HPLA100 - Heavy thermoelastic hollow roll in uniform rotation

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Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

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P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

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Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

Organization (S):

EDF-R & D/AMA

Manual of Validation
V7.01 booklet: Thermomechanical linear of the axisymmetric systems
V7.01.100 document

HPLA100 - Heavy thermoelastic hollow roll
in uniform rotation

Summary

The purpose of this test is to test the second members corresponding to the effects of gravity, of a dilation
thermics and of acceleration due to a uniform rotation. For modelings C and D (hull 3D), a calculation
thermo chained rubber band and a thermoelastoplastic calculation without plastic evolution was carried out.

The analytical solution of reference is described in the document [V7.90.03]. One has the results for
modelings:

axisymmetric 2D: axisymmetric isoparametric finite elements on meshs QUAD8,

axisymmetric hulls: axisymmetric isoparametric finite elements on meshs SEG3
(linear mesh of the meridian section),

hulls 3D: finite elements MEC3QU9H, MEC3TR7H on meshs QUAD9 and TRIA7,
respectively,

plates DKT: finite elements plans DKQ, DKT on meshs QUAD4 and TRIA3, respectively. One
test also the orthotropic hulls of

DEFI_COQU_MULT

for two layers of the same material

isotropic and the key word

ELAS_COQU

DEFI_MATERIAU

for the assignment of characteristics of

homogenized plates.

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Problem of reference

1.1 Geometry

With

Interior radius

19.5 mm

External radius

20.5 mm

Not F

R =

20.0 mm

Thickness

H =

1.0 mm

Height

L =

10.0 mm

H
+

1.2

Properties of material

The material is homogeneous isotropic, thermoelastic linear, the initial state is virgin. Coefficients

are:

NR mm

kg mm

2 10

0 3

810

(coefficient of

dilation).

1.3

Boundary conditions and loadings

gravity:

, according to axis OZ

force traction on the higher face: -

16010

, that is to say one

traction distributed on [CD]: -

810

NR/mm

rotation:

according to axis OZ

thermal dilation:

()

() (

)

(

) (

)

ref.

with:

case 1:

ref.

= -

0 5

case 2:

ref.

These fields of temperature are calculated with

THER_LINEAIRE

, using a stationary calculation on

the same mesh, but with a plane model in order to have a solution refines in the thickness.

Boundary conditions in displacement (and rotation) being different according to modeling
considered, they will be described later on (in the paragraphs relating to modelings).

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Reference solution

2.1

Method of calculation used for the reference solution

To refer to the document [V7.90.03] to have the complete analytical solutions.

The analytical results of reference are:

displacements and rotations,

axial stress, generalized efforts (in theory of hulls),

in skins internal and external on the sections AB and CD.

In axisymmetric 2D, the complete solutions given in [V7.90.03] are such as

= 0

where R and Z

are the directions radial and axial cylinder, respectively. For the loadings of rotation
uniform and of thermal dilation, the boundary conditions are selected so that them
solutions do not depend on Z (one has in particular

= 0

For the hulls, with boundary conditions equivalent, rotation

around the axis

orthoradial is null for the loadings of uniform rotation and thermal dilation, which is not
not the case of the loading of gravity where rotation is constant (the cylinder formats then
conical). On the other hand in all the cases, the transverse distortion is null; thus theories of
Coil-Kirchhoff and those of Hencky-Mindlin provide the same reference solution.

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3 Modeling

With

3.1

Characteristics of modeling

Finite elements 2D axisymmetric

J C

With

19.5

20.5

The discretized geometry is represented above:

Edge

group_no

BC BC
DA DA

LOW AB

CD HIGH

3.2

Characteristics of the mesh

The mesh is regular: 4 elements in the height, 8 in the thickness.

A number of nodes: 121

A number of meshs and type: 32 QUAD8

3.3

Boundary conditions in displacement

3.3.1 Gravity

Displacement DY is locked at the point F alone.

3.3.2 Rotation

Displacement DY is locked on sides [AB] (GROUP_NO: LOW) and on [CD] (GROUP_NO:
HIGH).

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3.3.3 Thermal case of dilation n°1

Displacement DY is locked on all the structure.

