Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 1/18
Organization (S): EDF-R & D/AMA, DeltaCAD
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.102
SSLL102 - Embedded Poutre subjected to efforts
unit
Summary:
This test allows a simple checking of calculations of right beams and hull 1D in mechanics of the structures
linear statics. The model is linear.
· 7 modelings make it possible to test the various types of elements of rectangular beams in Code_Aster.
For each modeling, one calculates simultaneously 3 beams of different sections: rectangle, circle,
angle.
Modeling A makes it possible of more than test the change of reference mark: the beam is directed according to
trisecting with the total reference mark.
Modeling E tests the loading distributed on voluminal edges of elements.
Modeling F corresponds to a loading distributed varying linearly with modeling
POU_D_E.
Modeling G corresponds to a loading distributed varying linearly with modeling
POU_D_TG.
· Modeling H makes it possible to test the element of hull 1D (COQUE_C_PLAN) subjected to loads
unit.
· Modeling I makes it possible to test a loading distributed varying linearly with modeling
TUYAU_3M.
The values tested are the generalized displacements, efforts and the constraints.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 2/18
1
Problem of reference
1.1 Geometry
Right beam length L, direction X.
y
L
O
X
O
B
L = 2
Z
One calculates simultaneously 3 types of different cross sections:
B = 0.1
1 rectangular section
= 0.2 have
G
0.008
Z
1 corner section with equal wings
0.12
Gy
0.008
H = 0.12
1 circular section
1.2
Material properties
E = 2. 1011 Pa = 0.3
1.3
Boundary conditions and loadings
Embedding out of O
· 6 unit loadings in b:
Fx = 1
MX = 1
Fy = 1
My = 1
Fz = 1
Mz = 1
· 1 loading combined inflection + traction: Fx = 1 My = 1 Mz = 1
· 1 loading combined sharp efforts + torsion: Fy = 1 Fz = 1 MX = 1
· 1 loading distributed linear: Circular Fy = 1000.x section (modelings F, G, I) (with
support simple of A and B in this case)
1.4
Notation of the characteristics of cross sections
The geometrical characteristics of the cross sections are noted:`
A:
surface of the section
I, I
y
Z:
geometrical moments of inertia compared to the principal axes
of inertia of the section
JX:
constant of torsion
ay, az:
coefficients of shearing in the directions Gy and Gz
With
With
A' =
and A'
y
=
:
equivalent reduced surfaces
ay
Z
az
E, E
eccentricity of the center of torsion
y
Z:
JG:
constant of warping
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 3/18
2
Reference solution
2.1
Method of calculation used for the reference solution
· Analytical solution [bib1] and [bib2]: displacements out of B
L
Simple traction
U = F
X
X E S
F L3
2
y
(4+ y)
L Fy
Pure bending
uy =
=
12th I
Z
2nd I
Z
Z
3
2
L
L F
Pure bending
U =
4 +
= -
Z
F
12th I
Z (
Z)
Z
y
2nd I
y
y
MR. L
Torsion
X
X
=
G Jx
Mr. L2
MR. L
y
y
Pure inflection
uz = -
=
2nd I
y
E I
y
y
M2
M
Pure inflection
Z L
Z L
uy =
= +
2nd I
Z
Z
E Iz
12th I
12th I
with y
=
=
L2 GA'
Z
2
'
y
L Gas
Notice 1:
For the corner section, as the center of shearing is not confused with the center
of gravity (ey)
0, it are necessary to add the torque:
M = F .E
X
Z
y with the Fz loading = 1
This modifies displacement:
L3
U =
F
Z
Z (4 + Z
) + .e
12th I
X
y
y
Mr. L
X
X
= G.Jx
In the same way, the loading MX = 1 involves a displacement U = + .e
Z
X
y.
Loading distributed linear:
4
2
2
4
max
00652
.
0
4
U
=
3
- 10
+ 7
=
y ()
px
X
(X
L X
L)
pL
U
360LEI
y
I.E.(internal excitation)
in X = 519
.
0
L
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 4/18
Notice 2:
1
1
With regard to modeling A, the beam is carried by the vector e1 =
1.
