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Key word SENSITIVITY

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Organization (S): EDF-R & D/SINETICS
Handbook of Utilization
U4.5- booklet: Methods of resolution
Document: U4.50.02
Key word SENSITIVITY

1 Goal

Calculations of sensitivity of a result compared to a parameter are controlled by the insertion of the key word
SENSIBILITE in the command which produces the result. It is thus detailed in this document, in
specifying the limits of validity. Indeed sensitivities of all the results compared to all them
parameters all are not available!

Generally, for a creation of result, that means that one wants to calculate the derivative of
usual result compared to the indicated parameters. It is what occurs for the operators
principal
THER_LINEAIRE,
THER_NON_LINE,
MECA_STATIQUE,
MODE_ITER_SIMULT,
MODE_ITER_INV, STAT_NON_LINE, DYNA_LINE_HARM, DYNA_LINE_TRAN, DYNA_NON_LINE or
for the operators of enrichment of results CALC_G_THETA_T, CALC_ELEM, CALC_NO and
NORM_MODE.

For a postprocessing of results, that means that one is not interested in the result in itself
but with its derivative compared to the indicated parameters. It is what occurs for the operators
IMPR_RESU, POST_RELEVE_T, RECU_CHAMP, EXTR_RESU and TEST_RESU.

The sizes given in the list associated with key word SENSIBILITE are of two types:

· significant parameters, para_sensi,
· fields theta, theta_geom, for Lagrangian derivations.

Note:

One will refer to the document [U2.08.02] for a general note on calculations of
sensitivity. The theoretical bases of these calculations of sensitivity are described in:
[R4.03.01]: Sensitivity of the mechanical thermo fields to a variation of the field
[R4.03.02]: Calculation of sensitivity in thermics
[R4.03.03]: Calculation of sensitivity in mechanics
[R4.03.04]: Calculation of sensitivity in dynamics
[R4.03.07]: Calculation of sensitivity in postprocessings
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2 Syntax
(SENSIBILITE
=
(ps1, ps2,…)
[l_para_sensi]
(theta1,
theta2,
…)
[l_theta_geom)
)
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3 Operand
SENSIBILITE

SENSIBILITE =

This key word makes it possible to choose the parameters by report/ratio to which one derives the result.
They are significant parameters, defined by command DEFI_PARA_SENSI (cf document
[U4.31.04]):

ps1,
ps2,… [l_para_sensi]

That can also be fields theta in the case of derivation compared to the field
geometrical:

theta1, theta2,… [l_theta_geom]

Key word SENSIBILITE can be followed of 1 or several names of parameters. Their command is
indifferent. On the other hand, the key word itself can be present only only once in
order.

4
Convention of drafting

We will review the three types of operators who accept key word SENSIBILITE:
main line operator, of enrichment, postprocessing.

·
Main line operator: it is an operator who carries out the resolution of the problem and creates one
new structure of result. They are the THER_LINEAIRE, MECA_STATIQUE, etc Dans it
case, the insertion of key word SENSIBILITE means that Code_Aster will calculate the result
usual, but also each one of derived from this result compared to each one of
parameters transmitted by the key word.

·
Operator of enrichment: it is an operator who starting from the principal result (temperature,
displacement,…) product of the secondary results (flow, forced,…). They are them
operators CALC_ELEM and CALC_NO for example. In this case, the insertion of the key word
SENSIBILITE means that Code_Aster will calculate the derivative of the secondary result by
report/ratio with each parameter transmitted by the key word.

·
Operator of postprocessing: it is an operator who does not make calculation but which puts in
form a result to make it available to the user. They are the operators
POST_RELEVE_T, IMPR_RESU for example. In this case, the insertion of the key word
SENSIBILITE means that Code_Aster will exploit the derivative of the result compared to
each parameter transmitted by the key word. Attention, only these derivative are
exploited.

In the continuation of this document, we will enumerate the operators concerned with the sensitivity. By
convention, only the operators mentioned hereafter are concerned. In the same way, for an operator
given, only the types of derivations mentioned are accessible.

