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Organization (S): EDF-R & D/AMA
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Document: U2.07.02
Note of use of the static under-structuring
Summary
This document is an introduction to the use of the static under-structuring.
While being based on a detailed example, whose command file is presented in appendix,
·
one will read paragraphs 1, 2, 3, 4;
·
one will refer to the description of the specific commands:
MACR_ELEM_STAT [U4.44.01]
DEFI_MAILLAGE [U4.12.04] and,
DEPL_INTERN [U4.65.01],
·
one will return to the detailed comments of the command file [§6].
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1 General information
The static under-structuring established in Aster is usable in linear mechanics and in
nonlinear mechanics on linear parts of a model. It can be done a priori with
several levels: a substructure can contain other substructures of lower level.
All the types of elements of the “mechanical” phenomenon are accepted thus that all them
loadings supported by these elements.
The under-structuring is currently established within the framework of the ordinary commands [U4.4-] and
[U4.5-]. It is however not established within the framework of the total commands:
MECA_STATIQUE, CALC_ELEM, CALC_NO, POST_ELEM,…
An exception exists: commands STAT_NON_LINE and DYNA_NON_LINE accept
static macronutrients (see [§2]).
The static under-structuring consists in “condensing” statically the problem to be treated: one is eliminated
certain number of unknown factors (interns). There then remain the unknown factors known as “external” in less large
numbers.
It is a method which reduces the size of the problem. One can thus expect savings of time CPU from them
and in occupation of the discs. This static condensation applies naturally to the matrix of
rigidity and of mass and with the second members representing the various loadings. In this case,
method of condensation can be interpreted algebraically like a resolution of the system
linear by the method “of elimination”. The solution of a linear problem of statics is thus not
modified by the under-structuring. On the other hand, it is possible to condense the matrix statically
of mass (condensation of Guyan) but in this case the search of the clean modes of the structure
condensed is deteriorated by the method of under-structuring (see for example IMBERT [bib1]). It
exist other methods of under-structuring for the problems of dynamics in Aster [U4.55].
The theoretical principles of the static under-structuring are well explained in the book of IMBERT
[bib1] and handbooks PERMAS [bib2].
The use of the static under-structuring into nonlinear is approached in a first chapter
distinct.
In the continuation of this document, one will suppose known these theoretical principles and one will not be interested
that with the aspects “user”. For that, one will be useful oneself much of an example: the case test SSLP100 of
handbook of Aster validation. We tested, through this case test, to illustrate a great number of
possibilities of the software, by complicating voluntarily the test:
·
under-structuring on several levels (2),
·
use of a macronutrient to generate by successive rotations several under
structures,
·
boundary conditions and loadings on several levels,
·
mix ordinary substructures and finite elements,
·
“following” loading or not.
The command file of this case test which one numbered the lines is given in appendix of it
document. When one wants to refer to line N of this file, one will write {line N}.
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2
Use of macronutrients in STAT_NON_LINE (or
DYNA_NON_LINE)
One can make a nonlinear calculation with STAT_NON_LINE [U4.51.03] on a model containing of
macronutrients. The interest of this type of calculation is a possible gain of performances (memory and/or
CPU).
So that calculation with macronutrients is more economic, it is necessary that the model has the broad ones
linear elastic zones (possibly repetitive). It is necessary as that these elastic zones (as one
will condense in macronutrients) have a border as small as possible. A favorable situation
will be for example the case of an entirely elastic structure with a small zone of plasticity
confined [Figure 2-a].
rubber band
fissure
zone of potential plasticity
Appear 2-a
One will then condense all the elastic part on the only nodes of the interface with the zone of
potential plasticity.
The use of macronutrients in STAT_NON_LINE (see case tests SSLP100C and D) is conditioned
by the following requirements:
· each macronutrient must be elastic linear, its temperature should not vary with the course
time,
· there cannot be contact with macronutrients,
· the loadings assigned to the macronutrients “constant” (are not multiplied by
“FONC_MULT”),
· the macronutrients should not undergo great rotations,
· “linear search” is not possible.
