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Code_Aster
®
Version
7.4
Titrate:
Modelings
AXIS_INCO
,
D_PLAN_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.13.07-D
Page
:
1/4
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD















Instruction manual
U3.13 booklet: Mechanical finite elements 2D
Document: U3.13.07



Modelings
AXIS_INCO
,
D_PLAN_INCO




Summary:

This document describes for modelings
AXIS_INCO
,
D_PLAN_INCO
:
·
degrees of freedom carried by the finite elements which support modeling,
·
the related meshs supports,
·
supported loadings,
·
non-linear possibilities,
·
case-tests implementing modelings.

This modeling is based on finite elements adapted to the processing of the problems
quasi-incompressible. It is essential to carry out calculations of limiting analysis with the law of Norton-
Hoff and is also useful for the studies presenting of strong plastic deformations for which
conventional formulation in displacement appears insufficient (oscillation of the stresses). The formulation used
is a formulation with 3 fields: displacement-pressure-swelling [R6.03.05], usable with all them
behaviors written in incremental form. Modelings are supported by plane meshs of
degree 2 (
TRIA6
and
QUAD8
).
background image
Code_Aster
®
Version
7.4
Titrate:
Modelings
AXIS_INCO
,
D_PLAN_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.13.07-D
Page
:
2/4
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/05/004/A
1 Discretization
1.1
Degrees of freedom
Modeling
Ddl with all the nodes
Ddl only with the nodes
nodes
D_PLAN_INCO
DX, DY
CLOSE (*), GONF
AXIS_INCO
DX, DY
CLOSE (*), GONF
* no kinematic condition can be imposed on the degree of freedom
NEAR
.

1.2
Net support of the matrices of rigidity
The meshs support of the finite elements can be triangles, or quadrangles (degree 2) for
modelings
D_PLAN_INCO
and
AXIS_INCO
.
Modeling Nets Interpolation
in displacement
Interpolation
in pressure and
swelling
D_PLAN_INCO TRIA6
Quadratic Linear
QUAD8
Quadratic Linear
AXIS_INCO TRIA6
Quadratic Linear
QUAD8
Quadratic Linear

1.3
Net support of the surface loadings
Modeling
Net
Interpolation in displacements
D_PLAN_INCO
and
AXIS_INCO
SEG3
Quadratic

2 Loadings
supported
The loadings available are as follows:
·
“CONTACT”
Allows to define the areas subjected to conditions of contact.
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO
·
“FORCE_CONTOUR”
Allows to apply linear forces at the edge of a field 2D.
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO
·
“FORCE_INTERN”
Allows to apply voluminal forces.
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO
·
“GRAVITY”
Allows to apply a loading of the gravity type.
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO
·
“PRES_REP”
Allows to apply a pressure to a field of continuous medium.
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO
background image
Code_Aster
®
Version
7.4
Titrate:
Modelings
AXIS_INCO
,
D_PLAN_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.13.07-D
Page
:
3/4
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/05/004/A
3 Possibilities
non-linear
Attention, this modeling is accessible only from
STAT_NON_LINE
. It cannot be
used with
MECA_STATIQUE
or by a manual assembly.

3.1
Laws of behaviors
All the laws of behavior usable on meshs of continuous mediums have a physical direction
for these modelings and are allocatable as from the moment when they are accessible from
COMP_INCR
in
STAT_NON_LINE
(Cf [U4.51.11]).
A law of behavior is specific to this modeling (dedicated to the calculation of limiting load,
cf [R7.07.01]):
/“NORTON_HOFF”
Supported modelings:
D_PLAN_INCO
,
AXIS_INCO

3.2 Deformations
Deformations available, used in the relations of behavior under the key word
DEFORMATION
for the operators
STAT_NON_LINE
and
DYNA_NON_LINE
are (cf [U4.51.11]):
/“SMALL”
The deformations used for the relation of behavior are the deformations
linearized.
/“SIMO_MIEHE”
Allows to carry out calculations in great plastic deformations.

3.3
Method of Newton
For the resolution of the problem by the method of Newton-Raphson, the elastic matrix is not
available. It is thus necessary to use under the key word
NEWTON
for the operators
STAT_NON_LINE
and
DYNA_NON_LINE
(Cf [U4.51.11]):
/PREDICTION = “TANGENT”
The phase of prediction is carried out with the tangent matrix.
/MATRIX = “TANGENT”
The matrix used for the iterations total is the tangent matrix.
Note:
The formulation used leads to nonpositive matrices and the current solveurs do not know
to solve always well the linear systems which are associated for them. In the event of difficulty of
convergence, it can thus be useful to test the other solveurs available in the code or them
other methods of renumérotations (cf [U4.50.01]).
background image
Code_Aster
®
Version
7.4
Titrate:
Modelings
AXIS_INCO
,
D_PLAN_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.13.07-D
Page
:
4/4
Instruction manual
U3.13 booklet: Mechanical finite elements 2D
HT-66/05/004/A
4
Examples of implementation: case-tests
·
AXIS_INCO
­ Incompressible Elasticité:
SSLV130D [V3.04.130]: analyze of a hollow roll subjected to an internal pressure.
material has a Poisson's ratio equal to 0.4999.
­ Limiting Exemple of analysis:
SSNV146A [V6.04.146]: spherotoric bottom tank

·
D_PLAN_INCO
­ Elastoplastic Matériau:
SSNP123B [V6.03.123]: Analyze of a notched rectangular plate consisted of one
elastoplastic material with isotropic work hardening which is subjected to a traction with its
ends.
­ Limiting Exemple of analysis:
SSNV124A [V6.04.146]: calculation of load limits of a rectangular plate