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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
1/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN, SAMTECH SA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.303
SSNP303 - Element in plane stress and traction -
Perfect plasticity
Summary:
This test of quasi-static mechanics nonlinear 2D consists in charging three superimposed elements of plate
(type of element mecpqu4). The 4 nodes are common to the 3 elements. The elements have properties
different (perfect plasticity) to obtain a suitable traction diagram. This test is drawn from the guide
NAFEMS.
The goal is to compare the various methods of the Newton-Raphson type making it possible to solve the system
nonlinear equations (
NEWTON: (“ELASTIC” MATRIX
) and
NEWTON: (“TANGENT” MATRIX
)
with
REAC_INCR
and
REAC_ITER
). The selected criterion of convergence corresponds to 0.01% of the residual force
(
RESI_GLOB_RELA
).
Modeling is carried out with plane elements of type MECPQU4.
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
2/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
With
B
C
D
p/2
p/2
B
has
= B has = 1.0
1.2
Material properties
y
E
T
Material 1
E = 100000 MPa
= 0.25
y
= 3 MPa
E
T
= 0.0
Material 2
E = 60000 MPa
= 0.25
y
= 6 MPa
E
T
= 0.0
Material 3
E = 40000 MPa
= 0.25
y
= 8 MPa
E
T
= 0.0
1.3
Boundary conditions and loadings
Not a:
U
X
=0.
U
y
= 0.
Not b:
U
y
=0.
Not D:
U
X
=0.
Loading by a force P/2 on the point B and C. the force P is increased in 6 stages in the manner
following:
Force P
3.00
6.00
9.00
12.95
15.00
16.93
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
3/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
The results considered as reference were obtained by the SAMCEF software by using 60 increments
for each stage of loading. The characteristics of the various methods of resolution are
the following ones:
With
Use of the elastic matrix.
B
Use of the tangent matrix; the aforementioned is revalued only with the first iteration of each
increment (
REAC_INCR
= 1 and
REAC_ITER
= 0). It is about the method of Newton modified.
C
Use of the tangent matrix; the aforementioned is revalued with each iteration of each
increment (
REAC_INCR
= 1 and
REAC_ITER
= 1). It is about the method of Newton conventional.
2.2
Results of reference
Results obtained with 60 increments for each stage of loading
Element 1
Element 2
Element 3
Force
xx
yy
xx
yy
xx
yy
3.00
1.500000D+00
6.938894D18
9.000000D01
­ 1.040834D17
6.000000D01
­ 6.938894D18
6.00
3.000000D+00
4.861944D13
1.800000D+00
­ 2.081668D17
1.200000D+00
­ 3.469447D18
9.00
3.147155D+00
3.199571D01
3.511707D+00
­ 1.900098D01
2.341138D+00
­ 1.279828D01
12.95
3.252919D+00
5.950074D01
5.814267D+00
­ 3.523377D01
3.878832D+00
­ 2.380030D01
15.00
3.213822D+00
4.873069D01
6.017834D+00
3.174572D02
5.768340D+00 ­ 5.231355D01
16.93
3.2092970D+00
4.753345D01
6.149462D+00
3.048490D01
7.571241D+00
­ 7.863557D01
2.3
Uncertainty on the solution
Uncertainty lower than 1%.
2.4 References
bibliographical
[1]
Fundamental tests for two and three dimensional, small strain, elastoplastic finite element
analysis, 1987, NAFEMS
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
4/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling A
Use of elements QUAD4
N04
N03
N02
N01
Modeling in plane stresses: C_PLAN
The loading and the boundary conditions are modelized by:
·
DDL_IMPO: (Node NO1 DX = 0, DY = 0)
(Node NO2 DY = 0)
(Node NO4 DX = 0)
·
forces imposed on nodes NO2 and NO3.
