5. Choosing the object of post-processing#

These keywords make it possible to define the object of post-processing. They refer to:

  • a size field: keywords CHAM_GD, RESULTAT (and its associated keywords),

  • a quantity associated with the components of the field: keywords TOUT_CMP, NOM_CMP,, INVARIANT,,,, ELEM_PRINCIPAUX, TRAC_NOR,,, TRAC_DIR, DIRECTION, REPERE, SOMME, RESULTANTE,,. MOMENT POINT

5.1. Magnitude field#

5.1.1. Syntax#

♦/CHAM_GD = chpgd,

/RESULTAT = resu, ♦ NOM_CHAM = chpsymbol, [K16] ♦/TOUT_ORDRE = “OUI”, /NUME_ORDRE = the order, [L_i] /LIST_ORDRE = slow, [listis] /NUME_MODE = lmode, [L_i] /LIST_MODE = slow, [listis] /NOM_CAS = nomcas, [K24] //FREQ = lfreq, [L_r] /LIST_FREQ = lreel, listr8 /INST = link, [L_r] /LIST_INST = lreel, listr8 ◊ | ACCURACY=/prec, [R] /1.D—6, [DEFAUT] ◊ | CRITERIA=/”RELATIVE”, [DEFAULT] /”ABSOLU”,

◊ FORMAT_C =/”MODULE”, [DEFAUT]

/”REEL”, /”IMAG”,

5.1.2. Operand CHAM_GD#

The argument to CHAM_GD is the name of a concept such as cham_no_*or cham_elem_*.

Operands RESULTAT/NOM_CHAM/TOUT_ORDRE/NUME_ORDRE/LIST_ORDRE//NUME_MODE/LIST_MODE//NOM_CAS//FREQ/LIST_FREQ/BELLA INST LIST_INST PRECISION CRITERE ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

See [U4.71.00].

5.1.3. Operand FORMAT_C#

In the case of complex fields, you can extract:

/”MODULE” the module /”REEL” the real part /”IMAG” the imaginary part

5.2. Field components and derived quantities#

For 2nd order vectors and tensors, it is possible to request the evaluation of the components in a coordinate system and to derive quantities obtained per contracted product. The keywords REPERE, TRAC_NOR, TRAC_DIR and DIRECTION define these quantities.

5.2.1. Syntax#

♦/TOUT_CMP = 'OUI',

/NOM_CMP = lcmp, [l_K8] ◊/REPERE =/”GLOBAL”, [DEFAUT] /”POLAIRE”, /”LOCAL”, ◊ VECT_Y =( oy1, oy2, oy3), [L_r] /”UTILISATEUR”, ♦ ANGL_NAUT = (a, b, c), [L_r] /”CYLINDRIQUE”, ♦ ORIGINE = (x, y, z), [L_r] ♦ AXE_Z =( oz1, oz2, oz3), [l_R] ◊/TRAC_NOR = “OUI”, /TRAC_DIR = “OUI”, ♦ DIRECTION = (x, y, [z]), [L_r] /INVARIANT = “OUI”, /ELEM_PRINCIPAUX = “OUI”, /RESULTANTE = lcmp, [l_K8] ◊ MOMENT = lcmp, [l_K8] ♦ POINT = (x, y, [z]), [L_r]

5.2.2. Operand TOUT_CMP#

/TOUT_CMP

This keyword only accepts the text “OUI” as an argument and selects all the components defined in the quantity catalog for the quantity relating to the fields specified by the keywords RESULTAT and CHAM_GD.

5.2.3. Operands NOM_CMP#

Allows you to define the components of the quantity of the treated field:

/NOM_CMP: components are introduced by name

5.2.4. Operand REPERE#

/REPERE

Allows you to choose a coordinate system from among the following coordinates:

  • coordinate system GLOBAL: Cartesian coordinate system for defining the mesh,

  • coordinate system POLAIRE: standard polar coordinate system of the \((\mathit{OXY})\) plane (order of components: \((r,\theta )\))

  • coordinate LOCAL: coordinate system consisting of tangent and normal vectors (in this order) instead of post-processing. The normal vector is defined at each post-treatment point as the average of the right and left normals.

Definition of normal instead of post-treatment.

At each post-treatment point the normal is defined as the average of the normals on the right and on the left.

_images/100004E200000DF400000ADAD353FDB2C062059D.svg

Figure 5.2.4-a

The tangent vector is obtained by rotating \(\mathrm{-}\pi \mathrm{/}2\) from the normal vector.

In the case of coordinate system LOCAL and a 3D line, you will need to provide:

VECT_Y = (oy1, oy2, oy3)

The coordinates of a vector whose projection on the plane orthogonal to the direction axis of the line will be taken as the normal to the line. The order of the components in a local coordinate system is \((t,n,k)\).

Example of use:

O

_images/10001198000069D500005B433BF929FCF819D56D.svg

Figure 5.2.4-b

We want to do an extraction on line \(\mathit{ABC}\) according to the local coordinate system defined above (local axis y in the global direction \(\mathit{OX}\)).

Here, we can find a constant vector at any point in the line to define the vector VECT_Y =( 1.,0.,0.).

This is possible because at every point this vector is already in the plane orthogonal to the line.

_images/1000159E000069D5000064C526B4F3F2762F9FE5.svg

Figure 5.2.4-c

If, on the other hand, we want to have the local axis \(z\) in the global direction \(\mathit{OX}\) [Figure 5.2.4-c], the vector VECT_Y will depend on the point in question:

\((0.\mathrm{,0}\mathrm{.}\mathrm{,1}\mathrm{.})\) fits except in \(A\) (where \((0.,\mathrm{-}1.\mathrm{,0}\mathrm{.})\) fits)

\((0.,\mathrm{-}\mathrm{1.0.})\) fits except in \(C\) (where \((0.,0.\mathrm{,1}\mathrm{.})\) fits)

In this case, you will therefore have to cut the line into two pieces (\(\mathit{AB}\) and \(\mathit{BC}\)) and define a different VECT_Y on each piece.