Once calculation makes with STAT_NON_LINE, the post usual processing (CALC_ELEM, CALC_NO,
POST_ELEM) will not have an effect that on the ordinary finite elements of the model (the macronutrients are
been unaware of). If one wants to examine for example the state of stress inside a macronutrient, it is necessary
to use the basic commands: CREA_CHAMP/EXTR, DEPL_INTERN,… (see [§4.3] and [§4.4]).
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3
Presentation of the case test being used as example
E
F3
F2
B3
C
G
B2
N12
N9
F1
N6
B1
N11
N8
F
N3
N5
H
D
N2
B
N1
O
With
N4
N7
N10
N14
N16
N18
N20
N13
N15
N17
N19
I
P1
F4
J
It is about a plane structure subjected to the boundary conditions following:
·
on side [GH]:
U + v = 0
(slipping support)
·
nodes B1, B2, B3:
U = v = 0
·
node J:
U = 2.0
·
loading case 1: chf1: pressure distributed on ADFH p = 10.0
·
loading case 2: chf2: specific forces on the nodes F1, F2, F3, F4 and P1,
Fy = - 20.0
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4 Processing of the case test by the method of
under-structuring
·
the initial grid contains only the meshs (and the nodes) of polygon IJBCDA,
·
one defines a macronutrient (S_1) corresponding to polygon ABCD,
·
the macronutrient (S_1) is repeated 2 times per rotation around 0,
·
one obtains then the macronutrient (S_123) corresponding to polygon ABCEGHFD,
·
the final model (on which one makes the resolution) is obtained while adding to the macronutrient
(S_123) finite elements of quadrilateral IJBA.
5
General organization of calculations and definitions
5.1
Construction of the total model
The principle of the establishment of the static under-structuring in Aster is that of a step
ascending:
a model having been defined, one condenses it (operator MACR_ELEM_STAT) on some of its
nodes. One then obtains a macronutrient which, functionally resembles new much
finite element “larger”. This macronutrient can then be integrated in a model of level
superior (operators DEFI_MAILLAGE and AFFE_MODELE). This new model can then be
digest in its turn and so on without limitation a priori of the number of levels.
Definition:
·
the nodes on which a macronutrient is condensed are known as “external” (the others are
“interns”),
·
level: it is a notion useful for comprehension of the text of commands; any level described
relations of structuring between the various models and the various macronutrients.
For us, it is an entirety. The operation of condensation increases the level by + 1: one
model of level N gives by condensation a macronutrient of level N + 1 which will be
integrated into a model of level N + 1,
·
operator MACR_ELEM_STAT is the only operator allowing to create a macronutrient in
static under-structuring,
·
operator DEFI_MAILLAGE is the only operator using the macronutrients in
static under-structuring.
For our example:
·
MO_1 {line 22} is the model moreover low level (- 2),
·
S_1 {lines 45, 59} is the intermediate macronutrient of level (- 1),
·
MA_123 and MO_123 {lines 68, 87} represent the grid and the model of level
intermediary (- 1),
·
S_123 {line 104} is the macronutrient of higher level (0),
·
MAG0, MAG and MOG {lines 120, 125, 129} represent grids and a model moreover
high level (0): the distinction between grids MAG0 and MAG will be explained to [§6.6] and
[§6.7].
The structuring of the model of higher level MOG can arise graphically by one
tree structure, distinction between macronutrient and substructure being explained in the paragraph
according to.