3 1
other vectors of the local reference mark are:
- 1
- 1
1
1
e2 =
1 and E =
- 1
2
3
6
0
2
The components of the vector displacement in the total reference mark are obtained by:
1
- 1 - 1
3
2
6
1
1
- 1
U =
U
G
room
3
2
6
1
2
0
3
6
· Generalized efforts and constraints out of O:
NR
NR (O) = Fx
xx = S
M y
T
M
Z
y
Z (O) = T. L
T = F
y
y
y
xx (y) =
=
I
xy
K S
Z
y
- Mr. Z
y
T
M
Z
y (O) = - T. L
T
Z
Z ()
O = Fz xx (y) =
=
I
xz
K S
y
Z
MR. R
M
X
T
X (O) = MX ()
B
xy = xz = Jx
Mr. Z
M
y
y (O) = My ()
B
xx (Z) = Iy
M y
M
y
Z (O) = Mz ()
B
xx (y) = Iz
Loading distributed linear:
1000
1000 L 2 1000 x2
M max. R
M
2
3
Z
Z (X) = -
(L X X) V y (X) = +
-
max
xx
=
6
6
2
Iz
L 3
in X =
3
2.2
Results of reference
· Displacement of the point B,
· efforts generalized at the point O,
· constraints of the point O.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 5/18
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
J.L. BATOZ, G. DHATT: “Modeling of the structures by finite elements” - Volume 2
ED. HERMES.
[2]
N.D. PIKLEY: “Formulated for Stress, Stain & Structural Matrices” ED. John Wiley & Sounds.
3 Modeling
With
3.1
Characteristics of modeling
2 elements POU_D_E K = K
y
Z = 1 = 0 per type of section
S1: Rectangular section modelled by SECTION: “GENERALE”
With =
Iy =
- 4
Iz =
- 4
J
-
0 02
01666 10
0 6666 10
4
.
.
.
X = 0 45776
.
10
Ry = 01
.
Rz = 0 0
. 5
RT = 0 0892632
.
(Not of calculation of the constraints)
S2: Corner section
With =
-
1856
.
10 3
Iy =
-
4 167339
.
10 4 Iz =
-
1045547
.
10 4 J
- 8
X = 03 9595
.
10
E =
-
41012
.
10 3rd
y
Z = 0.
S3: Rectangular section modelled by SECTION: RECTANGLE
Hy = 0 2
.
Hz = 01
.
S4: Section RINGS R = 01
.
R4
I = I
- 4
10
.
y
Z =
=
4
4
3.2
Characteristics of the grid
4 X 2 elements POU_D_E. The beam is directed according to the vector (1, 1, 1).
3.3 Functionalities
tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
“RECTANGLE”
“CERCLE”
CALC_ELEM “EFGE_ELNO_DEPL”
“SIGM_ELNO_DEPL”
“SIPO_ELNO_DEPL”
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 6/18
4
Results of modeling A
4.1 Values
tested
Loading case
Beam
Identification
Reference
Aster %
difference
Fx = 1
S1 = S3 ux (B)
2.887 1010 2.887
1010 0
xx (0)
50. 50.
