Discretization
==============


Degrees of freedom
------------------

DX, DY, and DZ refer to degrees of freedom of movement.

PRE1 and PRE2 refer to two degrees of freedom of pressure, whose precise meaning depends on the laws of behavior used. TEMP refers to temperature.


.. csv-table::

    "**Finite element**", "**Degrees of Freedom**"



.. csv-table::

    "3D_HM", "DX, DY, DZ, PRE1"
    "3D_ HHM ", "DX, DY, DZ, PRE1, PRE2"
    "3D_ THM ", "DX, DY, DZ, PRE1, TEMP"
    "3D_ THH "," PRE1, PRE2, TEMP"
    "3D_ THHM ", "DX, DY, DZ, PRE1, PRE2, TEMP"
    "3D_ HM_DIL ", "DX, DY, DZ, PRES, PRE1, TEMP, GONF"
    "3D_ THM_DIL ", "DX, DY, DZ, PRES, PRE1, TEMP, GONF"
    "3D_ HHM_DIL ", "DX, DY, DZ, PRES, PRE1, PRE2, GONF"



Stiffness matrix support mesh
----------------------------------------

The finite element support meshes can only be hexahedra. The elements are iso‑parametric.


.. csv-table::

    "**Modeling**", "**Mesh**", "**Interpolation**", "**Remarks**"



.. csv-table::

    "3D_HM", "HEXA20 ", "Serendip 20 knots in tri-linear motion over 8 knots in pressure", "The pressure of a middle node is the average of the peak nodes in the segment"
    "3D_ HHM "," HEXA20 ", "Serendip 20 knots in tri-linear motion over 8 knots in pressure", "The pressures of a middle node are the averages of the vertices of the segment nodes"
    "3D_ THM "," HEXA20 ", "Serendip 20 knots in tri-linear motion over 8 knots in pressure and temperature", "The pressure and temperature of a middle node are the average of the node vertices of the segment"
    "3D_ THH "," HEXA20 ", "Tri-linear over 8 knots in pressure and temperature", "The pressures and temperature of a middle node are the average of the vertices of the segment"
    "3D_ THHM "," HEXA20 ", "Serendip 20 knots in tri-linear motion over 8 knots in pressure and temperature", "The pressures and temperature of a middle node are the average of the node vertices of the segment"
    "3D_ HM_DIL "," HEXA20 ", "Serendip 20 knots in motion, tri-linear over 8 knots in pressure, volume deformation and Lagrange multiplier", "The pressure of a middle node is the average of the node vertices of the segment"
    "3D_ HHM_DIL "," HEXA20 ", "Serendip 20 knots in motion, tri-linear over 8 knots in pressure, volume deformation and Lagrange multiplier", "The pressures of a middle node are the averages of the node vertices of the segment"
    "3D_ THM_DIL "," HEXA20 ", "Serendip 20 knots in tri-linear motion over 8 knots in pressure, temperature, volume deformation and Lagrange multiplier", "The pressure and the temperature of a middle node are the average of the node vertices of the segment"



Cargo support mesh
------------------------------


.. csv-table::

    "**Modeling**", "**Mesh**", "**Interpolation**", "**Remarks**"



.. csv-table::

    "3D_HM", "QUAD8 ", "Serendip 8 knots in bi-linear motion over 4 knots in pressure and temperature", "The pressure of a middle node is the average of the peak nodes in the segment"
    "3D_ HHM "," QUAD8 ", "Serendip 8 knots in bi-linear motion over 4 knots in pressure", "The pressures of a middle node are the averages of the vertices of the segment nodes"
    "3D_ THM "," QUAD8 ", "Quadratic in linear displacement in pressure and temperature", "The pressure and temperature of a middle node are the average of the vertices of the segment"
    "3D_ THH "," QUAD8 ", "Bi-linear over 4 knots in pressure and temperature", "The pressures and temperature of a middle node are the average of the peak nodes of the segment"
    "3D_ THHM "," QUAD8 ", "Serendip 8 knots in bi-linear motion over 4 knots in pressure and temperature", "The pressures and the temperature of a middle node are the average of the node vertices of the segment"


The load support cells for the _ DIL models are identical to those of the corresponding HM, THM or HHM models.