM FROM SD LISTE_RELA

    C LA LISTE_RELA EST DETRUITE

    C TO THE FIN OF THE ROUTINE

    C --------------------------------------------------------

    C CHARGE IN/ JXVAR - K8 -: NOM FROM SD CHARGE

    C LA CHARGE EST ENRICHIE

    C --------------------------------------------------------