3.3.4 Thermal case of dilation n°2

Displacement DY is locked on sides [AB] (GROUP_NO: LOW) and [CD] (GROUP_NO: HIGH).

3.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“AXIS”

AFFE_CHAR_MECA GRAVITY

ROTATION
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER

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HPLA100 - Thermoelastic hollow roll

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

Results of modeling A

4.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the N78 node

 2.34000 10

 2.339999 10

Displacement DY of the N120 node

 1.185 10

 1.184999 10

Displacement DY of the N13 node

1.2150 10

1.214999 10

Axial stress Siyy with the node N78 (M13)

8.0000 10

7.9999 10

Uniform rotation - centrifugal force

Displacement DX of the N120 node

 2.94240 10

2.942374 10

0.001

Displacement DX of the N13 node

2.88010 10

2.880065 10

0.001

Axial stress Siyy with the node N120 (M1)

9.94880 10

9.948902 10

0.001

Axial stress Siyy with the node N13 (M32)

9.26310 10

9.263187 10

0.001

Dilation case 1

Displacement DX of the N120 node

1.056145 10

1.05625 10

0.01

Displacement DX of the N13 node

1.110317 10

1.1104166 10

0.009

Axial stress Siyy with the node N120 (M1)

1.4321427

1.4321429

Dilation case 2

Displacement DX of the N120 node

2.53500 10

2.5349999 10

Axial stress Siyy with the node N120 (M1)

 2.00000 10

 1.99999 10

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5 Modeling

5.1

Characteristics of modeling

Elements of axisymmetric hull

The discretized geometry is represented above. One chooses the theory of hulls of Coils-Kirchhoff
(for that one takes a transverse coefficient of shearing of 10

). One neglects the correction of

metric in the thickness. The thickness is: 1 Misters.

node

group_no

J GRNO13

H GRNO14

F GRNO6

5.2

Characteristics of the mesh

A number of nodes: 21

A number of meshs and type: 10 SEG3

5.3

Boundary conditions in displacement and rotation

5.3.1 Gravity

Displacement DY is locked at the point F alone (GRNO6).

5.3.2 Rotation

Displacement DY is locked at the point F (GRNO6) at the point J (GRNO13).
Rotation around axis Z is null in these two points.

5.3.3 Thermal case of dilation n°1

Displacement DY as well as rotation around axis Z. are locked on all the structure
(GROUP_NO: GRNO15)

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5.3.4 Thermal case of dilation n°2

Displacement DY is locked at the point F (GROUP_NO: GRNO6) and at the point J (GROUP_NO:
GRNO13). Rotation around axis Z is null on the same groups of nodes.

5.4 Functionalities

tested

Controls

AFFE_MODELE AFFE MODELING

“COQUE_AXIS”

AFFE_CARA_ELEM HULL

THICK

A_CIS

MODI_METRIQUE

“NOT”

AFFE_CHAR_MECA GRAVITY

ROTATION
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

Results of modeling B

6.1 Values

tested

Note:

Index X corresponds here to the first direction of the local reference mark of the element.

Identification Reference

Aster %

difference

Gravity

Displacement DX of the node J

 2.40000 10

 2.400016

Displacement DY of the node H

5.00000 10

Rotation DRZ of the node H

2.40000 10

2.400015

Normal effort Nxx, M10 mesh, node J

8.00000 10

Axial stress Sixx, internal skin,

8.00000 10

net M10, node J

Rotation - centrifugal force

Displacement DX of the node F

2.91200 10

2.91201 10

Normal effort Nxx, M1 mesh, node F

9.60000 10

9.60005 10

Axial stress Sixx, internal skin,

9.60000 10

9.600013

net M1, node F

Dilation case 1

Moment Mxx, M1 mesh, node F

 2.38095 10

Axial stress Sixx, internal skin,

1.428571

net M1, node F

Dilation case 2

Displacement DX of the node F

26.0000 10

26.0001 10

Normal effort Nxx, M1 mesh, node F

 2.00000 10

 1.99999 10

Axial stress Sixx, internal skin,

 2.00000 10

 1.99999

net M1, node F

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7 Modeling

7.1

Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of hull 3D: QUAD9

The discretized geometry is represented above.

not node

K NO72

L NO1

MR. NO33

NR NO39

P NO186

Q NO190

The factor of correction of shearing A_CIS is worth 5/6 (theory of hulls of Reissner).

