D modeling
==============

Characteristics of the mesh
----------------------------

Type of mesh:

• surface master meshes: 4 QUAD4 meshes;

• surface slave mesh: 1 QUAD4 mesh.

The meshes are shown in figures and. Surface meshes have :math:`1.0m` edges. The mesh QUA4 figure is placed in such a way that the nodes 11, 12, 14, 15 are in the center of gravity of a master mesh QUA4, figure.


Relationships between slave nodes and master meshes
-----------------------------------------------------

The coefficient between the slave and master nodes is :math:`1/4`.

There are four relationships per degree of freedom that relate to the following nodes:

• slave node 11 is connected to nodes 1, 3, 8, 10 of the master mesh.

• slave node 12 is connected to nodes 3, 2, 10, 9 of the master mesh.

• slave node 14 is connected to nodes 8, 10, 5, 6 of the master mesh.

• slave node 15 is connected to the nodes 10, 9, 6, 7 of the master mesh.

The first relationship is of the form, there are three others to be defined:

**_F (NOEUD** **=** ('N11', 'N11', 'N1', 'N3', 'N8', 'N10'),

**DDL** **=** ('DX', 'DX', 'DX', 'DX', 'DX', 'DX',),

**COEF_MULT =** (-1.0,0.25,0.25,0.25,0.25,0.25,),

**COEF_IMPO =** 0.0,

**)**


Tested sizes and results
------------------------------

The sizes tested are:

• All the components of the movements at all the nodes of the mesh;

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

Four calculations are carried out with relationships on the degrees of translation then translation and rotation:

• with the LIAISON_PROJ keyword from the AFFE_CHAR_MECA command;

• with the LIAISON_DDL keyword from the AFFE_CHAR_MECA command.

For each calculation and for each field, a table is created and then combined in order to differentiate between the two solutions obtained. These solutions must be exactly the same, so the value to be tested is :math:`0`.

The displacement fields are normalized with respect to the imposed displacement, the constraint fields are normalized with respect to :math:`\mathrm{1MPa}`.

The tolerance for all fields, for all nodes, and for all components is :math:`1.0E-06`.