Unless otherwise specified, all the derivative accessible are it for all the types of elements, for
all types of model and as well in hover as in transient.
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Key word SENSITIVITY

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5
In a main line operator

5.1 General

The main line operator calculates the principal result and his derivative.

Example:

reth = THER_LINEAIRE
(MODELE = model,
CHAM_MATER = chmat,
EXCIT = (...),
SENSIBILITE = (ps1, ps2));

This sequence will solve a linear problem of thermics and will produce the structure of result
reth. This structure contains the field of temperature TEMP. Moreover, there will be calculation of derived from
the temperature compared to ps1 and of derived from the temperature compared to ps2. These derivative
have same nature as the temperature: they are represented in the shape of fields to the nodes.
These fields are then easy to handle like the usual field of temperature: extraction of
values, impressions, etc

In a subjacent way, there is creation of as many structures of results of sensitivities
asked. Their names are established automatically by the program. They do not have to be known
explicitly because one will always reach information by a couple (name of standard result, name
parameter of sensitivity). Each field which makes one of these structures of results
the derivative of this field compared to the parameter of sensitivity concerned will contain.

Example:

Field TEMP of the structure reth of the evol_ther type contains the field of temperature with
nodes of standard calculation. Field TEMP of the structure of the evol_ther type known by the couple
(reth, ps1) the field with the nodes of the derivative partial of the temperature will contain compared to
T

ps1,
. The same rule applies to all the fields which will be calculated by enrichment.
1
PS

5.2 Operator
THER_LINEAIRE

5.2.1 By
ameters
sensitive

It is possible to derive the field from temperature compared to a significant parameter when it was
used to define:

·
a condition of imposed temperature,
·
a loading:
- source,
- flow,
-
coefficient of exchange and outside temperature,
-
coefficient of walls exchange,
·
a material:
- conductivity
thermics
,
- heat
voluminal
CP.

Note:

Derivations in the problems of linear thermics in hull are not available.
One will look at the test [V1.01.151] for an example of sensitivity in linear thermics.
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5.2.2 Derivation
Lagrangian

Derivation known as “Lagrangian” makes it possible to calculate the sensitivity of the field of temperature
position of the edge of the field. That is not possible that for modelings “PLAN” and “AXIS”.

The edge by report/ratio to which one wishes to derive the temperature must be rectilinear, parallel to the axis of
y. The matter must be “on the right” of this edge.

y

Edge

Matter

The designation of this edge is made by the data of a field “theta”:

SENSIBILITE = (theta)

This field is defined by operator CALC_THETA, by using option THETA_BANDE to give
position of the edge cf [U4.82.02].

Note:

There is no checking of coherence between the data of the X-coordinate of the edge in
definition of the field theta and the position of the edge such as it is defined in the grid. One
will look at the test [V7.01.101] for an example of Lagrangian derivation in thermics.

5.3 Operator
THER_NON_LINE

It is possible to derive the field from temperature compared to a significant parameter when it was
used to define:

·
a condition of imposed temperature,
·
a loading:
- source,
-
linear and nonlinear flow,
- emissivity,
- temperature
with
the infinite one,
-
coefficient of exchange and outside temperature,
-
coefficient of walls exchange,
·
a material:
- conductivity
thermics
,
- heat
voluminal
CP.
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Derivation is available for the isoparametric finite elements and following modelings:
PLAN, PLAN_DIAG, AXIS, AXIS_DIAG, 3D and 3d_DIAG.

Note:

One will look at the test [V1.01.154] for an example of sensitivity in non-linear thermics.

5.4 Operator
MECA_STATIQUE

5.4.1 Parameters
sensitive

It is possible to derive the field from displacement compared to a significant parameter when it was
used to define:

·
a condition of imposed displacement (DDL_IMPO or FACE_IMPO),
·
a loading:
-
a pressure distributed,
-
a force nodal or distributed linear,
·
a material:
-
Young modulus for an isotropic, orthotropic elastic law or isotropic-transverse.
-
Poisson's ratio

The functionality of derivation is available in 2D and 3D, isothermal continuous medium, POU_D_E.