7.2

Characteristics of the mesh

A number of external nodes: 121

A number of meshs and types: 32 QUAD9 + 8 SEG3

7.3

Boundary conditions in displacement and rotation

7.3.1 Gravity

Displacement DZ is locked on the group of nodes LM.
Displacement DY as well as rotations around axes X and Z are locked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are locked on the group of
nodes MN.

7.3.2 Rotation

Displacement DZ as well as rotations around axes X and Y are locked on the groups of
nodes KNSANSKN and LMSANSLM.
Displacement DY as well as rotations around axes X and Z are locked on the group of
nodes KL.
Displacement DX as well as rotations around the axes Y and Z are locked on the group of
nodes MN.
Displacement DZ as well as rotation around the axis Y are locked on the group of nodes KETL.
Displacement DZ as well as rotation around axis X are locked on the group of nodes
METN.

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7.3.3 Thermal case of dilation n°1

7.3.4 Thermal case of dilation n°2

7.4 Functionalities

tested

Controls

AFFE_MODELE AFFE MODELING

“COQUE_3D”

AFFE_CARA_ELEM HULL

THICK
A_CIS

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
ROTATION
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

STAT_NON_LINE COMP_INCR

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Results of modeling C

8.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.32821

2.991

Displacement DY of the point NR

 2.40000 10

 2.32709

 3.038

Displacement DZ of the point P

5.00000 10

4.99919

 0.016

Displacement DZ of the point Q

5.00000 10

4.99911

 0.018

Rotation DRY of the point P

2.40000 10

2.44618

1.924

Rotation DRX of the point Q

2.40000 10

2.44574

1.906

Normal effort Nyy, M4 mesh, not K

8.00000 10

8.00157

0.020

Normal effort Nyy, M32 mesh, not NR

8.00000 10

8.00184

0.023

Axial stress Siyy, internal skin,

net M4, not K

8.00000 10

8.20512

2.564

Axial stress Siyy, internal skin,

net M32, not NR

8.00000 10

8.20459

2.557

Rotation centrifugal force

Displacement DX of the point L

2.91200 10

2.91181 10

 0.006

Displacement DY of the point M

2.91200 10

2.91073 10

 0.044

Normal effort Nyy, M1 mesh, not L

9.60000 10

9.60002 10

0.000

Normal effort Nyy, M29 mesh, not M

9.60000 10

9.60004 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

9.84600 10

9.83997 10

 0.061

Axial stress Siyy, internal skin,

net M29, not M

9.84600 10

9.83961

 0.065

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

 2.38096 10

0.000

Myy moment, M29 mesh, not M

 2.38095 10

 2.38096

0.000

Axial stress Siyy, internal skin,

net M1, not L

1.428571

1.42858

0.000

Axial stress Siyy, internal skin,

net M29, not M

1.428571

1.42858

0.000

Dilation case 2

Displacement DX of the point L

25.9946 10

25.9907 10

 0.015

Displacement DY of the point M

25.9946 10

25.9989

0.016

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M29 mesh, not M

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

 1.97800 10

 1.97862 10

0.031

Axial stress Siyy, internal skin,

net M29, not M

 2.97800 10

 1.97864

0.032

8.2 Remarks

Satisfactory and identical results for calculations with

MECA_STATIQUE

and

STAT_NON_LINE

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9 Modeling

9.1

Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of hull 3D: TRIA7

The discretized geometry is represented above.

not node

K NO72

L NO1

MR. NO33

NR NO39

P NO186

Q NO190

The factor of correction of shearing A_CIS is worth 5/6 (theory of Reissner hulls).

