Benchmark solution
=====================

Calculation method
-----------------

The reference solution is obtained by a calculation carried out with *Code_Aster* by explicitly giving the relationships between the degrees of freedom with the keyword LIAISON_DDL of the AFFE_CHAR_MECA command.

The relationships are of the following form:

• For the degrees of freedom of the slave nodes given under the simple keyword DDL.

:math:`\mathrm{DDL}({N}_{\mathrm{escl}})={\sum }_{i}{\mathrm{Coeff}}_{i}\ast \mathrm{DDL}({N}_{\mathrm{maître}}^{i})`

with i: master mesh node containing the slave node.

• In the case where TYPE = EXCENTREMENT, the relationship on the degrees of translational freedom of the slave nodes becomes:

:math:`\mathrm{DDL}({N}_{\mathrm{escl}})={\sum }_{i}{\mathrm{Coeff}}_{i}\ast (\mathrm{DDL}({N}_{\mathrm{maître}}^{i})+\overrightarrow{\omega ({N}_{\mathrm{maître}}^{i})}\wedge \overrightarrow{{N}_{\mathrm{maître}}^{i}{N}_{\mathrm{escl}}})`

Command PROJ_CHAMP gives the coefficient matrix:

**matcoeff** = **PROJ_CHAMP (**

**PROJECTION =** **' NON '**, **METHODE '**, **=** **' COLLOCATION '**,

**MAILLAGE_1 =** **mail**, **MAILLAGE_2 =** **mail**,

**VIS_A_VIS = _F (GROUP_MA_2 =** **' MILCUB '**, **GROUP_MA_1 =** **'**' LESCUBES '**,**) **)**, **)**, **)**,

**)**

This matrix is then used in the AFFE_CHAR_MECA keyword LIAISON_PROJ command in the following way:

**CLPROJ =** AFFE_CHAR_MECA (

**... ,**

LIAISON_PROJ = _F (MATR_PROJECTION = **matcoeff,** DDL =( **'DX', 'DY', 'DZ'**) **,**) **)**, **)**, **

**)**

Reference quantities and results
-----------------------------------

The sizes tested are:

• All movement components at all mesh nodes.

• All components of SIEF_ELGA constraints at all Gauss points and at all subpoints of the model.


Uncertainties about the solution
----------------------------

None. It is a comparison between two ways of giving the kinematic relationships between the same degrees of freedom of the slave and master nodes.