Code_Aster
®
Version
7.4
Titrate:
Modeling
3d_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.14.06-D
Page
:
1/4
Instruction manual
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD
Instruction manual
U3.14 booklet: Mechanical finite elements 3D
Document: U3.14.06
Modeling
3d_INCO
Summary:
This document describes for modeling
3d_INCO
:
·
degrees of freedom carried by the finite elements which support modeling,
·
the related meshs supports,
·
laws of behavior and loadings supported,
·
non-linear possibilities,
·
case-tests implementing modeling.
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. Modeling
3d_INCO
has voluminal meshs supports and
accept them
TETRA10
, them
HEXA20
, and them
PENTA15
.
Code_Aster
®
Version
7.4
Titrate:
Modeling
3d_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.14.06-D
Page
:
2/4
Instruction manual
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A
1 Discretization
1.1
Degrees of freedom
Modeling
Ddl with all the nodes
Ddl only with the nodes nodes
3D
DX, DY, DZ
CLOSE (*), GONF
* no kinematic condition can be imposed on the degree of freedom
NEAR
.
1.2
Net support of the matrices of rigidity
For modeling 3D, the meshs support of the finite elements can be tetrahedrons,
hexahedrons or of the prisms.
Modeling Nets
Interpolation
in
displacements
Interpolation in
pressure and swelling
3D TETRA10
Quadratic Linear
HEXA20
Quadratic Linear
PENTA15
Quadratic Linear
1.3
Net support of the surface loadings
Modeling
Net
Interpolation in displacements
3D TRIA6
Quadratic
QUAD8
Quadratic
2 Loadings
supported
Loadings available under
AFFE_CHAR_MECA_
are as follows:
·
“FORCE_ARETE”
Allows to apply linear forces, with an edge of voluminal element.
·
“FORCE_FACE”
Allows to apply surface forces to a voluminal face of element.
·
“FORCE_INTERN”
Allows to apply voluminal forces.
·
“GRAVITY”
Allows to apply a loading of the gravity type.
·
“PRES_REP”
Allows to apply a pressure to a field of continuous medium.
Code_Aster
®
Version
7.4
Titrate:
Modeling
3d_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.14.06-D
Page
:
3/4
Instruction manual
U3.14 booklet: Mechanical finite elements 3D
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 behavior
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]).
Let us announce that a law of behavior is specific to this modeling (dedicated to the calculation of load
limit, cf [R7.07.01]):
/“NORTON_HOFF”
3.2 Deformations
Deformations available, used in the relations of behavior under the key word
DEFORMATION
for the operators
STAT_NON_LINE
,
DYNA_NON_LINE
and
DYNA_TRANS_EXPLI
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]).
Code_Aster
®
Version
7.4
Titrate:
Modeling
3d_INCO
Date:
01/06/05
Author (S):
S. MICHEL-PONNELLE, F. LEBOUVIER
Key
:
U3.14.06-D
Page
:
4/4
Instruction manual
U3.14 booklet: Mechanical finite elements 3D
HT-66/05/004/A
4
Examples of implementation: case-tests
·
Small deformations:
SSLV130A [V3.04.130]: Analyze of a hollow roll into incompressible, subjected to a pressure
intern.
·
Great deformations:
SSNV112A [V6.04.112]: Analyze of a hollow roll into incompressible in great deformations,
subjected to an internal radial displacement.
·
Analyze limit:
SSNV124B [V6.04.124]: Determination of the load limits of a cube subjected to loadings
on its edges.