0
S2
ux (B)
3.11 109 3.11
109 0
S4
ux (B)
1.838 1010 1.838
1010 0
xx
31.83 31.831
0
Fy = 1
S1 = S3 uy (B)
+1.414 107 1.414
107 0
Z (B)
1.225 107 1.225
107 0
xx (0)
3000 3000
0
S2
uy (B)
9.017 108 9.017
108 0
S4
xx (0)
2546.479 2546.48
0
Fz = 1
S1 = S3 uz (B)
6.532 107 6.532
107 0
y (B)
4.243 107 4.243
107 0
xx (0)
6000 6000
0
xz (0)
50 50
0
S2
uz (B)
9.279 107 9.279
107 0
y (B)
1.553 105
1.553 105
0
X (B)
1.555 105 1.555
105 0
S4
uz (B)
1.386 107 1.386
107 0
y (B)
9 108 9
108 0
xx (0)
2546.479 2546.479
0
xz (0)
31.831 31.831
0
MX = 1
S1 = S3 X (B)
3.279 107 3.279
107 0
xy = xz (0)
1950 1950
0
S2
X (B)
3.791 104 3.791
104
uz (B)
2.199 105 2.199
105 0
S4
X (B)
9.556 108 9.556
108 0
xy = xz (0)
636.62 636.62
0
My = 1
S1 = S3 uz (B)
4.899 107 4.899
107 0
y (B)
4.243 107 4.243
107 0
xx (0)
3000 3000
0
S2
uz (B)
1.959 108 1.959
108 0
y (B)
1.697 108 1.697
108 0
S4
uz (B)
1.04 107 1.04
107 0
y (B)
9 108
9 108
0
xx (0)
1273.2395 1273.2395
0
Mz = 1
S1= S3
uy (B)
1.061 107 1.061
107 0
Z (B)
1.225 107
1.225 107
0
xx (0)
1500 1500
0
S2
uy (B)
6.763 108 6.763
108 0
Z (B)
7.809 108 7.809
108 0
S4
uy (B) 9
107 9
107 0
Z (B)
1.04 107
1.04 107
0
xx (0)
1273.2395 1273.2395
0
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 7/18
My = 1
S1= S3
xx max (0)
4550 4550
0
M
Z = 1
B has
1550
1550
0
F
,
X = 1
xx 2 2
S4
xx max (0)
1832.4636 1832.46
0
Fy = 1
S1, S3
xy (0)
2000 2000
0
Fz = 1
xz (0)
2000 2000
0
MX = 1
xx max (0)
9000 9000
0
B has
S1, S3
9000
9000
0
xx
,
2 2
S4
xx max (0)
3601.27 3601.27
0
xy (0)
668.451
0
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 8/18
5 Modeling
B
5.1
Characteristics of modeling
2 elements POU_D_T.
The coefficients of shearing are:
S1: Rectangular section
1
AY = AZ = 12
. =
ky
S2: Corner section
1
AY = AZ =
0 358
.
S4: Section RINGS
10
AY = AZ =
9
5.2
Characteristics of the grid
4 X 2 elements POU_D_T
5.3 Functionalities
tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
“RECTANGLE”
“CERCLE”
CALC_ELEM “EFGE_ELNO_DEPL”
“SIGM_ELNO_DEPL”
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 9/18
6
Results of modeling B
6.1 Values
tested
One gives only the values which differ from modeling A (because of the taking into account of
transverse shearing).
Loading Section
Identification Reference
Aster %
difference
Fy = 1
S1 = S3
uy (B)
2.0156 107 2.0156
107
0
xy (0)
60. 60.
0
S2
uy (B)
1.666552 107 1.666552
107
0
S4
uy (B)
1.70684 107 1.70684
107
0
xy (0)
35.367765 35.367765
0
Fz = 1
S1, S3
uz (B)
8.0156 107 8.0156
107
0
xz (0)
60. 60.
0
S2
uz (B)
1.17559754 106 1.17559754
106
0
S4
uz (B)
1.70684 107 1.70684
107
0
xz (0)
35.367765 35.367765
0
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 10/18
7 Modeling
C
7.1
Characteristics of modeling
2 elements POU_D_TG.
Warping is not constrained.
The coefficients of shearing are identical to those of modeling B.
7.2
Characteristics of the grid
4 X 2 elements POU_D_TG
7.3 Functionalities
tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
“RECTANGLE”
“CERCLE”
CALC_ELEM “EFGE_ELNO_DEPL”
“SIGM_ELNO_DEPL”
8
Results of modeling C
8.1 Values
tested
Loading Section
Identification
Reference
Aster %
difference
Fy = 1
S1 = S3
uy (B)
2.0156 107 2.0156
107
0
xy (0)
60. 60.
0
S2
uy (B)
1.666552 107 1.666552
107
0
S4
uy (B)
1.70684 107 1.70684
107
0
xy (0)
35.367765 35.367765
0
Fz = 1
S1, S3
uz (B)
8.0156 107 8.0156
107
0
xz (0)
60. 60.
0
S2
uz (B)
1.17559754 106 1.17559754
106
0
S4
uz (B)
1.70684 107 1.70684
107
0
xz (0)
35.367765 35.367765
0
8.2 Notice
Warping is not constrained. The results are thus identical to those of modeling B.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 11/18
9 Modeling
D
9.1
Characteristics of modeling
· Elements POU_D_TG,
· constrained torsion
- 8
·
5.5556 10
for S1
JG =
- 11
4.439822 10
for S2
· in 0 GRX = 0
9.2
Characteristics of the grid
· 10 elements,
· refinement towards embedding.