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MODEL MOG
Complete structure
level 0
finite elements
S_123 substructure
ordinary
S_123 macronutrient
polygon IJBA
polygon ABCEGHFD
MODELE MO_123
polygon ABCEGHFD
level - 1
S_1 substructure
S-2 substructure
S_3 substructure
S_1 macronutrient
S-1 macronutrient
S_1 macronutrient
polygon ABCD
polygon DCEF
polygon FEGH
model MO_1
model MO_1
model MO_1
polygon ABCD
polygon DCEF
polygon FEGH
level - 2
finite elements
finite elements
finite elements
ordinary
ordinary
ordinary
polygon ABCD
polygon DCEF
polygon FEGH
5.2
macronutrient and substructure
One calls macronutrient the result of operator MACR_ELEM_STAT: it is a condensed model
on its external nodes.
One calls substructure an occurrence of a macronutrient in a of the same model level.
A substructure is a macronutrient put in position in physical space. The position of one
substructure is given by the co-ordinates of the nodes of the super-mesh which is associated for him.
The same macronutrient can give rise to several substructures by defining several
positions: in our example, the S_1 macronutrient generates 3 substructures S_1, S_2 and S_3
by suitable rotations.
A substructure is to some extent a new “finite element”. The macronutrient is the “type” of
this element: one affects a macronutrient on a super-mesh to form a substructure.
One calls super-mesh, the geometrical support of a substructure. It is a named object included
in a grid. A super-mesh, like an ordinary mesh, is only one ordered list of names
nodes.
Like an ordinary finite element, a substructure has:
·
an “elementary” matrix of rigidity (and/or of mass, damping,…),
·
“elementary” vectors of loading,
·
a mesh support (one will speak about super-mesh),
·
nodes carrying of the ddl.
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With the difference of an ordinary finite element, a substructure has several limitations:
·
the mesh support is not a simple type: TRIA3,…, HEXA20: certain postprocessings
are thus not possible,
·
it does not have type_élément, not functions of form,…
·
the only options of calculation available are RIGI_MECA, MASS_MECA and CHAR_MECA,
·
the nodes can be nodes of LAGRANGE coming from the dualisation from
internal conditions kinematics.
Identification of the substructures and the macronutrients:
The macronutrients are concepts named by the user.
Substructures (as the ordinary finite elements) are identified by the name of
super-meshs which support them.
In our example:
·
S_1 and S_123 are the two macronutrients defined by the user {lines 45 and 104},
·
S_1, S_2, S_3, S_123 are the names of the super-meshs (and thus of the substructures) that
the user gives during the construction of grids MA_123 and MAG0.
Note:
There is no possible confusion (by the program) between a substructure and one
of the same macronutrient name (here S_1 and S_123 although that does not facilitate the reading of the file
commands!).
5.3
Redescente in the substructures
The ascending step, that we have just detailed, makes it possible to build the total model, or
final, (mog) on which one carries out the resolution:
·
CALC_MATR_ELEM
·
CALC_VECT_ELEM
·
ASSE_MATRICE
{lines 151-184}
·
…
·
RESO_LDLT
This resolution has as a result the field of displacements of the nodes of the total model. These nodes
are:
·
nodes of the ordinary finite elements of the model (here quadrilateral IJBA),
·
external nodes of the substructures of the model: (here only one substructure: S_123).
To find the field of displacements on the internal nodes of the substructures, it is necessary then
“to go down again” the tree structure of the substructures thanks to operator DEPL_INTERN.
This operator calculates the field of displacements on all the nodes of the substructure from
the data of the field of displacements on its external nodes.
For our example and load 1:
·
U1S_123
{line 193}
is displacement on the substructure
S_123
·
U1S_1
{line 197}
is displacement on the substructure
S_1
·
U1S_2
{line 199}
is displacement on the substructure
S_2
·
U1S_3
{line 201}
is displacement on the substructure
S_3
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5.4 Postprocessings
Usual postprocessings: calculation of the deformations, of the constraints,… can only be made
by the ordinary finite elements which only know the concept of function of interpolation.
