Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
:

14/01/03
Author (S):
Key S. MICHEL-PONNELLE
:
U2.01.10-A Page
: 1/6

Organization (S): EDF-R & D/AMA

Handbook of Utilization
U2.01 booklet: General concepts
Document: U2.01.10
Note of use on the choice of the finite elements
Summary:

The purpose of this document is to give some information on the choice of the finite elements and their modeling
associated in the case of studies thermal, thermo mechanical or mechanical non-linear. It acts in
some kind, to propose with the user a choice a priori, allowing to avoid certain current errors. In
cases of particular difficulties, other choices could be made.

Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
:

14/01/03
Author (S):
Key S. MICHEL-PONNELLE
:
U2.01.10-A Page
: 2/6

1 Introduction

One gives in this document the choices a priori which can be made concerning the finite elements. One
was placed in the case of a thermomechanical chaining but the consultings are valid on
thermal or mechanical not chained calculations (linear or not). A fast justification is given.
For more details on the justification of these choices, the user will be able to refer to the documents R of
Code_Aster like with the note H [bib1].

2
Choice a priori

2.1
grid

The elements can be indifferently:

·
triangular elements or quadrangles in 2D,
·
tetrahedrons or hexahedrons in 3D.

Indeed, contrary to the often spread idea, the elements of the triangle type or tetrahedron give
good results, even in plasticity, in condition of course of not using a grid too much
coarse. The advantage of this family of elements, it is that it makes it possible to use the software HOMARD which
carry out the adaptation of grids 2D/3D for finite elements of type triangular or tetrahedral by
refinement and déraffinement. One can thus obtain the optimum grid according to an indicator
of error (cf [R4.10.01], [R4.10.02], [R4.10.03], or the case test TPLL01j [V4.02.01] for one
demonstration) by call to command MACR_ADAP_MAIL in the command file Aster.

On the other hand, it is advised to use:

·
linear elements in thermics for chained calculations and calculations of thermics
fast transient. For the other cases, one can also choose quadratic elements,
·
quadratic elements in mechanics.

This choice is all the more important when one carries out thermal chained calculations then
mechanics. It is then necessary to use two grids for thermics and mechanics. Two strategies
are then possible:

·
that is to say independently to net the structure for thermal calculation and mechanical calculation
·
that is to say to carry out a grid with linear elements then to transform it into grid
quadratic thanks to the command CREA_MAILLAGE, key word factor LINE_QUAD.

Whatever the method chosen, one can optimize separately each grid with Homard grace
with the thermal and mechanical indicators of error available in Aster (cf case-test forma05b
[V6.03.120]).
Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
:

14/01/03
Author (S):
Key S. MICHEL-PONNELLE
:
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Note:

1) This remark is addressed to the users of GIBI which were accustomed to netting theirs
structures with quadrangles or cubes and which would wish “to rock” them
grid towards triangles or tetrahedrons.
In general, to net with tetrahedrons instead of cubes, it is not enough to change
in the command file OPTI DIME 3 ELEM CU20 by OPTI DIME 3 ELEM TE10.
Indeed, a certain number of commands GIBI are specific to the cubes and
do not function to net a structure with tetrahedrons (or do not give it
anticipated result). The user can thus be tempted to keep his command file
initial and to use at the end of the process of creation of grid command CHAN TET4
to make tilting.
By experiment, we disadvise to the users making this choice for several
reasons. First of all, on certain grids, one observed a not-convergence of
solution when one used an increasingly fine grid obtained by this method. In
more, the change is effective only on volume: the surface meshs are always
quadrangles what poses problem to impose the boundary conditions in
Aster. Lastly, to net with TETRA10, it is necessary to pass by the stage
TETRA4 then to make CHAN QUADRATIQUE. However this change poses problem for
SEG2.
Consequently, with GIBI, it is important to net directly the structure with
good elements leaves to have to rewrite its command file. One also announces,
that in certain cases, GIBI does not manage to net with tetrahedrons when one asks
an important refinement. It is then enough to net coarsely, then to refine it
uniform grid of way or not with the Homard software.
2) It is pointed out here that all the sizes of the type forced or deformation are calculated
at the points of Gauss, and that any passage to the nodes involves a skew. That is of as much
truer when one then seeks to calculate standards; we thus noticed
that the tetrahedrons were more sensitive than the hexahedrons to the method of calculation of
equivalent constraints for example. It is thus necessary to have an eye even more critical on
results calculated with the nodes.

2.2
modeling

That it is for the resolution of the thermal or mechanical problems, several modelings are
available in Aster. These various modelings can be characterized by the number or the type
degrees of freedom, the number of points of integration, processing particular… According to
calculation carried out, some of course are adapted than of others.

2.2.1 In thermics

To make thermal calculation in Aster, two types of modelings are accessible ([U3.23.01],
[U3.24.01], [R3.06.02], [R3.06.07]):

·
traditional finite elements: modeling 3D, AXIS or PLAN
·
finite elements lumpés or diagonalized
: modeling 3d_DIAG, AXIS_DIAG or
PLAN_DIAG

We propose like choice by defect:

modeling with linear elements
Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
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14/01/03
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Key S. MICHEL-PONNELLE
:
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Justification

In thermics, the step of time T
cannot be unspecified, it must check a condition
T
min < T
< T
max, T
min and T
max depending on the properties materials, the size of the elements
stop and parameters of temporal integration (cf [R3.06.07]).
In the case of fast transitory problems of thermics, one can be brought to use a step of
too small time. One can then observe oscillations of the solution and temperatures not
physics due to the violation of the principle of the maximum (temperature higher than the initial temperature
of a part which one cools). The modeling DIAG, which consists with diagonaliser the matrix of mass,
allows to free itself from the condition on T
min and to avoid the associated problems.
Let us note however that this diagonalisation is not enough to remove the oscillations with
quadratic elements. However, in Aster, a particular processing is made for the elements 2D:
the triangles are automatically cut in linear finite elements which themselves are lumpés.