10 Results of modeling D
10.1 Values
tested
Same results as for modeling C, except those which relate to the effects of warping.
Loading Section
Identification Reference
Aster %
difference
Fz = 1
S2
X = DRX
2.62034 105 2.62021
105 5.
105
uz = DZ
1.14578 106 1.14573
106 5.
105
GRX
1.34652 105 1.34652
105 1.
105
MX = 1
S1
X = DRX
5.52 107 5.52
107 5.
105
GRX
2.84 107 2.84
107
0
S2
uz
2.6203 105 2.6202
105 5.
105
X
6.3892 104 6.3889
104 5.
105
GRX
3.28324 104 3.28324
104
0
10.2 Remarks
For X the solution is (cf [bib1]):
Mr. L
M
X
X
2 L
L
GJ
2
X =
+
1 - E
- 2nd
=
3
2 L
G Jx
E JG (
1 + E
) (
)
E JG
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 12/18
11 Modeling
E
11.1 Characteristics of modeling
The beam is with a grid in solid elements quadratic HEXA20.
fz
L2
B = 0.1
surf1
Z
y
= 0.2 have
X
L = 2
The beam is embedded on the level of the section surf1. It is subjected to a unit sharp effort
who is modelled by a linear density of load fz applying to 4 constituent meshs SEG3
the higher edge L2.
11.2 Characteristics of the grid
The beam is with a grid with 640 solid elements quadratic HEXA20.
The model comprises 3665 nodes.
11.3 Functionalities
tested
One tests functionality FORCE_ARETE of AFFE_CHAR_MECA.
12 Results of modeling E
12.1 Values
tested
One tests the value of the arrow according to Z of the node medium of the section where the loading is applied
(N62 node).
Identification Reference Aster %
difference
dz of the N62 node
8 107 7.9523
107
0.596
12.2 Remarks
The value of reference corresponds to the value given by R.D.M.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 13/18
13 Modeling
F
13.1 Characteristics of modeling
The model is composed of 10 elements right beam of Euler. The section is circular full, of radius
0.1m.
13.2 Characteristics of the grid
It consists of 10 elements POU_D_E. The length of the beam is L = 6 m
13.3 Functionalities tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
AFFE_CHAR_MECA DDL_IMPO
CALC_ELEM EFGE_ELNO_DEPL
SIGM_ELNO_DEPL
14 Results of modeling F
14.1 Values
tested
14.1.1 Interior efforts
Results
analytical
Results
Aster Variation
(%)
Vy (0) 6.0000E+03 6.0000E+03
0.0000
Vy (6) 1.2000E+04 1.2000E+04
0.0000
MFZ (2 3)
1.3856E+04 1.3856E+04
0.0000
14.1.2 Constraint
Results
analytical
Results
Aster Variation
(%)
SIXX (2 3)
1.7642E+07 1.7642E+07
0.0000
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 14/18
15 Modeling
G
15.1 Characteristics of modeling
The model is composed of 10 elements right beam of Timoshenko with warping. The section
is circular full, of radius 0.1m.
15.2 Characteristics of the grid
It consists of 10 elements POU_D_TG. The length of the beam is L = 6 m
15.3 Functionalities tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
AFFE_CHAR_MECA DDL_IMPO
CALC_ELEM EFGE_ELNO_DEPL
SIGM_ELNO_DEPL
16 Results of modeling G
16.1 Values
tested
16.1.1 Interior efforts
Results
analytical
Results
Aster Variation
(%)
Vy (0) 6.0000E+03 6.0000E+03
0.0000
Vy (6) 1.2000E+04 1.2000E+04
0.0000
MFZ (2 3)
1.3856E+04 1.3856E+04
0.0000
16.1.2 Constraint
Results
analytical
Results
Aster Variation
(%)
SIXX (2 3)
1.7642E+07 1.7642E+07
0.0000
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 15/18
17 Modeling
H
17.1 Characteristics of modeling
y
Modeling COQUE_C_PLAN
4
X
- Rectangular Section
O
B
- Limiting Conditions: Not O U = v = Z = 0
Z
- Unit Loading: Not B Fx, Fy and Mz
17.2 Characteristics of the grid
A number of nodes: 9
A number of meshs and types: 4 SEG3
17.3 Functionalities tested
Commands
AFFE_MODELE AFFE
“COQUE_C_PLAN”
AFFE_CARA_ELEM HULL
EPAIS
CALC_ELEM OPTION
“EFGE_ELNO_DEPL”
“SIGM_ELNO_DEPL”
AFFE_CHAR_MECA
FORCE_NODALE
FX FY MZ
18 Results of modeling H
18.1 Values
tested
Loading case
Beam Identification
Reference
Aster %
difference
Fx = 1
S1
ux (B)
5. 1010 5.
