Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
1/10

Organization (S): EDF-R & D/AMA, CETIM
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
V3.02.304 document

SSLP304 - Orthotropic square Plaque in traction
uniaxial out of the axes of orthotropism

Summary:

This test represents the static calculation of a square plate, out of orthotropic elastic material, of which axes
othotropie are tilted 30 degrees compared to the basic edge, subjected to a uniaxial traction. It allows
to validate the good taking into account of orthotropic elastic materials and the change of associated reference mark.
4 modelings are used: C_PLAN with meshs QUAD8 and TRIA6, in a first reference mark, C_PLAN
in a second reference mark, COQUE_3D with meshs QUAD9 and TRIA7, in small displacements and COQUE_3D in
great displacements. Displacements and the constraints obtained are compared with a reference solution
analytical.

The first two modelings of this test result from the validation independent of version 3 of
Code_Aster (linear static batch).

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
2/10

1
Problem of reference

1.1 Geometry

A square plate, made up of a tilted orthotropic material of 30 degrees compared to edge AB.

y

D
C

B

y
L



With
B
X

B

With B = 1 m, unspecified thickness (plane constraints), angle of orthotropism: = 30 degrees.

1.2
Properties of materials

The properties of materials constituting the plate are:

orthotropic rubber band:
E_L = 4.E10 Pa
E_T = 1.E10 Pa
G_LT = 0.45E10 Pa
G_TN = 0.35E10 Pa
NU_LT = 0.075

The axis L is tilted 30 degrees compared to AB.

1.3
Boundary conditions and loadings

· At point a: DX = 0, DY = 0
· At point b: DX = 0,

· Linear loading distributed: Fx = 104 Pa on BC
· Linear loading distributed: Fx = - 104 Pa on DA

1.4 Conditions
initial

Without object.
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
3/10

2
Reference solution

2.1
Method of calculation used for the reference solution

Analytical solution, obtained with the assumption of uniaxiality of the constraints:

(X, y)




xx
= F
(X, y)
X
xy
=
(X, y)
yy
=
(X, y)
zz
= 0

maybe in the reference mark (A, L, T):

(X, y) = c2F, (X, y) = s2F
(X, y) = - csF
L
X
TT
X
LT
X

By the orthotropic law of behavior elastic, by using conventions of Code_Aster in what
relate to NU_LT, (cf document of use of command DEFI_MATERIAU [§3.5.2]), one obtains
directly (see for example [bib1]):



(X, y) Fx
=
xy
, (X, y) = -
F, 2
X
(X, y) =
F
xx
E
yy
X
E
xy
X
E
X
X
X

with:

1
4
4
C
S
1


1
1
1
xy
4
4

2 2
=
+
+ C S
- 2 LT
LT
= (C + S)
- c2s2
+
-

E ()
E
E
G
E
E ()
E
E
E
G
X
X
L
T
LT
T
T
L
T
LT


2
2

y
C
S


= - Cs
-
+



(

2
2
C - S)
1
2
LT -
Ex




()
E
E
E
2
L
T

G
T
LT
with
C = cos
S = sin

As the deformations are uniform in the plate one obtains, by integration, displacements
in the reference mark (A, X, y):

U (X, y) =. X
X
xx

U (X, y) =. y + 2. X
y
yy
xy

2.2
Results of reference

Displacements in the reference mark (A, X, y) (in m):

Not B
C
D
U
0.
5.917 10­7 5.917
10­7
X
U
­ 2.292 10­7 ­ 5.028
10­7 ­ 7.319
10­7
X

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
4/10

Constraints in the reference mark related to the orthotropism:

(X, y) = 7500Pa, (X, y) = 2500Pa, (X, y) = 4330.127Pa
L
TT
LT

2.3
Uncertainty on the solution

Analytical solution

2.4 References
bibliographical

[1]
GAY D: “Composite Materials”; 3rd edition, Hermčs

3 Modeling
With

3.1
Characteristics of modeling

Modeling C_PLAN. The plate is turned of - 30 degrees around Z, i.e. axis X total
is colinéaire with the axis of orthotropism L. Les boundary conditions and loadings, to apply in
locate (A, X, y) related to the plate, are thus projected on the total reference mark (A, X, Y) (use of
LIAISON_DDL in B).

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
5/10

3.2
Characteristics of the grid

A number of nodes: 391

A number of meshs and types: 50 QUAD8, 100 TRIA6

3.3 Functionalities
tested

Commands
AFFE-MODELE
“AFFE”
MODELING = “C_PLAN”
AFFE_CARA_ELEM
MASSIF
ANGL_REP = 0
AFFE_CHAR_MECA_F FORCE_CONTOUR FX,
FY
AFFE_CHAR_MECA_F LIAISON_DDL

DEFI_MATERIAU ELAS_ORTH

MODI_REPERE
DEFI_REPERE
LOCATE = “USER”

3.4 Values
tested

Value Identification Reference
Aster %
difference
Ux (c) = Ux (D)
DX (C)
5.917 10­7 5.9167
10­7
0.007
Uy (B) DY
(B)
­ 2.292 10­7 ­ 2.2916
10­7
0.01
Uy (C) DY
(C)
­ 5.028 10­7 ­ 5.0279
10­7
0.001
Uy (D)
DY (D)
­ 7.319 10­7 ­ 7.3196
10­7
0.008
Sigma L
SIXX (any point)
7500
7500.4
0.006
Sigma TT
SIYY (any point)
2500
2500.3
0.01
Sigma L
SIXY (any point)
4300.127
433.06
0.01

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
6/10

4 Modeling
B

4.1
Characteristics of modeling

Modeling C_PLAN. The plate is parallel to the total axes, i.e. total axis X is
colinéaire with axis X. It is thus the axis of orthotropism L which is to be directed (using key word MASSIF of
AFFE_CARA_ELEM).