9.2

Characteristics of the mesh

A number of external nodes: 153

A number of meshs and types: 64 TRIA7 + 8 SEG3

9.3

Boundary conditions in displacement and rotation

9.3.1 Gravity

9.3.2 Rotation

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9.3.3 Thermal case of dilation n°1

9.3.4 Thermal case of dilation n°2

9.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“COQUE_3D”

AFFE_CARA_ELEM HULL

THICK
A_CIS

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
ROTATION
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

STAT_NON_LINE COMP_INCR

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HPLA100 - Thermoelastic hollow roll

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10 Results of modeling D

10.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.32610

 3.079

Displacement DY of the point NR

 2.40000 10

 2.33110 10

 2.871

Displacement DZ of the point P

5.00000 10

4.99874 10

 0.025

Displacement DZ of the point Q

5.00000 10

4.99940

 0.012

Rotation DRY of the point P

2.40000 10

2.43797

1.582

Rotation DRX of the point Q

2.40000 10

2.43962 10

1.651

Normal effort Nyy, M60 mesh, not K

8.00000 10

7.99979

 0.003

Normal effort Nyy, M56 mesh, not NR

8.00000 10

8.00431 10

0.054

Axial stress Siyy, internal skin,

net M60, not K

8.00000 10

8.20178 10

2.522

Axial stress Siyy, internal skin,

net M56, not NR

8.00000 10

8.19909

2.489

Rotation centrifugal force

Displacement DX of the point L

2.91200 10

2.91170 10

 0.010

Displacement DY of the point M

2.91200 10

2.91091 10

 0.037

Normal effort Nyy, M25 mesh, not L

9.60000 10

9.60207 10

0.022

Normal effort Nyy, M53 mesh, not M

9.60000 10

9.59935 10

 0.007

Axial stress Siyy, internal skin,

net M25, not L

9.84600 10

9.84011 10

 0.060

Axial stress Siyy, internal skin,

net M53, not M

9.84600 10

9.84124

 0.048

Dilation case 1

Myy moment, M25 mesh, not L

 2.38095 10

 2.38097 10

0.001

Myy moment, M53 mesh, not M

 2.38095 10

 2.38096

0.000

Axial stress Siyy, internal skin,

net M25, not L

1.428571

1.42858

0.000

Axial stress Siyy, internal skin,

net M53 not M

1.428571

1.42858

0.000

Dilation case 2

Displacement DX of the point L

26.0000 10

25.9928 10

 0.028

Displacement DY of the point M

26.0000 10

25.9969

 0.012

Normal effort Nyy, M25 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M53 mesh, not M

 2.00000 10

 1.99999 10

0.000

Axial stress Siyy, internal skin,

net M25, not L

 1.97800 10

 1.97821 10

0.011

Axial stress Siyy, internal skin,

net M53, not M

 1.97800 10

 1.97898

0.050

10.2 Remarks

Satisfactory and identical results for calculations with

MECA_STATIQUE

and

STAT_NON_LINE

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11 Modeling

11.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKQ: QUAD4

The discretized geometry is represented above.

not

node

K NO160

L NO203

MR. NO11

NR NO1

P NO226

Q NO6

11.2 Characteristics of the mesh

A number of nodes: 231

A number of meshs and types: 200 QUAD4 + 80 SEG2

11.3 Boundary conditions in displacement and rotation

11.3.1 Gravity

11.3.2 Thermal case of dilation n°1

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11.3.3 Thermal case of dilation n°2

11.4 Functionalities

tested

Controls

AFFE_MODELE AFFE MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

STAT_NON_LINE COMP_INCR

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Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

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P. MASSIN,

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Key

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HT-66/03/008/A

12 Results of modeling E

12.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.37341

 1.108

Displacement DY of the point NR

 2.40000 10

 2.37341 10

 1.108

Displacement DZ of the point P

5.00000 10

5.00883 10

0.177

Displacement DZ of the point Q

5.00000 10

5.00883

0.177

Rotation DRY of the point P

2.40000 10

2.36136

 1.610

Rotation DRX of the point Q

2.40000 10

2.36136 10

 1.610

Normal effort Nyy, M181 mesh, not K

8.00000 10

7.56157

 5.480

Normal effort Nyy, M200 mesh, not NR

8.00000 10

7.56157 10

 5.480

Axial stress Siyy, internal skin,

net M181, not K

8.00000 10

7.56157 10

 5.480

Axial stress Siyy, internal skin,

net M200, not NR

8.00000 10

7.56157

 5.480

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M20 mesh, not M

 2.38095 10

 2.38095

0.000

Axial stress Siyy, internal skin,

net M1, not L

1.428571

0.000

Axial stress Siyy, internal skin,

net M20, not M

1.428571

0.000

Dilation case 2

Displacement DX of the point L

26.0000 10

0.000

Displacement DY of the point M

26.0000 10

26.0000

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M20 mesh, not M

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M20, not M

 2.00000 10

 2.00000

0.000

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

18/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

13 Modeling

13.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKT: TRIA3

The discretized geometry is represented above.