Note:

One will look at the test [V1.01.144] for an example of sensitivity in static mechanics.

5.4.2 Derivations
Lagrangian

Derivation known as “Lagrangian” applies under the same conditions as for the operator of
linear thermics. Only additional restriction: the elements must be degree 2.

Note:

One will look at the test [V7.01.101] for an example of Lagrangian derivation in mechanics.

5.5 Operator
MODE_ITER_SIMULT and MODE_ITER_INV

It is possible to derive the clean, real or complex modes, compared to a significant parameter
when it was used to define:

·
a condition of imposed displacement,
·
a material (available in 2D and 3D, continuous medium, POU_D_E):
- module
of Young,
-
Poisson's ratio.

The functionality of derivation of the clean modes is not available for the multiple modes.

Note:

One will look at the test [V1.01.188] for an example of sensitivity of clean modes.
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5.6 Operator
STAT_NON_LINE

It is possible to derive the field from displacement, constraints and internal variables by report/ratio
with a significant parameter when it was used to define:

·
a condition of imposed displacement (DDL_IMPO or FACE_IMPO),
·
a condition of the Neumann type:
-
a pressure distributed,
-
a force nodal or distributed linear,
·
a material:
- module
of Young
-
Poisson's ratio
- limit
of elasticity
-
slope of the traction diagram after the elastic limit

The functionality of derivation is available only for one elastic or elastoplastic structure
(Von Mises or Drucker-Prager) with isotropic linear work hardening, in 2D and 3D, continuous medium
isotherm, POU_D_E (only on the Young modulus and the Poisson's ratio).
It available in 2D is not forced plane.

Note:

One will look at the test [V1.01.181] for an example of sensitivity in static mechanics
non-linear.

5.7 Operator
DYNA_LINE_HARM

It is possible to derive the field from displacement compared to a significant parameter when it was
used to define:

· a condition of imposed displacement,
· a loading:
- force
nodal,
-
force distributed linear, surface or voluminal,
- pressure
distributed.
·
a material (available in 2D and 3D, continuous medium, POU_D_E):
-
Young modulus for an isotropic, orthotropic elastic law or isotropic-transverse,
-
Poisson's ratio.

Note:

One will look at the test [V1.01.158] for an example of sensitivity in linear dynamics
harmonic.

5.8 Operator
DYNA_LINE_TRAN

It is possible to derive the field from displacement compared to a significant parameter when it was
used to define:

· a condition of imposed displacement,
· a loading:
- force
nodal,
-
force distributed linear, surface or voluminal,
- pressure
distributed,
·
a material (available in 2D and 3D, medium continuous, POU_D_E, inalienable for the diagram
of integration clarifies with step of adaptive time):
-
Young modulus for an isotropic, orthotropic elastic law or isotropic-transverse,
-
Poisson's ratio.

Note:

One will look at the test [V1.01.171] for an example of sensitivity in linear dynamics
transient.
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5.9 Operator
DYNA_NON_LINE

It is possible to derive the fields from displacement, speed and acceleration compared to one
significant parameter when it was used to define:

·
a condition of the Neumann type:
-
a pressure distributed,
-
a force nodal or distributed linear,
·
a material:
- module
of Young,
-
Poisson's ratio,
- limit
of elasticity,
-
slope of the traction diagram after the elastic limit.

The functionality of derivation is available only for one elastic or elastoplastic structure
(Von Mises) with isotropic linear work hardening, in 2D and 3D, continuous medium, POU_D_E (only
on the Young modulus and the Poisson's ratio).
It available in 2D is not forced plane.

Note:

One will look at the test [V1.01.174] for an example of sensitivity in non-linear dynamics.
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6
In an operator of enrichment

6.1 General

The operator of enrichment calculates secondary results starting from the principal result.

