Code_Aster ®
Version
6.4
Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.13.06-A Page
: 1/6

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

Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
U3.13.06 document

Modelings D_PLAN_GRAD_EPSI,
C_PLAN_GRAD_EPSI

Summary:

Modelings D_PLAN_GRAD_EPSI, C_PLAN_GRAD_EPSI (Phénomène: MECANIQUE) correspond to
finite elements whose meshs supports are surface. These modelings enrich the finite elements
surface traditional of mechanics by adding degrees of freedom of generalized deformations
allowing to carry out nonlocal calculations, the regularization utilizing the gradient of the deformations
(from where the name of modeling), for more details to see document [R5.04.02].

The assumptions of modeling are as follows:

· D_PLAN_GRAD_EPSI for the plane deformations,
· C_PLAN_GRAD_EPSI for the plane constraints.
Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

Code_Aster ®
Version
6.4
Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.13.06-A Page
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1 Discretization

1.1
Degrees of freedom

Modeling
Degrees of freedom
(with each node node)
D_PLAN
DX: displacement following X
DY: displacement following Y
EPXX: generalized deformation XX
EPYY: generalized deformation YY
EPZZ: generalized deformation ZZ
EPXY: generalized deformation XY
C_PLAN
DX: displacement following X
DY: displacement following Y
EPXX: generalized deformation XX
EPYY: generalized deformation YY
EPZZ: generalized deformation ZZ
EPXY: generalized deformation XY

Modeling
Degrees of freedom
(with each node medium)
D_PLAN
DX: displacement following X
DY: displacement following Y
C_PLAN
DX: displacement following X
DY: displacement following Y

1.2
Net support of the matrices of rigidity

The meshs support of the finite elements can be quadratic triangle or quadrangles:
displacements are interpolated with a command higher than the deformations generalized. One indicates in
the column interpolation of the table following the couples of interpolation (displacements/deformations
generalized). The elements are isoparametric.

Modelings Nets
Interpolation
D_PLAN
TRIA6
Quadratic/linear
C_PLAN
QUAD8
Bilinear Serendip/

1.3
Net support of the loadings

Modeling does not require a boundary condition specific to the generalized deformations
(boundary condition natural), one thus uses for the meshs support of the loading
modeling D_PLAN or C_PLAN (Cf. [U3.13.01]).

2
Significance of the symbols

·
corresponds to a functionality available

corresponds to a functionality which could exist but noncurrently available
Name of corresponds to a test implementing the functionality
case-test
Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

Code_Aster ®
Version
6.4
Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.13.06-A Page
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3 Materials
supported

DEFI_MATERIAU
D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI

% General elastic Behaviors

ELAS
SSNV131B
% General nonlinear mechanical Behaviors

ECRO_LINE
SSNV131B
BETON_ECRO_LINE
·
MAZARS
·

The case of the nonlinear operators is approached further.

4 Loadings
supported

The loadings are to be affected on a modeling 3D, Cf. [§1.3].

5 Possibilities
non-linear

This modeling has direction only into non-linear.

5.1
STAT_NON_LINE

COMP_INCR
RELATION
D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
ENDO_FRAGILE
SSNV131B
ENDO_ISOT_BETON
·
MAZARS
·

COMP_INCR
DEFORMATION
D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
“PETIT”
SSNV131B

5.2
DYNA_NON_LINE

COMP_INCR
RELATION
D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
ENDO_FRAGILE
·
ENDO_ISOT_BETON
·
MAZARS
·

COMP_INCR
DEFORMATION
D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
“PETIT”
·
Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

Code_Aster ®
Version
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Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
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Author (S):
P. Key BADEL
:
U3.13.06-A Page
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6
Postprocessing of calculation

6.1 Option
CALC_ELEM


D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
ECIN_ELEM_DEPL
·
ENEL_ELGA
·
ENEL_ELNO_ELGA
·
EPME_ELGA_DEPL
·
EPME_ELNO_DEPL
·
EPOT_ELEM_DEPL
·
EPSI_ELGA_DEPL
·
EPSI_ELNO_DEPL
·
EQUI_ELGA_EPME
·
EQUI_ELGA_EPSI
·
EQUI_ELGA_SIGM
·
EQUI_ELNO_EPME
·
EQUI_ELNO_EPSI
·
EQUI_ELNO_SIGM
·
SIEF_ELGA_DEPL
·
SIEF_ELNO_ELGA
·
VARI_ELNO_ELGA
·

6.2 Option
CALC_CHAM_ELEM


D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
ECIN_ELEM_DEPL

EPOT_ELEM_DEPL
·
ENEL_ELGA
·
ENEL_ELNO_ELGA
·
EPSI_ELNO_DEPL
·
EQUI_ELGA_EPSI
·
EQUI_ELGA_SIGM
·
EQUI_ELNO_EPSI
·
EQUI_ELNO_SIGM
·
SIEF_ELGA_DEPL
·

Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

Code_Aster ®
Version
6.4
Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.13.06-A Page
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6.3 Option
CALC_NO


D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
FORC_NODA'
·
REAC_NODA'
·
ENEL_NOEU_ELGA'
·
EPME_NOEU_DEPL'
·
EPSI_NOEU_DEPL'
·
EQUI_NOEU_EPME'
·
EQUI_NOEU_EPSI'
·
EQUI_NOEU_SIGM'
·
SIEF_NOEU_ELGA'
·
VARI_NOEU_ELGA'
·

6.4 Option
POST_ELEM


D_PLAN_GRAD_EPSI
C_PLAN_GRAD_EPSI
MASS_INER
·
ENER_POT
·
ENER_CIN

ENER_TOTALE
·
ENER_ELAS
·

Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

Code_Aster ®
Version
6.4
Titrate:
Modelings D_PLAN_GRAD_EPSI, mechanical C_PLAN_GRAD_EPSI
Date:
27/06/03
Author (S):
P. Key BADEL
:
U3.13.06-A Page
: 6/6

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Handbook of Utilization
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

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