not

node

K NO1

L NO11

MR. NO161

NR NO227

P NO6

Q NO215

13.2 Characteristics of the mesh

A number of nodes: 231

A number of meshs and type: 400 TRIA3 + 80 SEG2

13.3 Boundary conditions in displacement and rotation

13.3.1 Gravity

13.3.2 Thermal case of dilation n°1

Code_Aster

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Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

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Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

19/34

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

13.3.3 Thermal case of dilation n°2

13.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

STAT_NON_LINE COMP_INCR

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

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Page:

20/34

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

14 Results of modeling F

14.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.32796

 3.002

Displacement DY of the point NR

 2.40000 10

 2.32796 10

 3.002

Displacement DZ of the point P

5.00000 10

5.02845 10

0.517

Displacement DZ of the point Q

5.00000 10

5.02845 10

0.517

Rotation DRY of the point P

2.40000 10

2.28975

 4.594

Rotation DRX of the point Q

2.40000 10

2.28975 10

 4.594

Normal effort Nyy, M362 mesh, not K

8.00000 10

7.61457

 4.818

Normal effort Nyy, M400 mesh, not NR

8.00000 10

7.61457 10

 4.818

Axial stress Siyy, internal skin,

net M362, not K

8.00000 10

7.61007 10

4.874

Axial stress Siyy, internal skin,

net M400, not NR

8.00000 10

7.61007

4.874

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M39 mesh, not M

 2.38095 10

 2.38095

0.000

Axial stress Sixx, internal skin,

net M1, not L

1.428571

0.000

Axial stress Sixx, internal skin,

net M39 not M

1.428571

0.000

Dilation case 2

Displacement DX of the point L

26.0000 10

25.9999 10

0.000

Displacement DY of the point M

26.0000 10

25.9999

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M39 mesh, not M

 2.00000 10

 1.99999 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M39, not M

 2.00000 10

 2.00000

0.000

Code_Aster

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Titrate:

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Date:

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P. MASSIN,

F. VOLDOIRE

Key

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Page:

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

15 Modeling

15.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKT: TRIA3. Modeling uses a double-layered plate of which them
characteristics of orthotropism are those of material defined in the §1.2.

The discretized geometry is represented above.

not

node

K NO1

L NO11

MR. NO161

NR NO227

P NO6

Q NO215

15.2 Characteristics of the mesh

A number of nodes: 231

A number of meshs and types: 400 TRIA3 + 80 SEG2

15.3 Boundary conditions in displacement and rotation

15.3.1 Gravity

15.3.2 Thermal case of dilation n°1

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HPLA100 - Thermoelastic hollow roll

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P. MASSIN,

F. VOLDOIRE

Key

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Page:

22/34

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

15.3.3 Thermal case of dilation n°2

15.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

DEFI_MATERIAU ELAS_ORTH

DEFI_COQU_MULT

THICK

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

23/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

16 Results of modeling G

16.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

2.32796

 3.002

Displacement DY of the point NR

 2.40000 10

 2.32796

 3.002

Displacement DZ of the point P

5.0 10

5.02845

0.517

Displacement DZ of the point Q

5.0 10

5.02845

0.517

Rotation DRY of the point P

2.40000 10

2.28975

 4.594

Rotation DRX of the point Q

2.40000 10

2.28975 10

 4.594

Normal effort Nyy, M362 mesh, not K

8.00000 10

7.61457

 4.818

Normal effort Nyy, M400 mesh, not NR

8.00000 10

7.61457 10

 4.818

Axial stress Siyy, internal skin,

net M362, not K

8.00000 10

7.61007 10

4.874

Axial stress Siyy, internal skin,

net M400, not NR

8.00000 10

7.61007

4.874

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M39 mesh, not M

 2.38095 10

 2.38095

0.000

Axial stress Sixx, internal skin,

net M1, not L

1.428571

0.000

Axial stress Sixx, external skin,

net M1, not L

 1.428571

0.000

Axial stress Sixx, internal skin,

net M39 not M

1.428571

0.000

Axial stress Sixx, external skin,

net M39 not M

 1.428571

0.000

Dilation case 2

Displacement DX of the point L

26.0 10

25.9999 10

0.000

Displacement DY of the point M

26.0 10

25.9999

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M39 mesh, not M

 2.00000 10

 1.99999 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M39, not M

 2.00000 10

 2.00000

0.000

Code_Aster

Version

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Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

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P. MASSIN,

F. VOLDOIRE

Key

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Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

17 Modeling

17.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKQ: QUAD4. Modeling uses a double-layered plate of which them
characteristics of orthotropism are those of material defined in the §1.2.

