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Code_Aster
®
Version
7.4
Titrate:
Modeling
COQUE_3D
Date:
01/06/05
Author (S):
X. DESROCHES, F. LEBOUVIER
Key
:
U3.12.03-D
Page
:
1/4
Instruction manual
U3.12 booklet: Mechanical elements of structure 2D
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA, DeltaCAD














Instruction manual
U3.12 booklet: Mechanical elements of structure 2D
Document: U3.12.03


Modeling
COQUE_3D

Summary:
Modeling
COQUE_3D
presented here corresponds to a formulation of general kinematics of hulls and
plates, of Naghdi-Reissner type, where the generalized stresses are obtained starting from the laws of
three-dimensional behavior of constitutive materials [R3.07.04]. Contrary to modelings
DKT
-
DST
,
Q4G
corresponding to the formulations of elements of plate developed by J.L. BATOZ [bib1] which use
plane finite elements, modeling
COQUE_3D
allows to carry out structural analyzes hulls of forms
unspecified, with a good approximation of the geometry. Moreover this modeling is able of
to represent great rotations of the structures [R3.07.05] under the assumption of small deformations.
The degrees of freedom are displacements and the rotations, taken with the nodes of the elements.
The nonlinear behavior is discretized by P2 polynomials, which allows a precise calculation of
stresses.
It is usable for problems of structures three-dimensional hulls in linear mechanical analysis and
nonlinear.

This formulation also exists for problems of sections, or revolution. It rests on elements
1D: (see [U3.12.02]).
Thermomechanical calculations are chained starting from the finite elements of thermal hulls (see [U3.22.01]).
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Code_Aster
®
Version
7.4
Titrate:
Modeling
COQUE_3D
Date:
01/06/05
Author (S):
X. DESROCHES, F. LEBOUVIER
Key
:
U3.12.03-D
Page
:
2/4
Instruction manual
U3.12 booklet: Mechanical elements of structure 2D
HT-66/05/004/A
1 Discretization
1.1
Degrees of freedom
For modeling hull into three-dimensional the degrees of freedom of discretization are, in each
node of the mesh support six components of displacement (three translations and three rotations)
with the nodes nodes and mediums on the sides of the mesh support. With the central node of the mesh support
the degrees of freedom are reduced to only rotations. These nodes belong to the average layer of
the hull.
Modeling
Degrees of freedom (with each node)
COQUE_3D
DX DY DZ DRX DRY DRZ
DRX DRY DRZ
only with the central node

1.2
Net support of the matrices of rigidity, mass…
The meshs support of the finite elements, in displacement formulation, can be triangles with
7 nodes or of the quadrangles with 9 nodes. These meshs are not supposed to be plane; they are
created starting from mesh in
TRIA6
and
QUAD8
by the control
CREA_MAILLAGE
(see [U4.23.02]).
Modeling Nets Element
finished
COQUE_3D TRIA7
QUAD9
MEC3TR7H
MEC3QU9H

1.3
Net support of the loadings
All the loadings applicable to the breakages of the elements of hull are treated by discretization
direct on the mesh support of the element in displacement formulation.
No mesh support of loading is thus necessary for the faces of the elements of hull.
For the applicable loadings on the edges of the elements of hull, a mesh support of the type
SEG3
is usable:
Modeling Nets Element
finished
Remarks
COQUE_3D SEG3 MEBOCQ3

2
Assignment of the characteristics
For these elements of structures 2D ½, it is necessary to affect geometrical characteristics
who are complementary to the data of mesh. The definition of these data is carried out with
order
AFFE_CARA_ELEM
associated the key word following factor:
·
HULL
Allows to define and affect on the meshs, the thickness, the coefficient of shearing,
offsetting,…
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Code_Aster
®
Version
7.4
Titrate:
Modeling
COQUE_3D
Date:
01/06/05
Author (S):
X. DESROCHES, F. LEBOUVIER
Key
:
U3.12.03-D
Page
:
3/4
Instruction manual
U3.12 booklet: Mechanical elements of structure 2D
HT-66/05/004/A
3 Loadings
supported
The loadings available are as follows:
·
“FORCE_ARETE”
Allows to apply linear forces, with an edge of voluminal element.
·
“FORCE_COQUE”
Allows to apply surface efforts.
·
“GRAVITY”
Allows to apply a loading of the gravity type.
·
“TEMP_CALCULEE”
Allows to apply a thermal loading.
·
“PRES_REP”
Allows to apply a pressure to a field of continuous medium.
·
“ROTATION”
Allows to define the rotational speed and the vector of rotation.

4 Possibilities
non-linear
4.1
Law of behaviors
All relations in stresses plane, usable under
COMP_INCR
in
STAT_NON_LINE
, and
DYNA_NON_LINE
are available, like all the other relations 3D while using
ALGO_C_PLAN
= “DEBORST”
(Cf [U4.51.11]).
4.2 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.
/“PETIT_REAC”
The increments of deformations used in the incremental relation of behavior are
linearized deformations of the increment of displacement in the reactualized geometry.
/“GREEN_GR”
Allows to carry out calculations in great displacements and great rotations.
deformations used in the relation of behavior are the deformations of
GREEN-LAGRANGE.
Note:
·
Attention, the calculation of the deformations using
PETIT_REAC
is only one approximation of
assumptions of great displacements. It requires to carry out very small increments of
loading. To correctly take into account great displacements, and especially them
great rotations, it is recommended to use
DEFORMATION=' GREEN_GR'
.
·
It is possible while using under the key word factor
EXCIT
(TYPE_CHARGE=' SUIV')
of
to take into account a following pressure.
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Code_Aster
®
Version
7.4
Titrate:
Modeling
COQUE_3D
Date:
01/06/05
Author (S):
X. DESROCHES, F. LEBOUVIER
Key
:
U3.12.03-D
Page
:
4/4
Instruction manual
U3.12 booklet: Mechanical elements of structure 2D
HT-66/05/004/A
5
Examples of implementation: case-tests
·
Linear statics
SSLP304C [V3.02.304]: Analyze of an orthotropic square plate subjected to a uniaxial traction
out of the axes of orthotropism
·
Non-linear statics
HPLA100C [V7.01.100]: Thermoelastic analysis of a heavy hollow roll in uniform rotation.
·
Linear dynamics
SDLS01E [V2.03.01]: Calculation of the frequencies and the modes associated with bending of a plate
square thin into free-free and embedded on an edge.

6 Bibliography
[1]
J.L. BATOZ, G. DHATT: Modeling of the structures by finite elements. Vol.2 - beams and
plates - HERMES, PARIS, 1990.