Example:

reth = CALC_ELEM
(RESULTAT = reth,
MODELE = model,
EXCIT = (...),
OPTION = (“FLUX_ELGA_TEMP”),
SENSIBILITE = (ps1, ps2)),

This sequence will enrich the structure of reth results by calculating the derivative by the heat flux with
points of Gauss compared to ps1 and that compared to ps2.
These derivative have same nature as flow: they are fields at the points of Gauss. These fields
are then easy to handle like the field of usual flow: extraction of values, impressions, etc

Note:

For making such an enrichment, it is necessary that the derivative of the principal field (temperature,
displacement,…) was calculated.
The arrangement of the various derived fields is done according to the rule described with [§5.1].

6.2 Operator
CALC_ELEM

The operator of enrichment calculates secondary results starting from the principal result.

6.2.1 Parameters
sensitive

In or not linear linear thermics:

·
FLUX_ELGA_TEMP: derived from the heat flow.

In static mechanics:

·
EPSI_ELGA_DEPL: derived from the deformations,
·
SIEF_ELGA_DEPL: derived from the constraints.

In transitory linear dynamics:

·
**** _ **** _DEPL: derived from the strains or the stresses.

6.2.2 Derivation
Lagrangian

In linear thermics:

·
DETE_ELNO_DLTE: derived eulérienne from the temperature.

In static mechanics:

·
DEDE_ELNO_DLDE: derived eulérienne from the temperature,
·
SIEF_ELGA_DEPL: Lagrangian derivative of the constraints,
·
DESI_ELNO_DLSI: derived eulérienne from the constraints.

6.3 Operator
CALC_NO

There is no particular restriction: as from the moment when the derivative by element was calculated, its
projection on the nodes is possible.
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6.4 Operator
NORM_MODE

It is a question here of multiplying the derivative of the clean vector by a coefficient depend on the standard
asked by the user.

6.5 Operator
CALC_G_THETA_T

The rate of refund of energy can be derived. The field of validity is that of the derivation of
fields of displacements and associated constraints.
It is possible to derive the rate of refund from energy compared to a significant parameter when it has
summer used to define:

·
a loading:
-
a force distributed linear (2D) or surface (3D),
-
a voluminal force (2D or 3D),
-
a pressure distributed on the lips of the fissure,
-
a nodal force,
·
a material:
-
Young modulus for an isotropic elastic law.

Limitations:

· It is not possible to derive the rate of refund from energy compared to a condition from
imposed displacement because the term corresponding in G is not established.
· The functionality of derivation is available in 2D and 3D, medium continuous.

The result is a table, like the rate of standard refund.

Example:

ga = CALC_G_THETA_T (…
SENSIBILITE = (ps1, ps2)),

This sequence will produce the derivative of the rate of refund ga compared to the significant parameter ps1.
The exploitation of this derivative will be done by providing the couple (ga, ps1); for example, for one
impression one will use usual command IMPR_TABLE.

Note:

One will look at the test [V7.02.101] for an example of sensitivity in breaking process.

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7
In an operator of postprocessing

7.1 General

The operator of postprocessing formats the derivatives of the results.

IMPR_RESU (RESU = _F (MAILLAGE = mall,
RESULTAT = reth,
NOM_CHAM = “TEMP”
SENSIBILITE = (ps1, ps2)) ),

This sequence will print the derivative of the field of temperature contained in the reth result
compared to ps1 and ps2. Attention, that will not print the standard temperature.

One notes in these commands that the name of the structure of results which contains the derivative
never appears in light. The structure is always known by the couple (name of standard result,
name of the significant parameter). It is what is described with [§5.1].

7.2 Operators
concerned

The postprocessing of derivations of the results is possible with the following operators:

·
IMPR_RESU: impression of structures of results,
·
IMPR_TABLE: impression of tables,
·
POST_RELEVE_T: extraction of values,
·
TEST_RESU: comparison of values,
·
EXTR_RESU: extraction of results,
·
CREA_CHAMP: creation of a field.

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