Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
1/6
Organization (S): EDF/EP/AMV
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.101
SSNL101 - Non-linear Comportement 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 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
2/6
1
Problem of reference
1.1 Geometry
1 discrete element of null size to 2 nodes.
Locate 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.
The 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 “ARME” in effort-displacement introduced by a material
characteristic.
1.2
Material properties
Dependant on an incremental behavior “ARME” with 5 parameters: of (key word “DLE”) = 0.048 m, DLL
(“DLP”) = 0.7 m, Kel (“KYE”) = 1.67 E4 NR/m, Kpl (“KYP”) = 2.9 E3 NR/m, KG (“KYG”) = 1 E6 NR/Mr.
“of” displacement elastic range limits,
“DLL” displacement limits plastic range,
“Kel” slope of the elastic range,
“K pl” slope of the plastic range,
“KG” ultimate slope,
Behavior of an arm of armament in longitudinal stress
F
KG
Fm
K
L
pl
E
Kel
of
D
DLL
D
of = 0.048 m, DLL = 0.7 m, It = 800 NR, Fm = 2800 NR
One-way behavior in force-displacement with 1 internal variable: D - D
p
E defined by
5 parameters: of, DLL, Kel, Kpl and KG.
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 (= total Y) 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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
3/6
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:
10
Fy
9
4
11
3
2
8
12
5
7
1
6
D = Uy
2.2
Results of reference
Direct calculations on the curve limits relation of behavior:
F
= K U
if U
< D
y
el
y
y
E
F
= K D + K
-
if
y
el
E
pl (U
D
y
E)
Uy [D, D
E
L]
Vari = U - D
y
E
Varimax = D - D
L
E
F
= K D + K
-
+
-
if Vari =
y
el
E
pl (D
D
L
E)
kg (U
D
y
L)
Varimax
2.3
Uncertainty on the solution
Exact solution: Imposed Fy and Uy deduce 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 white frost on an experimental line with Medium Average ".
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
4/6
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 blocked.
A N3 node: one imposes Fy by step 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 grid
1 SEG2.
2 nodes.
3.3 Functionalities
tested
Commands
Key word factor
Key word
Key
DEFI_MATERIAU
ARME
KYE, DLE, DYP,
[U4.23.01]
DLP, KYG
STAT_NON_LINE
COMP_INCR
RELATION:
[U4.32.01]
“ARME”
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
Uy displacement: N3 node, Command 2 (F =
y
)
1000
1.1641 101
idem
0
Uy displacement: N3 node, Command 8 (F =
y
)
2000
4.6124 101
idem
0
Uy displacement: N3 node, Command 10 (F =
y
)
3000
7.0030 101
idem
0
Variable interns 1: Command 2 (F =
y
)
1000
6.8414 102
idem
0
Variable interns 1: Command 8 (F =
y
)
2000
4.13241 101
idem
0
Variable interns 1: Command 10 (F =
y
)
3000
0.52 101
idem
0
4.2 Remarks
General:
Behavior “ARME” is usable also in non-linear dynamic Analyze
but is not tested.
4.3 Parameters
of execution
Version: 3.03.07
Machine: CRAY C90
Obstruction memory: 8
MW
Time CPU To use: 9.1
seconds
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Non-linear SSNL101 Comportement of an element of conductor arrangement
Date:
30/01/98
Author (S):
G. DEVESA
Key:
V6.02.101-A Page:
6/6
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.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HI-75/96/041 - Ind A