Code_Aster
®
Version
6.0
Titrate:
SSLL108 - Discrete elements 2D
Date:
19/08/02
Author (S):
J.M. PROIX, G. BERTRAND
Key
:
V3.01.108-A
Page:
1/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA, CS IF
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.108
SSLL108 - Discrete elements 2D
Summary:
The problem is quasi-static linear in mechanics of the structures.
One analyzes the response of a bar, modelized by 10 discrete elements, with a loading of traction, for
to validate the two-dimensional discrete elements.
Only one modeling uses at the same time the operators
MECA_STATIQUE
, and
STAT_NON_LINE
, to validate
the use of these elements (of which the behavior remains linear) with other finite elements with behavior
unspecified.
Code_Aster
®
Version
6.0
Titrate:
SSLL108 - Discrete elements 2D
Date:
19/08/02
Author (S):
J.M. PROIX, G. BERTRAND
Key
:
V3.01.108-A
Page:
2/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
A bar L=10m length, along axis X, modelized by 10 discrete elements with 2 nodes.
1.2
Material properties
Each discrete element has a stiffness: K = 1.000 NR/m
1.3
Boundary conditions and loadings
In x=0
dx = Dy = 0
In x=L
Fx=10N
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution: displacement for an element is given by:
Ux=F/Kx
Thus for N springs: Ux = N F/Kx
2.2
Results of reference
Values of displacement for x=L/2 and X=L, as well as effort in the elements (constant):
U (L/2) = 0.05 m, U (L) = 0.1 m, N=10N
2.3
Uncertainty on the solution
Exact analytical solution.
Code_Aster
®
Version
6.0
Titrate:
SSLL108 - Discrete elements 2D
Date:
19/08/02
Author (S):
J.M. PROIX, G. BERTRAND
Key
:
V3.01.108-A
Page:
3/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling
2d_DISCRET
3.2
Characteristics of the mesh
10 meshs SEG2.
3.3 Functionalities
tested
Order
Key word factor
Simple key word
Argument
AFFE_CARA_ELEM
DISCRETE
K_T_D_L
MECA_STATIQUE
STAT_NON_LINE
COMP_INCR
RELATION
ELAS
CALC_ELEM
OPTION
SIEF_ELGA_DEPL
OPTION
SIEF_ELGA_DEPL
4
Results of modeling A
4.1 Values
tested
Identification Reference
Aster %
difference
MECA_STATIQUE
DX (L/2)
0.05 0.05 0s
DX (L)
0.1.0.1 0
NR (
SIEF_ELGA_DEPL
)
10 10 0
STAT_NON_LINE
DX (L/2)
0.05 0.05 0s
DX (L)
0.1.0.1 0
NR (
SIEF_ELGA
)
10 10 0
Code_Aster
®
Version
6.0
Titrate:
SSLL108 - Discrete elements 2D
Date:
19/08/02
Author (S):
J.M. PROIX, G. BERTRAND
Key
:
V3.01.108-A
Page:
4/4
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
5
Summary of the results
This very simple test voluntarily makes it possible to check the correct operation of the discrete elements 2D
with
STAT_NON_LINE
, which makes it possible to use them with other modelings.