Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
1/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
Organization (S):
EDF-R & D/MMC
Manual of Validation
V6.04 booklet: Non-linear statics of the voluminal structures
Document: V6.04.163
SSNV163 - Clean calculation of creep
with model UMLV
Summary:
This test makes it possible to validate the clean model of creep UMLV. The results of this test are compared with
analytical solution for three modelings: 3D, axisymmetric and plane stresses.
Code_Aster
®
Version
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Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
2/16
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
1
Problem of reference
1.1 Geometry
Z
X
y
L
H
E
height:
H = 1,00 [m]
width:
L = 1,00 [m]
thickness:
E = 1,00 [m]
1.2
Properties of material
31
=
E
GPa
2
,
0
=
Here one informs also the curve sorption-desorption which connects the water content
C
with the hygroscopy
H
.
In this case one supposed that the numerical values of
C
and of
H
are the same ones.
Parameters specific to clean creep:
5
0
,
2
+
=
E
K
Sr
[MPa]
spherical part: rigidity connects associated with the formed skeleton
by blocks of hydrates on a mesoscopic scale
4
0
,
5
+
=
E
K
if
[MPa]
spherical part: rigidity connects intrinsically associated
with the hydrates on a microscopic scale
4
0
,
5
+
=
E
K
D
R
[MPa]
deviatoric part: rigidity associated with the capacity with water
adsorbed to transmit loads (load bearing toilets)
10
0
,
4
+
=
E
Sr
[MPa.s]
spherical part:viscosity connects associated with the mechanism
of dissemination within capillary porosity
11
0
,
1
+
=
E
if
[MPa.s]
spherical part: viscosity connects associated with the mechanism
of dissemination interlamellaire
10
0
,
1
+
=
E
D
R
[MPa.s]
deviatoric part:viscosity associated with the water adsorbed by
layers of hydrates
11
0
,
1
+
=
E
D
I
[MPa.s]
deviatoric part: viscosity of interstitial water.
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
1.3
Boundary conditions and loadings
In this test, one creates a homogeneous field of drying invariant in the structure, moisture is worth
100% (condition of a sealed test-tube). The mechanical loading corresponds to a compression
one-way according to the vertical direction (Z in 3D or there of 2D); its intensity is 1 [MPa].
load is applied in 1s and is maintained constant for 100 days.
1.4 Conditions
initial
The beginning of calculation is supposed the moment 1. At this moment there is neither field of drying, nor forced
mechanics.
At moment 0, one applies a field of drying corresponding to 100% of hygroscopy.
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
4/16
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
2
Reference solution
2.1
Method of calculation
This section presents the analytical resolution supplements problem of a body of test subjected to
a homogeneous and one-way stress field applied instantaneously to the initial moment
and maintained constant thereafter (case of a creep test in simple compression):
Z
Z
E
E
=
0
éq 2.1-1
Whose partly spherical and deviatoric decomposition is written:
(
)
4
4
4
4
4
4
4
3
4
4
4
4
4
4
4
2
1
3
2
1
ue
déviatoriq
part
spherical
part
y
y
X
X
Z
Z
E
E
E
E
E
E
+
-
+
=
0
0
0
3
1
3
2
1
3
1
éq
2.1-2
By operating a spherical/deviatoric decomposition identical to that of the stresses,
axial deformation is written in the form:
(
)
(
)
3
2
3
0
0
fd
fs
zz
+
=
éq
2.1-3
It is thus necessary successively to solve the response to a level of spherical stress and one
level of deviatoric stresses.
2.2
Resolution of the equations constitutive of spherical creep [bib2]
The process of deformation spherical of creep is controlled by the system of coupled equations
according to (equations [éq 2.2-1] and [éq 2.2-2], cf [R7.01.06]):
[
]
fs
I
fs
R
Sr
S
Sr
fs
K
H
&
&
-
-
=
1
éq
2.2-1
where
Sr
K
indicate rigidity connect associated with the skeleton formed by blocks with hydrates on the scale
mesoscopic;
and
Sr
viscosity connects associated with the mechanism with dissemination within capillary porosity.