3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 3 MECPQU4
3.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE
COMP_INCR
DEFORMATION
“SMALL”
[U4.32.01]
NEWTON
STAMP
“ELASTIC”
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
5/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Moment
Reference
Aster
% difference
SIXX (mesh 1)
1
1,500000E+00
1,500000E+00
0
SIYY (mesh 1)
1
6,938894E18
1,291047E14
0
SIXX (mesh 2)
1
9,000000E01
9,000000E01
0
SIYY (mesh 2)
1
­ 1,040834E17
­ 1,509903E14
0
SIXX (mesh 3)
1
6,000000E01
6,000000E01
0
SIYY (mesh 3)
1
­ 6,938894E18
­ 2,107830E14
0
SIXX (mesh 1)
2
3,000000E+00
3,000000E+00
0
SIYY (mesh 1)
2
4,861944E13
1,359551E13
0
SIXX (mesh 2)
2
1,800000E+00
1,800000E+00
0
SIYY (mesh 2)
2
­ 2,081668E17
­ 1,093097E13
0
SIXX (mesh 3)
2
1,200000E+00
1,200000E+00
0
SIYY (mesh 3)
2
­ 3,469447E18
­ 1,007126E13
0
SIXX (mesh 1)
3
3,147155E+00
3,145788E+00
­ 0,043
SIYY (mesh 1)
3
3,199571E01
3,167040E01
­ 1,017
SIXX (mesh 2)
3
3,511707E+00
3,512527E+00
0,023
SIYY (mesh 2)
3
­ 1,900098E01
­ 1,900224E01
0,007
SIXX (mesh 3)
3
2,341138E+00
2,341685E+00
0,023
SIYY (mesh 3)
3
­ 1,279828E01
­ 1,266816E01
­ 1,017
SIXX (mesh 1)
4
3,252919E+00
3,250728E+00
­ 0,067
SIYY (mesh 1)
4
5,950074E01
5,887464E01
­ 1,052
SIXX (mesh 2)
4
5,814267E+00
5,816159E+00
0,033
SIYY (mesh 2)
4
­ 3,523377E01
­ 3,521695E01
­ 0,048
SIXX (mesh 3)
4
3,878832E+00
3,882391E+00
0,092
SIYY (mesh 3)
4
­ 2,380030E01
­ 2,364650E01
­ 0,646
SIXX (mesh 1)
5
3,213822E+00
3,214367E+00
0,017
SIYY (mesh 1)
5
4,873069E01
4,887527E01
0,297
SIXX (mesh 2)
5
6,017834E+00
6,015985E+00
­ 0,031
SIYY (mesh 2)
5
3,174572E02
3,209818E02
1,11
SIXX (mesh 3)
5
5,768340E+00
5,769681E+00
0,023
SIYY (mesh 3)
5
­ 5,231355E01
­ 5,207413E01
­ 0,458
SIXX (mesh 1)
6
3,209297E+00
3,210194E+00
0,028
SIYY (mesh 1)
6
4,753345E01
4,777143E01
0,501
SIXX (mesh 2)
6
6,149462E+00
6,146791E+00
­ 0,043
SIYY (mesh 2)
6
3,048490E01
3,052330E01
0,126
SIXX (mesh 3)
6
7,571241E+00
7,572486E+00
0,016
SIYY (mesh 3)
6
­ 7,863557E01
­ 7,826545E01
­ 0,471
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
6/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
4.2 Remarks
To obtain a correct precision, it is necessary to force a significant number of increments for each
stage of loading (60 increments).
The iteration count is equal to 411.
4.3 Parameters
of execution
Version: 3.09
Machine:
System:
Overall dimension memory: 8
megawords
Time CPU To use:
507.8 seconds
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
7/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling B
Use of elements QUAD4
N04
N03
N02
N01
5.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 3 MECPQU4
Modeling in plane stresses: C_PLAN
The loading and the boundary conditions are modelized by:
·
DDL_IMPO: (Node NO1 DX = 0, DY = 0)
(Node NO2 DY = 0)
(Node NO4 DX = 0)
·
forces imposed on nodes NO2 and NO3.