One will be able to thus calculate the constraints in a given point of the structure only with the model
containing the ordinary finite element containing this point. For that, it will have been necessary to calculate the field of
displacements on this model:
Example:
·
to calculate the constraints on quadrilateral IJBA the model will be used: MOG and them
displacements: U1
·
to calculate the constraints on polygon DCEF the model will be used: MO_1 and them
displacements: U1S_2
Note:
Since command CALC_CHAM_ELEM “was strongly degreased”, it is necessary to use
CALC_ELEM but for that, one is obliged to create a SD evol_elas by the command
CREA_RESU.
6
Some comments on the command file
The purpose of the few comments which follow are to illustrate the commands which intervene in
static under-structuring. The comprehension of these comments supposes obviously the reading
precondition of the notes of use of the commands concerned:
·
Commands specific to the static under-structuring:
-
MACR_ELEM_STAT [U4.44.01]
-
DEFI_MAILLAGE [U4.12.04]
-
DEPL_INTERN [U4.65.01]
·
Commands modified for the static under-structuring:
-
AFFE_MODELE [U4.22.01]
-
CAL_VECT_ELEM [U4.41.02]
·
Commands useful for the static under-structuring:
-
ASSE_MAILLAGE [U4.12.02]
-
DEFI_GROUP [U4.12.03]
6.1 Operator
AFFE_MODELE {line 22}
Since one wants to build a macronutrient starting from polygon ABCD and that the grid my contains
all the elements of IJBCDA, one cannot employ the assignment: TOUT: “OUI”.
It is necessary to affect only the group of mesh ABCD (grsd2) and not to forget to affect the elements
edge AD (grma14) because of the loading of pressure.
6.2 Operator
MACR_ELEM_STAT {lines 45-59}
·
The example illustrates the fact that one can define the macronutrient in several stages
successive (use of operator MACR_ELEM_STAT 3 times: {lines 45, 50 and 56} with
symbol of enrichment &).
In the first call, one defines truly the macronutrient:
-
its “volume”: the model mo_1
-
its external nodes {line 48}
- the material field and the conditions kinematics which are applied to him
{line 47}.
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At the time of the 2 following calls {line 50 and 56}, one enriches the structure of data of
macronutrient:
-
calculation of the matrix of condensed rigidity {line 52}
-
calculation of two “loading cases” {lines 53 and 58}.
This possibility of enriching the macronutrient makes it possible “to repair a lapse of memory” without setting out again with
zero:
-
addition of a new loading case,
-
calculation of the mass condensed for a method of Guyan.
·
Definition of the loading case 1: CHF1 {line 53}
This loading case is following (SUIV = “OUI”) because the pressure is a loading which acts
always according to the normal at the edge.
The fact of having specified like load CHBL_1, is not used for nothing here because the conditions
kinematics are null DX = 0.0 DY = 0.0 {line 29}.
6.3 Operator
DEFI_MAILLAGE {lines 68, 84}
·
{line 70}: one defines a substructure (and the super-mesh support) by giving him the same one
which the macronutrient that one to him names. It is not prohibited.
·
{line 74}
All the geometrically confused nodes “are unified”:
the side CD of S_1 merges with side AB of S_2,
the side CD of S_2 merges with side AB of S_3.
·
{line 76}
-
node
C, which has as a name N12 in initial grid MA, will have as a name NN112
in grid MA_123,
-
node
E, which is the image of C of grid MA in the S_2 substructure will have
for name NN212.
This node E can also be regarded as the image of the node B in
substructure S_3 it could thus have had name NN310 but the convention of
sticking together of the super-meshs [U4.12.04] chooses the first denomination.
·
{line 77}
Node A (N1), which had been named NN11 with line 76, is famous in N1. It is of
even for the N4 nodes, N7 and N10.
This renaming is necessary in the sight of the assembly of the grids which one will make {line 125}
because this assembly is made by pooling of the of the same nodes name.
·
{line 82}
One defines the group of nodes GH which will serve {line 107} for the definition of the outside of
S_123 macronutrient.