4.2
Characteristics of the grid

A number of nodes: 391

A number of meshs and types: 50 QUAD8, 100 TRIA6

4.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELING = “C_PLAN”
AFFE_CARA_ELEM
MASSIF
ANGL_REP = 30
AFFE_CHAR_MECA_F FORCE_CONTOUR
FX,
FY
DEFI_MATERIAU ELAS_ORTH

MODI_REPERE
DEFI_REPERE
LOCATE = “USER”
Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
7/10

4.4 Values
tested

Value Identification
Reference
Aster %
difference
Ux (c) = Ux (D)
DX (C)
5.917 10­7 5.9167
10­7
0.006
Uy (B) DY
(B)
­ 2.292 10­7 ­ 2.29166
10­7
0.015
Uy (C) DY
(C)
­ 5.028 10­7 ­ 5.0277
10­7
0.005
Uy (D)
DY (D)
­ 7.319 10­7 ­ 7.3194
10­7
0.006
Sigma L
SIXX (any point)
7500
7500
0.
Sigma TT
SIYY (any point)
2500
2500
0.
Sigma L
SIXY (any point)
4300.127
4330.127
0.

4.5 Remarks

Pace of the deformation: nonsymmetrical because of the orthotropism.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
8/10

5 Modeling
C

5.1
Characteristics of modeling

Modeling COQUE_3D. The plate is parallel to the total axes, i.e. total axis X is
colinéaire with axis X. It is thus the axis of orthotropism L which is to be directed (using key word MASSIF of
AFFE_CARA_ELEM). The grid is identical to that of modeling B.

5.2
Characteristics of the grid

A number of nodes: 541

A number of meshs and types: 50 QUAD9, 100 TRIA7

5.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION = “COQUE_3D”
AFFE_CARA_ELEM
COQUE
ANGL_REP = 30
AFFE_CARA_ELEM
COQUE
EPAIS = 1
AFFE_CHAR_MECA_F FORCE_ARETE
FX,
FY
DEFI_MATERIAU ELAS_ORTH


5.4 Values
tested

Value Identification
Reference Aster %
difference
Ux (c) = Ux (D)
DX (C)
5.917 10­7 5.9167
10­7
0.006
Uy (B) DY
(B)
­ 2.292 10­7 ­ 2.29166
10­7
0.015
Uy (C) DY
(C)
­ 5.028 10­7 ­ 5.0277
10­7
0.005
Uy (D)
DY (D)
­ 7.319 10­7 ­ 7.3194
10­7
0.006
Sigma L
SIXX (any point)
7500
7500
0.
Sigma TT
SIYY (any point)
2500
2500
0.
Sigma L
SIXY (any point)
4300.127
4330.127
0.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
9/10

6 Modeling
D

6.1
Characteristics of modeling

Modeling COQUE_3D in great displacements. The plate is parallel to the total axes,
i.e. total axis X is colinéaire with axis X. It is thus the axis of orthotropism L which is to be directed
(using key word MASSIF of AFFE_CARA_ELEM). The grid is identical to that of
modeling B.

6.2
Characteristics of the grid

A number of nodes: 541

A number of meshs and types: 50 QUAD9, 100 TRIA7

6.3 Functionalities
tested

Commands Key word
factor
Key word
AFFE_MODELE
AFFE
MODELISATION = “COQUE_3D”
AFFE_CARA_ELEM
COQUE
ANGL_REP = 30
AFFE_CARA_ELEM
COQUE
EPAIS = 1
AFFE_CHAR_MECA_F FORCE_ARETE
FX,
FY
DEFI_MATERIAU ELAS_ORTH

STAT_NON_LINE COMP_ELAS
DEFORMATION=' GRENN_GR'

6.4 Values
tested

Value Identification
Reference Aster %
difference
Ux (c) = Ux (D)
DX (C)
5.917 10­7 5.9167
10­7
0.006
Uy (B) DY
(B)
­ 2.292 10­7 ­ 2.29166
10­7
0.015
Uy (C) DY
(C)
­ 5.028 10­7 ­ 5.0277
10­7
0.005
Uy (D)
DY (D)
­ 7.319 10­7 ­ 7.3194
10­7
0.006
Sigma L
SIXX (any point)
7500
7499.99
0.001
Sigma TT
SIYY (any point)
2500
2499.93
0.003
Sigma L
SIXY (any point)
4300.127
4329.99
0.007

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSLP304 - Orthotropic square Plaque in traction


Date:
12/12/02
Author (S):
J.M. PROIX, J.F. Key BILLAUD
:
V3.02.304-A Page:
10/10

7
Summary of the results

The results of four modelings are very close to the analytical solution: to the maximum 0.015
% of variation for 4 modelings.

This test thus validates the taking into account of orthotropic elasticity.

Handbook of Validation
V3.02 booklet: Linear statics of the plane systems
HT-66/02/001/A

Outline document