2. Benchmark solution#

2.1. 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.

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

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:

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

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”) ,) ), ), **

)

2.2. 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.

2.3. 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.