2.2.2 In
mechanics

Three types of modelings are available to solve problems of non-linear mechanics
using “traditional” laws of behavior (of the elastoplasticity type):

·
isoparametric traditional finite elements: 3D, D_PLAN, C_PLAN, AXIS ([U3.14.01],
[U3.13.01]),
·
under-integrated elements
: 3D_SI, D_PLAN_SI, C_PLAN_SI, AXIS_SI ([U3.14.01],
[U3.13.05]),
·
elements being based on an quasi-incompressible formulation
: 3d_INCO,
D_PLAN_INCO, AXIS_INCO ([U3.14.06], [U3.13.07], [R3.06.08]).

We propose like choice a priori to use:

quadratic elements

With regard to the choice of modeling, it is a function of the type of elements and the need to treat
the condition of incompressibility. These considerations are summarized in the table below.

normal
quasi-incompressible
(strong
plasticity or >0.45)
standard triangles/tetrahedrons
INCO
quadrilaterals/hexahedrons
IF
IF or INCO

Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
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14/01/03
Author (S):
Key S. MICHEL-PONNELLE
:
U2.01.10-A Page
: 5/6

Justifications and precautions:

·
If the material is quasi-incompressible (> 0.45), it is preferable to use the formulation
INCO, because the standard formulation in displacement does not give good results.
·
The plastic flow is done with constant volume. This condition of incompressibility can
to cause difficulties with traditional modeling of knowing a too rigid behavior
and especially appearance of oscillations on the level of the constraints. Under-integration allows
to improve these problems, because one then checks the condition of incompressibility in less
points of Gauss. However, only elements QUAD8 and HEXA20 are really
under-integrated, for the other meshs, it is the traditional integration which is preserved. In
consequence, when phenomena of oscillations are observed for a grid
composed of triangles or tetrahedrons, it is preferable to use formulation INCO. This
improve the result clearly but calculations will be longer.
·
In the general case, under-integrated modeling gives of as good results as them
traditional finite elements, and this for a faster calculating time since one uses less
points of Gauss. In in the case of mechanical thermo calculations, that allows
to limit the difficulties at the time of the passage of the thermal deformation of origin to calculation
mechanics when refinements of the grids thermics and mechanics differ. However,
under-integration can sometimes lead to the appearance of parasitic modes. If at the end of
calculation the deformation presents this kind of nonphysical modes of deformation, it is better
to make calculation with traditional or quasi-incompressible modeling if levels of
plasticity are very important.

3
Implementation Aster

One points out here the principal stages of Aster calculation in the case of a calculation in plane deformations,
while specifying explicitly where the specifications intervene about which one spoke. For the part
mechanics, one wrote in fat what is specific to the case of a thermomechanical calculation.

3.1 Study
Thermics

·
Reading of the thermal grid

PRE_GIBI (UNITE_GIBI=19,
PRE_GMSH (UNITE_GMSH=19,
UNITE_MAILLAGE=20,)
UNITE_MAILLAGE=20,)


MA=LIRE_MAILLAGE (UNITE=20,)
MA=LIRE_MAILLAGE (UNITE=20,)

·
Choice of the thermal model

MOTH 2D=AFFE_MODELE (MAILLAGE=MA,
VERIF=' MAILLE',
AFFE=_F (GROUP_MA= (“GMA1”, “GMA2”,…),
PHENOMENE=' THERMIQUE',
MODELISATION=' PLAN_DIAG',),)

·
Thermal properties of material

·
Thermal loading

·
THER_LINEAIRE or THER_NON_LINE
THER =…

·
Post possible processing
Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

Code_Aster ®
Version
6.3
Titrate:
Note of use on the choice of the finite elements
Date
:

14/01/03
Author (S):
Key S. MICHEL-PONNELLE
:
U2.01.10-A Page
: 6/6

3.2 Study
mechanics

·
Mechanical reading grid

PRE_GIBI () or PRE_GMSH ()
MAME=CREA_MAILLAGE (

GRID = MA,
MAME=LIRE_MAILLAGE ()
LINE_QUAD=_F (TOUT=' OUI'))

·
Definition of the mechanical model
MOME=AFFE_MODELE (MAILLAGE=MAME,
VERIF=' MAILLE',
AFFE=_F (GROUP_MA= (“GMA1”, “GMA2”,…),
PHENOMENE=' MECANIQUE',
MODELISATION=' D_PLAN_SI',),);

·
Projection of thermal calculation if calculation chained on 2 different grids
CHTHER=PROJ_CHAMP (METHODE=' ELEM',
RESULTAT=THER,
MODELE_1=MOTH 2D,
MODELE_2=MOME,);

·
Mechanical characteristics of material


CHMAT = AFFE_MATERIAU (GRID = MAME,
AFFE
=
F (TEMP_REF = 20.,…)

·
Mechanical and thermal loading

CLIM=AFFE_CHAR_MECA (MODELE=MOME,
TEMP_CALCULEE=CHTHER or THER if not of projection,
DDL_IMPO= (...),
…);

·
STAT_NON_LINE

·
Postprocessings

4 Bibliography

[1]
S. MICHEL-PONNELLE, A. RAZAKANAIVO: Quality of Etudes in Mécanique of Solides:
study of the finite elements. Note EDF HT-64/02/007/B

Handbook of Utilization
U2.01 booklet: General concepts
HT-66/02/003/A

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