The discretized geometry is represented above.

Not

node

K NO160

L NO203

MR. NO11

NR NO1

P NO226

Q NO6

17.2 Characteristics of the mesh

A number of external nodes: 231

A number of meshs and types: 200 QUAD4 + 80 SEG2

17.3 Boundary conditions in displacement and rotation

17.3.1 Gravity

17.3.2 Thermal case of dilation n°1

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

17.3.3 Thermal case of dilation n°2

17.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

DEFI_MATERIAU ELAS_ORTH

DEFI_COQU_MULT

THICK

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

26/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

18 Results of modeling H

18.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.37341

 1.108

Displacement DY of the point NR

 2.40000 10

 2.37341 10

 1.108

Displacement DZ of the point P

5.00000 10

5.00883 10

0.177

Displacement DZ of the point Q

5.00000 10

5.00883

0.177

Rotation DRY of the point P

2.40000 10

2.36136

 1.610

Rotation DRX of the point Q

2.40000 10

2.36136 10

 1.610

Normal effort Nyy, M181 mesh, not K

8.00000 10

7.56157

 5.480

Normal effort Nyy, M200 mesh, not NR

8.00000 10

7.56157 10

 5.480

Axial stress Siyy, internal skin,

net M181, not K

8.00000 10

7.56157 10

 5.480

Axial stress Siyy, internal skin,

net M200, not NR

8.00000 10

7.56157

 5.480

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M20 mesh, not M

 2.38095 10

 2.38095

0.000

Axial stress Siyy, internal skin,

net M1, not L

1.428571

0.000

Axial stress Siyy, external skin,

net M1, not L

 1.428571

0.000

Axial stress Siyy, internal skin,

net M20, not M

1.428571

0.000

Axial stress Siyy, external skin,

net M20, not M

 1.428571

0.000

Dilation case 2

Displacement DX of the point L

26.0000 10

0.000

Displacement DY of the point M

26.0000 10

26.0000

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M20 mesh, not M

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M1, not L

 2.00000 10

0.000

Axial stress Siyy, internal skin,

net M20, not M

 2.00000 10

 2.00000

0.000

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

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P. MASSIN,

F. VOLDOIRE

Key

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Page:

27/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

19 Modeling

19.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKQ: QUAD4. Assignment of characteristics of homogenized plates
corresponding to material of the §1.2.

The discretized geometry is represented above.

Not

node

K NO160

L NO203

MR. NO11

NR NO1

P NO226

Q NO6

19.2 Characteristics of the mesh

A number of external nodes: 231

A number of meshs and types: 200 QUAD4 + 80 SEG2

19.3 Boundary conditions in displacement and rotation

19.3.1 Gravity

19.3.2 Thermal case of dilation n°1

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Titrate:

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P. MASSIN,

F. VOLDOIRE

Key

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28/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

19.3.3 Thermal case of dilation n°2

19.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

DEFI_MATERIAU ELAS_COQU

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

29/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

20 Results of modeling I

20.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

 2.37341

 1.108

Displacement DY of the point NR

 2.40000 10

 2.37341 10

 1.108

Displacement DZ of the point P

5.00000 10

5.00883 10

0.177

Displacement DZ of the point Q

5.00000 10

5.00883

0.177

Rotation DRY of the point P

2.40000 10

2.36136

 1.610

Rotation DRX of the point Q

2.40000 10

2.36136 10

 1.610

Normal effort Nyy, M181 mesh, not K

8.00000 10

7.56157

 5.480

Normal effort Nyy, M200 mesh, not NR

8.00000 10

7.56157 10

 5.480

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M20 mesh, not M

 2.38095 10

 2.38095

0.000

Dilation case 2

Displacement DX of the point L

26.0000 10

0.000

Displacement DY of the point M

26.0000 10

26.0000

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M20 mesh, not M

 2.00000 10

0.000

20.2 Remarks

The local stresses are not calculated since the characteristics material of
plate are supposed to come from a calculation of homogenization.

