Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Organization (S):
EDF/EP/AMV
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.101
SSNL101 - Non-linear behavior of an element
of conductor arrangement
Summary:
One considers in this test, 1 discrete element with 2 nodes subjected to a transverse effort in static analysis not
linear.
The element has a behavior governed by a nonlinear relation expressed in effort and displacement
one-way in the transverse and local direction
y
.
The interest of the test is to simulate in an exhaustive way the ways of possible loading, in load and
discharge, in each field of the relation of behavior: rubber band, plastic and ultimate.
The reduced dimension of the problem with 1 unknown factor (the transverse displacement of the end) makes it possible to have
as solution the result d'1 algebraical expression found exactly by
Aster
.
Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
1
Problem of reference
1.1 Geometry
1 discrete element of null size to 2 nodes.
Identify local = total reference mark.
1 matrix of rigidity
“K_TR_D_L'
affected by defect:
1.6 NR/m in translation, 1.9 NR/m in rotation.
Characteristics of rigidity according to the local direction
y
(here with the total axis Y equalizes) are modified by
a relation of behavior of the type
“WEAPON”
in effort-displacement introduced by a material
characteristic.
1.2
Material properties
Dependant on an incremental behavior
“WEAPON”
with 5 parameters:
D
E
(key word
“DLE”
) = 0.048 m,
D
L
(
“DLP”
) = 0.7 m,
K
el
(
“KYE”
) = 1.67 E4 NR/m,
K
pl
(
“KYP”
) = 2.9 E3 NR/m,
K
G
(
“KYG”
) = 1 E6 NR/Mr.
“
D
E
“displacement limits elastic range,
“
D
L
“displacement limits plastic range,
“
K
el
“slope of the elastic range,
“
K
pl
“slope of the plastic range,
“
K
G
“ultimate slope,
Behavior of an arm of armament in longitudinal stress
F
L
E
K
el
of
K
pl
D
D
L
D
F
m
K
G
D
E
= 0.048 m,
D
L
= 0.7 m,
L
E
= 800 NR,
F
m
= 2800 NR
One-way behavior in force-displacement with 1 internal variable:
D
D
p
E
-
defined by
5 parameters:
D
E
,
D
L
,
K
el
,
K
pl
and
K
G
.
Affected with a discrete element with 2 nodes.
1.3
Boundary conditions and loadings
Embedding in one of the 2 nodes.
Force imposed in the local direction
(
)
y
Y
=
total
on the second node, by increments of
charge. A unit increment being worth 500 NR.
1.4 Conditions
initial
Internal displacements, efforts and variables null.
Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
One reproduces on an element a course of loading in each of the 3 fields (rubber band,
plastic, limits) of an one-way relation of behavior (local direction
y
). Parameters
are described on joined figure 1.
The way of load comprises 12 stages thus definite:
12
11
10
9
8
7
5
6
4
3
1
2
Fy
D
=
Uy
2.2
Results of reference
Direct calculations on the curve limits relation of behavior:
(
)
[]
(
)
(
)
F
K
U
U
D
F
K
D
K
U
D
U
D D
U
D
D
D
F
K
D
K
D
D
K
U
D
y
el
y
y
E
y
el
E
pl
y
E
y
E
L
y
E
L
E
y
el
E
pl
L
E
G
y
L
=
<
=
+
-
=
-
= -
=
+
-
+
-
=
if
if
Vari
Varimax
if Vari
Varimax
,
2.3
Uncertainty on the solution
Exact solution:
Fy
imposed and
Uy
deduced directly from the relations in [§2.2].
2.4 References
bibliographical
[1]
Note HM-77/94/368, G. DEVESA. “Dynamic Study of rupture of conductor and discharge
of ice on an experimental line with Medium Average ".
Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
An element
DIS_TR_L
with 2 nodes of null size (idem [§1.1]).
A node N2: all is locked.
A N3 node: one imposes
F
y
by pitches of 500 NR with the card of time:
T
0.
4.
6.
10.
12.
F (T)
0.
4.
2.
6.
4.
3.2
Characteristics of the mesh
1 SEG2.
2 nodes.
3.3 Functionalities
tested
Controls
Key word factor
Key word
Key
DEFI_MATERIAU
ARM
KYE, DLE, DYP,
[U4.23.01]
DLP, KYG
STAT_NON_LINE
COMP_INCR
RELATION:
[U4.32.01]
“WEAPON”
Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
Uy displacement: N3 node, Command 2
(
)
F
y
=
1000
1.1641 10
1
idem
0
Uy displacement: N3 node, Command 8
(
)
F
y
=
2000
4.6124 10
1
idem
0
Uy displacement: N3 node, Command 10
(
)
F
y
=
3000
7.0030 10
1
idem
0
Variable interns 1: Command 2
(
)
F
y
=
1000
6.8414 10
2
idem
0
Variable interns 1: Command 8
(
)
F
y
=
2000
4.13241 10
1
idem
0
Variable interns 1: Command 10
(
)
F
y
=
3000
0.52 10
1
idem
0
4.2 Remarks
General:
The behavior
“WEAPON”
is usable also in non-linear dynamic Analysis
but is not tested.
4.3 Parameters
of execution
Version: 3.03.07
Machine: CRAY C90
Overall dimension memory: 8
MW
Time CPU To use: 9.1
seconds
Code_Aster
®
Version
4.0
Titrate:
Non-linear SSNL101 Behavior of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
5
Summary of the results
The reduced dimension of the problem makes it possible to have only one unknown factor, transverse displacement
Uy
dependant on the internal variable, calculable exact solution by an algebraical expression and found by
Aster
with the identical one.