6.4 Operators
AFFE_MODELE and AFFE_CHAR_MECA {lines 86, 89}
·
{line 87}
All super-meshs MA_123 “are activated”: one affects the S_1 macronutrient to them.
·
{line 91}
The node NN33 which is the N3 node of the S_3 substructure is subjected to a condition
of slipping support.
6.5 Operator
MACR_ELEM_STAT {lines 104, 111}
·
{line 109}
The kinematic load CHBL_123 which corresponds to the support slipping on GH is introduced into
the S_123 macronutrient. It is advised in the note [U4.44.01] to introduce this condition
at the highest level: one could have done it at the total level bus GH belongs to outside
of S_123.
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·
{line 109}
For the S_123 macronutrient, one gives the same name of loading case CHF1 as for
S_1 macronutrient because the convention of definition of a loading case results in adding:
-
loadings defined by key word CHARGE (here: chbl_123 which is not used for nothing bus
imposed displacements are null),
-
loading cases possibly present on the substructures included in
model: here chf1 which is present in S_1, S_2, S_3.
6.6 Operator
DEFI_MAILLAGE {line 120}
·
{line 123} the nodes of MAG0 will have the same name as the nodes of the macronutrients
being used for its definition (S_123).
The nodes of MAG0 will be thus:
side AB: N1, N4, N7, N10
side GH: NN33, NN36, NN39, NN312
Grid MAG0 contains only one super-mesh and not ordinary mesh.
6.7 Operator
ASSE_MAILLAGE {line 125}
The grid final (or total) contains:
·
all meshs QUAD4 of initial grid MA,
·
the S_123 super-mesh of grid MAG0.
The super-mesh is connected to meshs QUAD4 thanks to the identity of the names of the N1 nodes, N2,
N7, N10 in grids MA and MAG0.
6.8
Calculation at the total level {lines 129-184}
·
{line 130} in the total grid, which contains all the meshs of my, one only affects
those of quadrilateral IJBA.
·
{line 131} one affects the S_123 substructure; the model thus contains: a substructure
(S_123) and of the ordinary finite elements (IJBA).
·
{line 165} one should not forget to indicate the loading case CHF1 which was defined in line 32
and which forwards by the two macronutrients S_1 and S_123 via name CHF1.
6.9 Operator
DEPL_INTERN
·
{line 193} U1S_123 is the field of displacements on the nodes of model MO_123
(i.e. nodes of AB, CD, EFF, GH). This field of displacements corresponds to the case
of load CHF1.
·
{line 199} U1S_2 is the field of displacements on the nodes of model MO_1
(i.e. nodes of ABCD). It should be noticed that one asked for the field of
displacement on the S_2 mesh, but there is not grid “finite elements” of this part
structure.
This is why, the field of displacement is restored in the “local” reference mark of
macronutrient S_1 (rotation of - 45°). This reference mark is the only one which allows the calculation of
constraints thanks to model MO_1.
7 Bibliography
[1]
J.F. IMBERT: “Analysis of the structures by finite elements”. Editions CEPADUES (1979)
[2]
E. SCHREM: “Handbook for linear analysis”. INTES Publication UM 404 REVC.
STUTTGART (1989)
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Appendix 1 command file example
1 # SSLP100/B
2 # STICK CHARGED IN STATIC SOUS-STRUCTURATION.
3 # MODELISATION: WITH SUBSTRUCTURES.