5.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE
COMP_INCR
DEFORMATION
“SMALL”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
REAC_INCR
1
REAC_ITER
0
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
8/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
6
Results of modeling B
6.1 Values
tested
Identification
Moment
Reference
Aster
% difference
SIXX (mesh 1)
1
1,500000E+00
1,500000E+00
0.000
SIYY (mesh 1)
1
6,938894E18
1,351398E14
0.000
SIXX (mesh 2)
1
9,000000E01
9,000000E01
0.000
SIYY (mesh 2)
1
­ 1,040834E17
­ 2,142673E14
0.000
SIXX (mesh 3)
1
6,000000E01
6,000000E01
0.000
SIYY (mesh 3)
1
­ 6,938894E18
­ 2,924612E14
0.000
SIXX (mesh 1)
2
3,000000E+00
3,000000E+00
0.000
SIYY (mesh 1)
2
4,861944E13
9,617834E14
0.000
SIXX (mesh 2)
2
1,800000E+00
1,800000E+00
0.000
SIYY (mesh 2)
2
­ 2,081668E17
­ 8,301280E14
0.000
SIXX (mesh 3)
2
1,200000E+00
1,200000E+00
0.000
SIYY (mesh 3)
2
­ 3,469447E18
­ 9,360717E14
0.000
SIXX (mesh 1)
3
3,147155E+00
3,145788E+00
­ 0.043
SIYY (mesh 1)
3
3,199571E01
3,167038E01
­ 1.017
SIXX (mesh 2)
3
3,511707E+00
3,512527E+00
0.023
SIYY (mesh 2)
3
­ 1,900098E01
­ 1,900225E01
0.007
SIXX (mesh 3)
3
2,341138E+00
2,341685E+00
0.023
SIYY (mesh 3)
3
­ 1,279828E01
­ 1,266817E01
­ 1.017
SIXX (mesh 1)
4
3,252919E+00
3,250686E+00
­ 0.069
SIYY (mesh 1)
4
5,950074E01
5,886265E01
­ 1.072
SIXX (mesh 2)
4
5,814267E+00
5,816233E+00
0.034
SIYY (mesh 2)
4
­ 3,523377E01
­ 3,520332E01
­ 0.086
SIXX (mesh 3)
4
3,878832E+00
3,883081E+00
0.110
SIYY (mesh 3)
4
­ 2,380030E01
­ 2,365921E01
­ 0.593
SIXX (mesh 1)
5
3,213822E+00
3,214343E+00
0.016
SIYY (mesh 1)
5
4,873069E01
4,886891E01
0.284
SIXX (mesh 2)
5
6,017834E+00
6,015971E+00
­ 0.031
SIYY (mesh 2)
5
3,174572E02
3,207056E02
1.023
SIXX (mesh 3)
5
5,768340E+00
5,769686E+00
0.023
SIYY (mesh 3)
5
­ 5,231355E01
­ 5,207599E01
­ 0.454
SIXX (mesh 1)
6
3,209297E+00
3,210140E+00
0.026
SIYY (mesh 1)
6
4,753345E01
4,775720E01
0.471
SIXX (mesh 2)
6
6,149462E+00
6,146788E+00
­ 0.043
SIYY (mesh 2)
6
3,048490E01
3,052260E01
0.124
SIXX (mesh 3)
6
7,571241E+00
7,573072E+00
0.024
SIYY (mesh 3)
6
­ 7,863557E01
­ 7,827984E01
­ 0.452
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
9/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
6.2 Remarks
Idem modeling A concerning the number of increments on the precision of the results.
The iteration count is equal to 361.
6.3 Parameters
of execution
Version: 3.09
Machine:
System:
Overall dimension memory:
8 megawords
Time CPU To use:
504.9 seconds
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
10/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling C
Use of elements QUAD4
N04
N03
N02
N01
7.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 3 MECPQU4
Modeling in plane stresses: C_PLAN
The loading and the boundary conditions are modelized by:
·
DDL_IMPO: (Node NO1 DX = 0, DY = 0)
(Node NO2 DY = 0)
(Node NO4 DX = 0)
·
forces imposed on nodes NO2 and NO3.