  • coordinate UTILISATEUR: defined by the data of 3 nautical angles (in degrees):

ANGL_NAUT = (a, b, c)

  • coordinate CYLINDRIQUE defined by:

ORIGINE = (x, y, z)

the coordinates of the \(O\) origin of the coordinate system

AXE_Z =( oz1, oz2, oz3)

the coordinates of a vector defining the \(\mathit{Oz}\) axis (cylinder axis). The order of the components in a cylindrical coordinate system is \((r,z,\theta )\).

5.2.5. Operand TRAC_NOR#

/TRAC_NOR: only for 2D and 3D models.

Determination of the normal trace of a vector or a tensor of order 2: this is the particular case of the directional trace obtained when the direction \(u\) is identified with the normal \(n\) instead of post-processing.

5.2.6. Operands TRAC_DIR/DIRECTION#

/TRAC_DIR: only for 2D and 3D models.

♦ DIRECTION

Determination of the directional trace of a vector \(v=({v}_{i})\) or a tensor of order 2 \(\sigma =({\sigma }_{i})\) in the direction \(u=({u}_{i})\); that is, of the scalar \({v}_{k}{u}_{k}\) or the vector \({\sigma }_{\mathit{ik}}{u}_{k}\).

The direction \(u\) is defined using the keyword DIRECTION whose arguments are the components of the vector \(u\) given in the order \(X,Y,Z\) and evaluated in the global coordinate system. If this list contains only two values then, conventionally, the next component \(Z\) of the \(u\) vector is considered to be zero.

5.2.7. Operand INVARIANT#

Post-treatment of a stress or deformation tensor of order 2 associated with the main directions of the tensor:

TRACE \(\mathrm{Tr}(\sigma )=\sum _{i=1}^{2\mathrm{ou}3}{\sigma }_{\mathrm{ii}}\)

VON_MIS \(\mathrm{VM}(\sigma )=\sqrt{\sum _{i=1}^{2\mathrm{ou}3}\frac{3}{2}{({\sigma }_{\mathrm{ij}}-\frac{1}{3}\mathrm{Tr}(\sigma ){\delta }_{\mathrm{ij}})}^{2}}\)

TRESCA \(\mathrm{TR}(\sigma )=\mathrm{max}(∣{\lambda }_{i}-{\lambda }_{j}∣)\) with \({\lambda }_{i}\) eigenvalues of \(\sigma\)

DETER \(\mathrm{DET}(\sigma )=\mathrm{déterminant}\mathrm{de}\sigma\)

5.2.8. Operand ELEM_PRINCIPAUX#

/ELEM_PRINCIPAUX

Determination of the main values of a \(2\mathrm{\times }2\) or \(3\mathrm{\times }3\) tensor of order 2. They are arranged in ascending order of their values.

5.2.9. Operands RESULTANTE/MOMENT/POINT#

Determination of the resultant and the moment of a torsor field at the post-treatment site.

RESULTANTE can only be used if OPERATION =” EXTRACTION “

Computatively, these keywords can be applied to any field of magnitude but for the results to have a physical meaning, we will have to limit ourselves to fields of nodal forces and nodal reactions.

In the latter case, 2 possibilities exist:

  • the user wants to calculate the resultant of certain components of the field: behind the keyword RESULTANTE, he will enter a list of components to take from \(\left\{\text{'}\mathit{DX}\text{'},\text{'}\mathit{DY}\text{'}\right\}\) in 2D and \(\left\{\text{'}\mathit{DX}\text{'},\text{'}\mathit{DY}\text{'},\text{'}\mathit{DZ}\text{'}\right\}\) in 3D or in structural elements (the resultant of components of rotations that have no physical meaning),

  • the user wants to calculate the result and the moment of certain components of the field: he will enter behind the keywords RESULTANTE and MOMENT 2 lists of components of the same length to take from

formula \(\left\{\text{'}\mathit{DX}\text{'},\text{'}\mathit{DY}\text{'},\text{'}\mathit{DZ}\text{'}\right\}\)

behind the RESULTANTE keyword

formula \(\left\{\text{'}\mathit{DRX}\text{'},\text{'}\mathit{DRY}\text{'},\text{'}\mathit{DRZ}\text{'}\right\}\)

behind the MOMENT keyword

In addition, it will introduce behind the keyword POINT the list of the coordinates of the point in relation to which the moment is evaluated.

If we note this point \(P\) and \({M}_{i}\) the post-treatment points, the evaluated quantities will be:

  • Resultant: \(F=\sum _{i}{F}_{i}=\sum _{i}({\mathrm{FX}}_{{M}_{i}},{\mathrm{FY}}_{{M}_{i}},{\mathrm{FZ}}_{{M}_{i}})\)

  • Moment: \(m=\sum _{i}(\overrightarrow{{\mathrm{PM}}_{i}}\wedge {F}_{i})+\sum _{i}{m}_{i}^{c}\)

where \({m}_{i}^{c}\) refers to the list of concentrated moments corresponding to the rotation components introduced by the MOMENT keyword, relevant only in the case of structural elements (beams, shells, discretes).

Notes:

1) In continuous environments, one should not introduce behind MOMENTdes translation components that would be considered as concentrated moments and therefore summed up with the real moments.

2) The calculation of RESULTANTE and/or of MOMENT is performed by a sum over a set of nodes. This sum only makes sense if all the nodal forces (or moments) are expressed in the same coordinate system. This means that the keyword REPERE can only take as a value “ GLOBAL “or “UTILISATEUR “.