3. Modeling A#

3.1. Characteristics of the mesh#

Type of mesh:

  • volume master meshes: 8 HEXA8 meshes;

  • volume slave mesh: 1 HEXA8 mesh.

The meshes are shown in figures and. Volume meshes have edges of length \(1.0m\). The mesh HEXA8 figure is placed in such a way that the nodes 30, 31, 33, 33, 33, 33, 33, 34, 34, 34, 36, 36, 37, 38, 39 are at the center of gravity of a master mesh HEXA8, figure.

3.2. Relationships between slave nodes and master meshes#

The coefficient between the slave and master nodes is \(1/8\).

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

  • slave node 33 is in relationship with nodes 5, 6, 8, 8, 8, 8, 10, 10, 24, 23, 28, 27 of the master mesh.

  • slave node 34 is connected to nodes 6, 7, 10, 10, 10, 9, 9, 27, 29, 23, 26 of the master mesh.

  • slave node 30 is in relationship with nodes 8, 10, 1, 1, 1, 1, 3, 3, 24, 23, 21, 22 of the master mesh.

  • slave node 31 is in relationship with nodes 3, 2, 10, 10, 10, 10, 9, 9, 22, 25, 23, 26 of the master mesh.

  • slave node 36 is connected to nodes 21, 22, 24, 24, 24, 23, 12, 13, 15, 14 of the master mesh.

  • slave node 37 is connected to nodes 22, 25, 23, 23, 23, 23, 23, 26, 26, 13, 16, 14, 17 of the master mesh.

  • slave node 38 is connected to nodes 14, 17, 18, 18, 18, 18, 20, 20, 27, 29, 23, 26 of the master mesh.

  • slave node 39 is in relationship with nodes 19, 18, 15, 15, 15, 15, 15, 14, 24, 23, 28, 27 of the master mesh.

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

_F (NOEUD = (“N33”, “N5”, “N5”, “N5”, “N6”, “N8”, “N10”, “N24”, “N23”, “N23”, “N23”, “N23”, “N23”, “N23”, “N28”, “N28”, “N27”,),

DDL = (“DX”, “DX”, “DX”, “DX”, “DX”, “DX”, “DX”, “DX”, “DX”, “DX”,),

COEF_MULT = (-1.0,0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.125,),

COEF_IMPO = 0.0,

)

3.3. 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 in the model.

Two calculations are carried out:

  • 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 \(0\).

The displacement fields are normalized with respect to the imposed displacement, the constraint fields are normalized with respect to \(\mathrm{1MPa}\).

The tolerance for all fields, nodes, and components is \(1.0E-06\).