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Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

21 Modeling

21.1 Characteristics of modeling

Modeling of a quarter of cylinder.

Elements of plate DKT: TRIA3. Assignment of characteristics of homogenized plates
corresponding to material of the §1.2.

The discretized geometry is represented above.

not

node

K NO1

L NO11

MR. NO161

NR NO227

P NO6

Q NO215

21.2 Characteristics of the mesh

A number of nodes: 231

A number of meshs and types: 400 TRIA3 + 80 SEG2

21.3 Boundary conditions in displacement and rotation

21.3.1 Gravity

21.3.2 Thermal case of dilation n°1

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F. VOLDOIRE

Key

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

21.3.3 Thermal case of dilation n°2

21.4 Functionalities

tested

Controls

AFFE_MODELE AFFE

MODELING

“DKT”

AFFE_CARA_ELEM HULL

THICK

DEFI_MATERIAU ELAS_COQU

AFFE_CHAR_MECA GRAVITY

FORCE_ARETE
TEMP_CALCULEE

MODEL MECA_STATIQUE

CHAM_MATER
CARA_ELEM

Code_Aster

Version

6.5

Titrate:

HPLA100 - Thermoelastic hollow roll

Date:

01/12/03

Author (S):

P. MASSIN,

F. VOLDOIRE

Key

V7.01.100-C

Page:

32/34

Manual of Validation

V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

22 Results of modeling J

22.1 Values

tested

Identification Reference

Aster %

difference

Gravity

Displacement DX of the point K

 2.40000 10

2.32796

 3.002

Displacement DY of the point NR

 2.40000 10

 2.32796

 3.002

Displacement DZ of the point P

5.0 10

5.02845

0.517

Displacement DZ of the point Q

5.0 10

5.02845

0.517

Rotation DRY of the point P

2.40000 10

2.28975

 4.594

Rotation DRX of the point Q

2.40000 10

2.28975 10

 4.594

Normal effort Nyy, M362 mesh, not K

8.00000 10

7.61457

 4.818

Normal effort Nyy, M400 mesh, not NR

8.00000 10

7.61457 10

 4.818

Dilation case 1

Myy moment, M1 mesh, not L

 2.38095 10

0.000

Myy moment, M39 mesh, not M

 2.38095 10

 2.38095

0.000

Dilation case 2

Displacement DX of the point L

26.0 10

25.9999 10

0.000

Displacement DY of the point M

26.0 10

25.9999

0.000

Normal effort Nyy, M1 mesh, not L

 2.00000 10

0.000

Normal effort Nyy, M39 mesh, not M

 2.00000 10

 1.99999 10

0.000

22.2 Remarks

The local stresses are not calculated since the characteristics material of
plate are supposed to come from a calculation of homogenization.

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P. MASSIN,

F. VOLDOIRE

Key

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V7.01 booklet: Thermomechanical linear of the axisymmetric systems

HT-66/03/008/A

23 Summary of the results

The very good results obtained for modelings A and B are explained by the fact why the solutions
of reference belong to the space generated by the selected finite elements. Only remain them
numerical round-off errors.

Satisfactory results were obtained for modelings of plates and hulls in
space C, D, E, F, G, H, I and J. For these last, a chained elastic thermo calculation was carried out.
The results with modeling DKT (E, F, G, H, I and J) show that the elements quadrangle have
a better behavior than the elements triangle. It is necessary to have a discretization
sufficient fine with these plane elements in order to be able to modelize the geometry correctly
circular of the cylindrical hull. Indeed, to discretize the geometry of the cylinder by plane breakages or
parabolic is not in conformity and induces a parasitic bending which decreases with the smoothness of mesh.
Thus a multiplication of the number of elements by two on the height of the structure makes fall
the maximum error relating of 5,48% (case presented here) to 2,8%. Results with modeling
COQUE_3D (C and D) is very good except for gravity with the element triangle.