====== BINDS ======
===== Description =====
These elements are used to impose a linear relationship between the DOF of some nodes\\
They must refer to the material law [[laws:binds|BINDS]] (ITYPE= 30)\\ 
Element type: 99\\
Implemented by: Bertarini I. (1986) & revised by Pascon F. (1999)\\

Example of relationship:
$\displaystyle\sum_{i=1}^{m} \alpha_i . \delta_i = \alpha_0$\\
With:\\
$\delta_i$: the degree of freedom (translation or rotation: 1, 2 ...)\\
$\alpha_i$ and $\alpha_0$: data specified in the section "COLAW" for the material: LMATE and specified in each relation\\
$m$: number of terms in the linear relationship\\

See example below\\
==== Files ====

Prepro: BINDSA.F \\
Lagamine: BINDSB.F
===== Input file =====
 
^ Title (A5)^^
|TITLE |"BINDS" |
^Control data (I5)^^
|NELEM |number of elements |
^ Definition of the elements (3I5/3*NNODE I5)^^
|LMATE |material number (type 30) |
|NNODE |number of terms in the relation (max: 10) (see note 1)|
|INDISO |position of $\alpha_0$ in the list of the $\alpha$ coefficients of the law LMATE |
|NODES(I) |node number in the relation |
|IDOF(I) |componant of the node used in the relation (1: first DOF, 2: second DOF ...) (see note 2) |
|INDIS(I) |position of the $\alpha_i$ coefficient in the law LMATE |
| **Note:** These 3 consecutive terms are written for I=1:NNODE on the same line|| 

__**Notes**__\\
1: if NNODE >10, the subroutines: BINDSA and BINDSB must be adapted \\
2: Number of DOF in global axes
   1= displacement in X direction
   2= displacement in Y direction
   3= displacement in Z direction
   4= rotation around the axis X
   5= rotation around the axis Y
   6= rotation around the axis Z
3: The $\alpha_0$ coefficient is multiplied by DMULT

===== Example =====
If you have the 2 following relations:\\
$4.U_1 + 2. V_2 - U_3 = 0$ (element n° 1) \\
$2.V_1 + 2. U_2 + 4.U_3 = 4$ (element n° 2)\\

where, for example, $U_3$ is related to the first DOF (U) of the node 3\\

You have to describe 1 law with all the $\alpha_i$ coefficients:\\
$\alpha_1$= 4\\ 
$\alpha_2$= 2\\ 
$\alpha_3$= -1\\ 
$\alpha_4$= 0\\ 

And you have to define 1 element for each relation (here: 2 elements) \\

After the title, you have 5 lines: \\
^ Line 1^
|NELEM = 2|
__**First element:**__ 
^Line 2^^^
|LMATE = law nb.|NNODE = 3 |INDISO = 4|

^Line 3^^^^^^^^^
|NODES(1) = 1 | IDOF(1) = 1 | INDIS(1) = 1 |NODES(2) = 2 |IDOF(2) = 2| INDIS(2) = 2|NODES(3) = 3 |IDOF(3) = 1 |INDIS(3) = 3 |
|  for $4.U_1$  |||  for $2.V_2$  |||  for $-U_3$  |||
__**Second element:**__ 
^Line 4^^^
|LMATE = law nb. |NNODE = 3 |INDISO = 1 |

^Line 5^^^^^^^^^
|NODES(1) = 1 |IDOF(1) = 2 |INDIS(1) = 2 | NODES(2) = 2 |IDOF(2) = 1 |INDIS(2) = 2 | NODES(3) = 3 |IDOF(3) = 1 |INDIS(3) = 1 |
|  for $2.V_1$  |||  for $2.U_2$  |||  for $4.U_3$  |||
===== Results =====
Effort in the spring