7.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ECRO_LINE
D_SIGM_EPSI
[U4.23.01]
SY
STAT_NON_LINE
COMP_INCR
DEFORMATION
“SMALL”
[U4.32.01]
NEWTON
STAMP
“TANGENT”
REAC_INCR
1
REAC_ITER
1
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Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
11/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
8
Results of modeling C
8.1 Values
tested
Identification
Moment
Reference
Aster
% difference
SIXX (mesh 1)
1
1,500000E+00
1,500000E+00
0
SIYY (mesh 1)
1
6,938894E18
1,351398E14
0
SIXX (mesh 2)
1
9,000000E01
9,000000E01
0
SIYY (mesh 2)
1
­ 1,040834E17
­ 2,142673E14
0
SIXX (mesh 3)
1
6,000000E01
6,000000E01
0
SIYY (mesh 3)
1
­ 6,938894E18
­ 2,924612E14
0
SIXX (mesh 1)
2
3,000000E+00
3,000000E+00
0
SIYY (mesh 1)
2
4,861944E13
9,617834E14
0
SIXX (mesh 2)
2
1,800000E+00
1,800000E+00
0
SIYY (mesh 2)
2
­ 2,081668E17
­ 8,301280E14
0
SIXX (mesh 3)
2
1,200000E+00
1,200000E+00
0
SIYY (mesh 3)
2
­ 3,469447E18
­ 9,360717E14
0
SIXX (mesh 1)
3
3,147155E+00
3,145788E+00
­ 0,043
SIYY (mesh 1)
3
3,199571E01
3,167040E01
­ 1,017
SIXX (mesh 2)
3
3,511707E+00
3,512527E+00
0,023
SIYY (mesh 2)
3
­ 1,900098E01
­ 1,900224E01
0,007
SIXX (mesh 3)
3
2,341138E+00
2,341685E+00
0,023
SIYY (mesh 3)
3
­ 1,279828E01
­ 1,266816E01
­ 1,017
SIXX (mesh 1)
4
3,252919E+00
3,250686E+00
­ 0,069
SIYY (mesh 1)
4
5,950074E01
5,886268E01
­ 1,072
SIXX (mesh 2)
4
5,814267E+00
5,816233E+00
0,034
SIYY (mesh 2)
4
­ 3,523377E01
­ 3,520328E01
­ 0,087
SIXX (mesh 3)
4
3,878832E+00
3,883081E+00
0,11
SIYY (mesh 3)
4
­ 2,380030E01
­ 2,365919E01
­ 0,593
SIXX (mesh 1)
5
3,213822E+00
3,214343E+00
0,016
SIYY (mesh 1)
5
4,873069E01
4,886892E01
0,284
SIXX (mesh 2)
5
6,017834E+00
6,015971E+00
­ 0,031
SIYY (mesh 2)
5
3,174572E02
3,207066E02
1,024
SIXX (mesh 3)
5
5,768340E+00
5,769686E+00
0,023
SIYY (mesh 3)
5
­ 5,231355E01
­ 5,207598E01
­ 0,454
SIXX (mesh 1)
6
3,209297E+00
3,210140E+00
0,026
SIYY (mesh 1)
6
4,753345E01
4,775721E01
0,471
SIXX (mesh 2)
6
6,149462E+00
6,146788E+00
­ 0,043
SIYY (mesh 2)
6
3,048490E01
3,052262E01
0,124
SIXX (mesh 3)
6
7,571241E+00
7,573072E+00
0,024
SIYY (mesh 3)
6
­ 7,863557E01
­ 7,827982E01
­ 0,452
background image
Code_Aster
®
Version
4.0
Titrate:
SSNP303 Elements in plane stress and traction - perfect Plasticity
Date:
01/12/98
Author (S)
:
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.303-A
Page:
12/12
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
8.2 Remarks
Idem modeling A concerning the number of increments on the precision of the results.
The iteration count is equal to 360.
8.3 Parameters
of execution
Version: 3.09
Machine:
System:
Overall dimension memory: 8
megawords
Time CPU To use:
471.2 seconds
9
Summary of the results
A significant number of increments is necessary to obtain a correct precision: for
information, ten increments per stage of loading are not sufficient.
The following table recapitulates, for each modeling, the performances in iteration count and of
time CPU.
Identification
Modeling A
Modeling B
Modeling C
Iteration count
411
361
360
Time CPU (seconds)
507.8
504.9
471.2