4 # ======================================================================
5
6
7 BEGINNING (CODE=_F (NAME = “SSLP100B”, NIV_PUB_WEB=' INTERNET'))
8
9 MA=LIRE_MAILLAGE ()
10
11 ACIER=DEFI_MATERIAU (ELAS=_F (E = 15., NAKED = 0.3))
12
13 CHMAT=AFFE_MATERIAU (MAILLAGE=MA, AFFE=_F (ALL = “YES”, MATER = STEEL))
14
15 # =======================================================================
16 #
17 # CONSTRUCTION OF THE MODEL MOREOVER LOW LEVEL (- 2)
18 #
19 # =======================================================================
20
21
22 MO_1=AFFE_MODELE (MAILLAGE=MA, AFFE= (
23
24 _F (GROUP_MA = “GRSD2”, MODELING = “D_PLAN”, PHENOMENON = “MECHANICAL”),
25 _F (GROUP_MA = “GRMA14”, MODELING = “D_PLAN”, PHENOMENON = “MECHANICAL”)))
26
27 CHBL_1=AFFE_CHAR_MECA (MODELE=MO_1,
28 # N8:
29 DDL_IMPO=_F (NODE = (“N8”,), DX = 0.0, DY = 0.0)
30)
31
32 CHF1_1=AFFE_CHAR_MECA (MODELE=MO_1,
33 PRES_REP=_F (GROUP_MA = (“GRMA14”,), CLOSE = 10.0))
34
35 CHF2_1=AFFE_CHAR_MECA (MODELE=MO_1,
36 FORCE_NODALE=_F (NODE = (“N11”,), FY = - 20.0))
37
38 # =======================================================================
39 #
40 # DEFINITION OF THE MACRONUTRIENT OF LEVEL (- 1)
41 #
42 # =======================================================================
43
44
45 S_1=MACR_ELEM_STAT (
46 # ---------------------
47 DEFINITION=_F (MODEL = MO_1, CHAM_MATER = CHMAT, CHAR_MACR_ELEM = CHBL_1),
48 OUTSIDE =_F (NODE = (“N1”, “N4”, “N7”, “N10”,), GROUP_NO = (“GRNM13”,)))
49
50 S_1=MACR_ELEM_STAT (reuse=S_1,
51 # ---------------------
52 RIGI_MECA=_F (),
53 CAS_CHARGE=_F (NOM_CAS = “CHF1”, LOAD = (CHBL_1, CHF1_1,), SUIV = “YES”)
54)
55
56 S_1=MACR_ELEM_STAT (reuse=S_1,
57 # ---------------------
58 CAS_CHARGE=_F (NOM_CAS = “CHF2”, LOAD = CHF2_1, SUIV = “NOT”)
59)
60
61 # =======================================================================
62 #
63 # DEFINITION OF THE MODEL OF LEVEL (- 1)
64 #
65 # =======================================================================
66
67
68 MA_123=DEFI_MAILLAGE (
69 # ---------------------
70 DEFI_MAILLE= (_F (MACR_ELEM_STAT = S_1, MESH = “S_1”),
71 _F (MACR_ELEM_STAT = S_1, MESH = “S_2”, ANGL_NAUT = (45.0,)),
72 _F (MACR_ELEM_STAT = S_1, MESH = “S_3”, ANGL_NAUT = (90.0,))),
73
74 RECO_GLOBAL=_F (ALL = “YES”),
75
76 DEFI_NOEUD= (_F (ALL = “YES”, PREFIX = “NR”, INDEX = (3,3,2,5,)),
77 _F (NOEUD_FIN = “N1”, MESH = “S_1”, NOEUD_INIT = “N1”),
78 _F (NOEUD_FIN = “N4”, MESH = “S_1”, NOEUD_INIT = “N4”),
79 _F (NOEUD_FIN = “N7”, MESH = “S_1”, NOEUD_INIT = “N7”),
80 _F (NOEUD_FIN = “N10”, MESH = “S_1”, NOEUD_INIT = “N10”)),
81
82 DEFI_GROUP_NO= (_F (MESH = “S_3”, GROUP_NO_FIN = “GH”, GROUP_NO_INIT = “GRNM13”),