(
)
[
] [
]
+
-
-
+
-
=
fs
R
Sr
S
fs
I
if
Sr
fs
Sr
if
fs
I
K
H
K
K
K
1
&
éq
2.2-1
where
if
K
indicate rigidity connect intrinsically associated with the hydrates on the scale
microscopic;
and
if
viscosity connects associated with the interfoliaceous mechanism of dissemination.
In [éq 2.2-2], hooks
+
appoint the operator of Mac Cauley:
(
)
X
X
X
+
=
+
2
1
The resolution of the preceding system of coupled equations requires to distinguish two cases according to
sign quantity ranging between the hooks of Mac Cauley. In the continuation, one presents
analytical resolution of the response to a level of stress
S
. The relative humidity is supposed
invariant; the medium is saturated with water.
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
5/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
2.2.1 Case of short-term creep
At the initial moment, T = 0, one applies a spherical stress
S
positive. Deformations of creep
reversible and irreversible are equal to zero (initial conditions). The equation of the system [éq 2.2-2]
is thus written:
(
)
[
]
[]
0
1
0
0
2
1
0
=
-
=
-
-
=
=
+
+
S
if
S
S
I
Sr
if
fs
I
K
K
T
&
éq
2.2.1-1
The speed of irreversible deformation of creep is thus equal to zero. One deduces from it that
irreversible deformation of creep is also equal to zero. The speed of deformation unrecoverable remains
equalize to zero until the moment
0
T
T
=
, defined by the relation [éq 2.2.1-2]:
()
()
Sr
S
fs
R
S
fs
R
Sr
K
T
T
K
=
=
-
2
0
2
0
0
éq
2.2.1-2
Until the moment
0
T
T
=
, the reversible deformation of creep is defined by the following relation:
[
]
()
-
-
=
-
=
Sr
Sr
S
Sr
Sr
Sr
S
Sr
Sr
T
K
T
K
exp
1
1
&
éq
2.2.1-3
Sr
Sr
Sr
K
=
is the characteristic time associated the reversible deformation of creep. The moment
0
T
is
thus defined by the relation [éq 2.2.1-4]:
()
()
Sr
Sr
Sr
Sr
S
Sr
S
fs
R
T
T
K
K
T
=
-
-
=
=
69
.
0
2
ln
exp
1
2
0
0
0
éq
2.2.1-4
The reversible and irreversible deformations of creep are thus determined by:
()
()
=
-
-
=
0
exp
1
T
T
K
T
fs
S
S
S
fs
I
R
R
R
éq
2.2.1-5
During the calculation of the deformations of creep for
0
T
T
>
, the new initial conditions are thus:
()
()
=
=
0
2
0
0
T
K
T
fs
S
S
fs
I
R
R
éq
2.2.1-6
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
6/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
2.2.2 Case of long-term creep
By expressing speeds of reversible and irreversible deformations of creep according to
deformations of creep, the relation then is obtained:
-
+
-
+
=
+
+
+
-
-
=
S
if
fs
I
if
I
fs
R
if
Sr
fs
I
S
if
Sr
fs
I
if
if
fs
R
if
Sr
Sr
Sr
fs
K
K
K
K
K
R
1
2
2
1
2
4
&
&
éq 2.2.2-1
In order to simplify calculations, the following intermediate variables are defined:
I
R
laughed
I
I
I
II
R
R
R
rr
K
U
K
U
K
U
=
=
=
=
=
:
1
:
,
1
:
and
éq
2.2.2-2
The system of equations [éq 2.2.2-1] can be put then in the following matric form:
4
4 3
4
4 2
1
3
2
1
4
4
4
3
4
4
4
2
1
&
&
&
B
laughed
laughed
rr
Sr
S
fs
I
fs
R
With
II
laughed
II
laughed
rr
fs
I
fs
R
fs
U
U
U
K
U
U
U
U
U
S
-
+
+
-
-
-
=
=
2
1
2
2
4
éq
2.2.2-3
I.e.:
B
With
S
fs
fs
+
=
&
éq
2.2.2-4
Let us suppose that the matrix
With
that is to say diagonalisable (this property will be checked thereafter):
1
-
=
P
D
P
With
where
D
indicate the diagonal matrix of the eigenvalues of the matrix
With
,
P
the matrix of the clean vectors of the matrix
With
and
1
-
P
the matrix reverses matrix
P
. In