1010 0.
xx (0)
5.
5.
0.
Fy = 1
S1
uy (B)
2. 107 2.007
107 0.333
Z (B)
1.5 107 1.5
107 0.
xx (0)
300. 289.27
3.576
Mz = 1
S1
uy (B)
1.5 107 1.5
107 0.
Z (B)
1.5 107
1.5 107
0.
xx (0)
150. 150.
0.
18.2 Remarks
The width for modeling COQUE_C_PLAN is imposed on 1 in Code_Aster. In
consequence, we multiplied by 0.1 the Young modulus to take account of the real width of
the beam. This width of 1 modifies the inertia of the beam and consequently the value of the constraint
xx which is 10 with times lower than the value of reference. Moreover, for displacements, the results
differ from modeling A because of the change of reference mark.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 16/18
19 Modeling
I
19.1 Characteristics of modeling
The model is composed of 21 elements TUYAU_3M.
19.2 Characteristics of the grid
It consists of 21 meshs SEG3. The length of the beam is L = 6 m
19.3 Functionalities tested
Commands
AFFE_CARA_ELEM
POUTRE: SECTION
“GENERALE”
AFFE_CHAR_MECA DDL_IMPO
AFFE_CHAR_MECA_F FORCE_POUTRE
MECA_STATIQUE
STAT_NON_LINE COMP_INCR
RELATION
ELAS
CALC_ELEM
OPTION
SIEF_ELNO_ELGA
CALC_NO
OPTION
FORC_NODA
CALC_NO
OPTION
REAC_NODA
CALC_NO
OPTION
EFGE_NOEU_DEPL
20 Results of modeling I
20.1 Values
tested
20.1.1 Displacements
Results
analytical
Results
Aster Variation
(%)
Maximum Dy
9.38888E-03
9.44033E-03
0.55
20.1.2 Interior efforts
Results
analytical
Results
Aster Variation
(%)
Vy (x=0) 6.0000E+03
6.0076E+03
0.127
Vy (x=L=6) 1.2000E+04 1.1995E+04
0.042
MFZ (2 3)
1.3856E+04 1.388E+04
0.171
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 17/18
21 Summary of the results
This test makes it possible simultaneously to check the correct operation of elements POU_D_E, POU_D_T and
POU_D_TG on 3 types of different sections. The perfect coincidence of the results with the solutions
analytical (RDM) is normal, and must always be observed, since the solution is contained in
functions of form of the elements.
Moreover, modeling E makes it possible to test the loading distributed on edges of elements
voluminal. The variation with the analytical solution (RDM) is lower than 0.6%.
Modelings F, G and I make it possible to test the loading distributed (linear variation) for
elements of beam POU_D_E, POU_D_TG and pipe sections. The variation with the analytical solution
(RDM) is lower than 0.6%.
For modeling COQUE_C_PLAN the results are satisfactory (displacements and constraints)
for the unit loadings of extension type and inflection (imposed moment). For the loading of
inflection (load imposed at an end) the error on displacement is weak 0.5%. It is more
important on the constraint: 3.6%.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Code_Aster ®
Version
6.2
Titrate:
SSLL102 - Embedded Poutre subjected to unit efforts
Date:
20/12/02
Author (S):
J.M. PROIX, J. PELLET, F. LEBOUVIER
Key: V3.01.102-D Page: 18/18
Intentionally white left page.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Outline document