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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
1/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A
Organization (S):
EDF-R & D/AMA















Instruction manual
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
(Phenomenon:
MECHANICS
) 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 stresses.
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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
2/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A
1 Discretization
1.1
Degrees of freedom
Modeling
Degrees of freedom
(with each node node)
D_PLAN
DX
: following displacement
X
DY
: following displacement
Y
EPXX
: generalized deformation XX
EPYY
: generalized deformation YY
EPZZ
: generalized deformation ZZ
EPXY
: generalized deformation XY
C_PLAN
DX
: following displacement
X
DY
: following displacement
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
: following displacement
X
DY
: following displacement
Y
C_PLAN
DX
: following displacement
X
DY
: following displacement
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
C_PLAN
TRIA6
QUAD8
Quadratic/linear
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
case-test
corresponds to a test implementing the functionality
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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
3/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A
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
“SMALL”
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
“SMALL”
·
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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
4/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A
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
·
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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
5/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A
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
·
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Code_Aster
®
Version
6.4
Titrate:
Modelings
D_PLAN_GRAD_EPSI
,
C_PLAN_GRAD_EPSI
mechanics
Date:
27/06/03
Author (S):
P. BADEL
Key
:
U3.13.06-A
Page
:
6/6
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/03/002/A

























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