carrying out term in the long term the product by the quantity
1
-
P
, [éq 2.2.2-4] can put itself under
form:
B
P
B
P
B
D
fs
fs
S
fs
fs
=
=
+
=
-
-
1
*
1
, *
*
, *
, *
and
with
&
éq
2.2.2-5
That is to say
1
and
2
eigenvalues of the matrix
With
. The quantities are defined:
=
=
* 2
*
1
*
* 2
*
1
, *
:
:
B
B
B
fs
and
[éq 2.2.2-5] is written then:
()
()
()
()
+
=
+
=
* 2
* 2
2
* 2
*
1
*
1
1
*
1
B
T
T
B
T
T
S
S
&
&
éq
2.2.2-6
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
7/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
System whose solution is written:
()
(
)
()
(
)
+
-
=
+
-
=
0
0
exp
exp
2
1
2
2
2
* 2
* 2
1
1
1
*
1
*
1
µ
µ
T
B
T
T
B
T
S
S
éq
2.2.2-7
One can then return to initial space, by the means of the matrix of passage; deformations of
creep reversible and irreversible are linear combinations of
*
1
and
* 2
. Eigenvalues
matrix
With
,
1
and
2
are obtained while solving:
(
)
(
)
0
4
0
2
2
4
0
1
det
2
=
+
+
+
+
=
-
-
-
-
-
=
-
II
rr
I
II
laughed
rr
I
I
II
laughed
II
I
laughed
rr
I
U
U
U
U
U
U
U
U
U
U
With
éq 2.2.2-8
By noticing that
rr
U
,
laughed
U
and
II
U
are strictly positive, the discriminant is thus always
strictly positive. The eigenvalues are thus real and distinct, the matrix
With
is thus
diagonalisable. In addition, none of the two eigenvalues is equal to zero
(
)
0
2
1
=
II
rr
U
U
. The two eigenvalues are defined by:
(
)
(
)
+
+
+
-
=
-
+
+
-
=
2
4
2
4
2
1
II
laughed
rr
II
laughed
rr
U
U
U
U
U
U
éq
2.2.2-9
One can show that the two eigenvalues are indeed negative. Let us show that
second eigenvalue is negative. The spherical deformation of creep is thus asymptotic,
assumption put forth in the model of clean creep spherical [bib1]. Let us determine one now
base clean vectors
(
)
2
1
,
X
X
associated the eigenvalues
1
and
2
. It is determined in
solving the equation
(
)
0
1
=
-
I
I
X
With
.
A particular base of clean vectors is written:
II
laughed
laughed
II
U
U
X
U
U
X
X
X
X
X
+
=
+
=
=
=
2
2
1
1
2
2
1
1
2
2
1
1
and
with
and
éq
2.2.2-10
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
8/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
After having checked that
P
can be reversed indeed, one deduces the solution in space from it
physics:
()
(
)
(
)
()
(
)
(
)
(
)
[
]
(
)
[
]
-
+
-
-
=
+
+
-
=
+
+
+
-
=
+
+
+
-
=
laughed
laughed
rr
laughed
laughed
rr
S
fs
I
S
fs
R
U
X
U
U
X
X
B
U
U
U
X
X
X
B
T
X
T
B
X
B
T
T
T
X
B
B
X
T
1
2
1
* 2
2
2
1
*
1
2
2
2
1
1
2
* 2
2
1
*
1
2
2
1
1
1
2
* 2
1
*
1
1
2
1
1
2
1
1
exp
exp
exp
exp
with
µ
µ
µ
µ
éq 2.2.2-11
Lastly,
1
µ
and
2
µ
are defined by the relations:
(
)
(
)
[
]
(
)
(
)
(
)
(
)
[
]
(
)
(
)
+
-
+
-
-
=
-
+
-
-
=
0
1
1
0
1
0
2
1
2
1
2
0
2
0
2
2
0
2
1
2
1
1
exp
1
exp
2
1
exp
1
1
exp
1
exp
2
1
exp
1
1
T
X
K
T
K
T
X
X
T
K
T
X
K
T
X
X
I
R
I
R
µ
µ
éq
2.2.2-12
2.3
Resolution of the equations constitutive of creep deviatoric
The deviatoric stresses comprise a reversible part and an irreversible part
(cf [R7.01.06]):
{
{
{
free
water
one
contributi
fd
I
absobée
water
one
contributi
fd
R
total
ue
déviatoriq N
déformatio
fd
+
=
éq
2.3-1
The J
ème
main component of the total deviatoric deformation is governed by the equations
[éq 2.3-2] and [éq 2.3-3]:
J
D
J
D
R
D
R
J
D
R
D
R
H
K
,
,
,
=
+
&
éq
2.3-2
where
D
R
K
indicate rigidity associated with the capacity with water adsorbed to transmit loads (load
bearing toilets);
and
D
R
viscosity associated with the water adsorbed by the layers with hydrates.