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83 _F (MESH = “S_1”, GROUP_NO_FIN = “AB”, GROUP_NO_INIT = “GRNM11”))
84)
85
86 MO_123=AFFE_MODELE (MAILLAGE=MA_123,
87 AFFE_SOUS_STRUC=_F (ALL = “YES”))
88
89 CHBL_123=AFFE_CHAR_MECA (MODELE=MO_123,
90 LIAISON_DDL= (# GH:
91 _F (NODE = (“NN33”, “NN33”,), DDL = (“DY”, “DX”,), COEF_MULT = (1.0, 1.0,), COEF_IMPO = 0.0),
92 _F (NODE = (“NN36”, “NN36”,), DDL = (“DY”, “DX”,), COEF_MULT = (1.0, 1.0,), COEF_IMPO = 0.0),
93 _F (NODE = (“NN39”, “NN39”,), DDL = (“DY”, “DX”,), COEF_MULT = (1.0, 1.0,), COEF_IMPO = 0.0),
94 _F (NODE = (“NN312”, “NN312”,), DDL = (“DY”, “DX”,), COEF_MULT = (1.0, 1.0,), COEF_IMPO = 0.0))
95)
96
97 # =======================================================================
98 #
99 # DEFINITION OF THE MACRONUTRIENT OF LEVEL 0
100 #
101 # =======================================================================
102
103
104 S_123=MACR_ELEM_STAT (
105 # ---------------------
106 DEFINITION=_F (MODEL = MO_123, CHAR_MACR_ELEM = CHBL_123),
107 EXTERIEUR=_F (GROUP_NO = (“GH”, “AB”,)),
108 RIGI_MECA=_F (),
109 CAS_CHARGE= (_F (NOM_CAS = “CHF1”, LOAD = CHBL_123, SUIV = “YES”),
110 _F (NOM_CAS = “CHF2”, LOAD = CHBL_123, SUIV = “NOT”))
111)
112
113 # =======================================================================
114 #
115 # DEFINITION OF THE TOTAL MODEL OF LEVEL 0
116 #
117 # =======================================================================
118
119
120 MAG0=DEFI_MAILLAGE (
121 #---------------------
122 DEFI_MAILLE=_F (MACR_ELEM_STAT = S_123, MESH = “S_123”),
123 DEFI_NOEUD=_F (ALL = “YES”, INDEX = (1,0,1,8,)) )
124
125 MAG=ASSE_MAILLAGE (OPERATION=' SOUS_STR'
126 MAILLAGE_1=MAG0, MAILLAGE_2=MA)
127
128
129 MOG=AFFE_MODELE (MAILLAGE=MAG,
130 AFFE=_F (GROUP_MA = “GRSD1”, MODELING = “D_PLAN”, PHENOMENON = “MECHANICAL”),
131 AFFE_SOUS_STRUC=_F (MESH = (“S_123”,)))
132
133 # =======================================================================
134 #
135 # RESOLUTION AT THE TOTAL LEVEL:
136 #
137 # =======================================================================
138
139
140 CHAGBL=AFFE_CHAR_MECA (MODELE=MOG,
141 DDL_IMPO=_F (NODE = (“N19”,), DX = 2.0))
142
143 CHAGF2=AFFE_CHAR_MECA (MODELE=MOG,
144 FORCE_NODALE=_F (NODE = (“N15”, “N17”,), FY = - 20.0))
145
146 # RIGIDITE:
147 # ---------
148
149 CHMATG=AFFE_MATERIAU (MAILLAGE=MAG, AFFE=_F (ALL = “YES”, MATER = STEEL))
150
151 MELGR=CALC_MATR_ELEM (OPTION=' RIGI_MECA',
152 MODELE=MOG, CHARGE=CHAGBL, CHAM_MATER=CHMATG)
153
154 NUG=NUME_DDL (MATR_RIGI=MELGR, METHODE=' LDLT')
155
156 MATAS=ASSE_MATRICE (NUME_DDL=NUG, MATR_ELEM=MELGR)
157
158 MATAS=FACT_LDLT (reuse=MATAS, MATR_ASSE=MATAS)
159
160 # 2ND MEMBRES:
161 # ------------
162