J
D
J
D
I
D
I
H
,
,
=
&
éq 2.3-3
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
9/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
where
D
I
indicate the viscosity of interstitial water. The system of equations [éq 2.3-2] and [éq 2.3-3] is more
simple to solve that that governing the spherical behavior owing to the fact that it is uncoupled. One
always suppose that moisture remains equal to 1 during all the loading. The equation [éq 2.3-2]
corresponds to the viscoelastic model of Kelvin whose response to a level of stress is of
exponential type. As for the equation [éq 2.3-3], the response in deformation is linear with time.
The total deformation of creep is thus written as the sum of the contribution of a channel of
Kelvin and of the contribution of a shock absorber and series:
)
(
1
1
)
(
,
,
T
H
E
K
T
T
J
D
T
K
D
R
D
I
J
D
D
R
D
R
-
+
=
-
éq
2.3-4
2.4
Summary of the analytical solution
For a uniaxial loading the analytical solutions of the two components of deformation are
known. The contribution of the deviatoric part is written:
()
-
-
+
=
D
R
D
R
D
R
D
I
fd
T
K
K
T
T
exp
1
1
3
2
0
éq
2.4-1
As for the contribution of the spherical part, the solution is defined on two intervals:
()
(
) ()
(
) ()
>
+
+
+
+
+
-
-
=
2
ln
exp
1
exp
1
1
1
3
2
ln
exp
1
3
2
2
2
1
1
1
0
0
Sr
Sr
S
I
Sr
Sr
Sr
Sr
Sr
Sr
fs
K
T
T
X
T
X
K
K
K
T
T
K
K
T
µ
µ
éq 2.4-2
The axial deformation is a linear function of the two preceding contributions:
(
)
(
)
3
2
3
0
0
fd
fs
zz
+
=
éq
2.4-3
2.5
Sizes and results of reference
The test is homogeneous. One tests the deformation in an unspecified node.
2.6
Uncertainties on the solution
Exact analytical result.
Code_Aster
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Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
10/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
2.7 References
bibliographical
[1]
BENBOUDJEMA, F.: Modeling of the deformations differed from the concrete under stresses
biaxial. Application to the ships jet engines of nuclear thermal power stations, Memory of D.E.A.
Advanced materials Ingénierie of the Structures and the Envelopes, 38 p. (+ appendices) (1999).
[2]
BENBOUDJEMA, F., MEFTAH, F., HEINFLING, G., the POPE, Y.: Numerical study and
analytical of the spherical part of the clean model of creep UMLV for the concrete, notes
technique HT-25/02/040/A, 56 p (2002).
[3]
The POPE, Y.: Relation of behavior UMLV for the clean creep of the concrete,
Reference material of Code_Aster [R7.01.06], 16 p (2002).
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
11/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Z
X
y
NO2
NO1
NO3
NO4
NO8
NO7
NO5
NO6
3.2
Characteristics of the mesh
A number of nodes: 8
A number of meshs: 1 of type HEXA 8
6 of type QUAD 4
The following meshs are defined:
S_ARR
NO3 NO7 NO8 NO4
S_AVT
NO1 NO2 NO6 NO5
S_DRT
NO1 NO5 NO8 NO4
S_GCH
NO3 NO2 NO6 NO7
S_INF
NO1 NO2 NO3 NO4
S_SUP
NO5 NO6 NO7 NO8
The boundary conditions in displacement imposed are:
On nodes NO1, NO2, NO3 and NO4: DZ = 0
On nodes NO3, NO7, NO8 and NO4: DY = 0
On nodes NO2, NO6, NO7 and NO8: DX = 0
The loading is consisted of the same field of drying and the same nodal force 1/4 applied
on the four nodes of S_SUP.
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
12/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
3.3 Functionalities
tested
Controls
Key word
DEFI_MATERIAU ELAS_FO
UMLV_FP
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
AFFE_CHAR_MECA DDL_IMPO
LIAISON_UNIF
FORCE_NODALE
SECH_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION= `UMLV_FP'
3.4
Sizes tested and results
The component
xx
with node NO6 was tested.
Moment Reference
Aster %
difference
0. 0. 0.
-
1.0000E+00 3.225814D-05
3.225810D-05
1.37E-04
9.7041E+04 3.867143D-05
3.867140D-05
8.95E-05
1.8389E+06 6.088552D-05
6.088554D-05
3.25E-05
8.6400E+06 1.100478D-04
1.100473D-04
7.27E-06
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
13/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
4 Modeling
B
4.1
Characteristics of modeling
Axisymmetric modeling 2D.
X
y
N1
N2
N4
N3
4.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs: 1 of type QUAD 4
4 of type SEG2
The following meshs are defined:
L_INF NO1
NO2
L_DRT NO2
NO4
L_SUP NO4
NO3
L_GCH NO3
NO1
The boundary conditions in displacement imposed are:
On L_GCH: DY = 0
On L_INF: DX = 0
The loading is consisted of the same field of drying and the same nodal force 1/2 applied
on the two nodes of L_SUP.
4.3 Functionalities
tested
Controls
Key word
DEFI_MATERIAU ELAS_FO
UMLV_FP
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
AFFE_CHAR_MECA DDL_IMPO
LIAISON_UNIF
FORCE_NODALE
SECH_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION= `UMLV_FP'
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
14/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
4.4
Sizes tested and results
The component
yy
with node NO3 was tested
Moment Reference
Aster %
difference
0. 0. 0.
-
1.0000E+00 3.225814D-05
3.225810D-05
1.37E-04
9.7041E+04 3.867143D-05
3.867140D-05
8.95E-05
1.8389E+06 6.088552D-05
6.088554D-05
3.25E-05
8.6400E+06 1.100478D-04
1.100473D-04
7.27E-06
5 Modeling
C
5.1
Characteristics of modeling
Modeling in Plane Stresses.
X
y
N1
N2
N4
N3
5.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs: 1 of type QUAD 4
4 of type SEG2
The following meshs are defined:
L_INF NO1
NO2
L_DRT NO2
NO4
L_SUP NO4
NO3
L_GCH NO3
NO1
The boundary conditions in displacement imposed are:
On L_GCH: DY = 0
On L_INF: DX = 0
The loading is consisted of the same field of drying and the same nodal force 1/2 applied
on the two nodes of L_SUP.
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
15/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
5.3 Functionalities
tested
Controls
Key word
DEFI_MATERIAU ELAS_FO
UMLV_FP
FONC_DESORP
K_RS
K_IS
K_RD
V_RS
V_IS
V_RD
V_ID
CREA_CHAMP “AFFE”
TYPE_CHAM=' NOEU_TEMP_R'
NOM_CMP=' TEMP'
AFFE_CHAR_MECA DDL_IMPO
LIAISON_UNIF
FORCE_NODALE
SECH_CALCULEE
STAT_NON_LINE COMP_INCR
RELATION= `UMLV_FP'
ALGO_C_PLAN=' DEBORST'
5.4
Sizes tested and results
The component
yy
with node NO3 was tested
Moment Reference
Aster %
difference
0. 0. 0.
-
1.0000E+00 3.225814D-05
3.225810D-05
1.40E-04
9.7041E+04 3.867143D-05
3.867140D-05
9.225E-05
1.8389E+06 6.088552D-05
6.088554D-05
3.08E-05
8.6400E+06 1.100478D-04
1.100478D-04
8.22E-06
Code_Aster
®
Version
6.4
Titrate:
SSNV163 -
Clean calculation of creep with model UMLV
Date:
01/10/03
Author (S):
Y. The POPE
Key
:
V6.04.163-A
Page:
16/16
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-26/03/023/A
6
Summary of the results
The values obtained with Code_Aster are in agreement with the values of the analytical solution of
reference. This same test was turned with Castem at the Laboratory of Mechanics at the University of
The Marne the Valley, the same results were obtained.