163 VELG1=CALC_VECT_ELEM (OPTION=' CHAR_MECA',
164 CHARGE=CHAGBL, MODELE=MOG,
165 SOUS_STRUC=_F (CAS_CHARGE = “CHF1”, MESH = “S_123”)
166)
167
168 VELG2=CALC_VECT_ELEM (OPTION=' CHAR_MECA',
169 CHARGE= (CHAGF2, CHAGBL,), MODELE=MOG,
170 # TO TEST THE KEY WORD ALL:“OUI”:
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Note of use of the static under-structuring
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171 # SOUS_STRUC:(CAS_CHARGE:“CHF2” MAILLE: S_123)
172 SOUS_STRUC=_F (CAS_CHARGE = “CHF2”, ALL = “YES”)
173)
174
175 VECAS1=ASSE_VECTEUR (NUME_DDL=NUG, VECT_ELEM=VELG1)
176
177 VECAS2=ASSE_VECTEUR (NUME_DDL=NUG, VECT_ELEM=VELG2)
178
179 # RESOLUTION:
180 # -----------
181
182 U1=RESO_LDLT (MATR_FACT=MATAS, CHAM_NO=VECAS1)
183
184 U2=RESO_LDLT (MATR_FACT=MATAS, CHAM_NO=VECAS2)
185
186 # =======================================================================
187 #
188 # REDESCENTE IN THE SUBSTRUCTURES:
189 #
190 # =======================================================================
191
192
193 U1S_123=DEPL_INTERN (DEPL_GLOBAL=U1, MAILLE=' S_123', NOM_CAS=' CHF1')
194
195 U2S_123=DEPL_INTERN (DEPL_GLOBAL=U2, MAILLE=' S_123', NOM_CAS=' CHF2')
196
197 U1S_1=DEPL_INTERN (DEPL_GLOBAL=U1S_123, MAILLE=' S_1', NOM_CAS=' CHF1')
198
199 U1S_2=DEPL_INTERN (DEPL_GLOBAL=U1S_123, MAILLE=' S_2', NOM_CAS=' CHF1')
200
201 U1S_3=DEPL_INTERN (DEPL_GLOBAL=U1S_123, MAILLE=' S_3', NOM_CAS=' CHF1')
202
203 U2S_1=DEPL_INTERN (DEPL_GLOBAL=U2S_123, MAILLE=' S_1', NOM_CAS=' CHF2')
204
205 U2S_2=DEPL_INTERN (DEPL_GLOBAL=U2S_123, MAILLE=' S_2', NOM_CAS=' CHF2')
206
207 U2S_3=DEPL_INTERN (DEPL_GLOBAL=U2S_123, MAILLE=' S_3', NOM_CAS=' CHF2')
208
209 # =======================================================================
210 #
211 # TEST OF THE VALUES OF REFERENCE:
212 #
213 # =======================================================================
214
215
216 TEST_RESU (
217 CHAM_NO= (
218 # VALUES OF REFERENCE OBTAINED BY ASTER WITHOUT SUBSTRUCTURES (SSLP100A)
219 # POINTS P1, P2, P4 AT THE TOTAL LEVEL:
220 _F (CHAM_GD = U1, NODE = “N15”, NOM_CMP = “DX”,
221 VALE = 1.88327E+0, PRECISION = 1.E-5, REFERENCE = “AUTRE_ASTER”),
222 _F (CHAM_GD = U1, NODE = “N15”, NOM_CMP = “DY”,
223 VALE = 2.59224E-2, PRECISION = 1.E-5, REFERENCE = “AUTRE_ASTER”),
224…
Handbook of Utilization
U2.07 booklet: Methods to reduce the size of modeling
HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Note of use of the static under-structuring
Date:
29/09/05
Author (S):
J. PELLET, O. Key NICOLAS
:
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: 14/14
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HT-66/05/004/A
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