6. A few comments on the command file#

The following few comments are intended to illustrate the commands involved in static substructuring. Understanding these comments obviously requires the prior reading of the instructions for using the commands in question:

  • Commands specific to static substructuring:

  • MACR_ELEM_STAT [U4.44.01]

  • DEFI_MAILLAGE [U4.12.04]

  • DEPL_INTERNE [U4.65.01]

  • Commands changed for static substructuring:

  • AFFE_MODELE [U4.22.01]

  • CAL_VECT_ELEM [U4.41.02]

  • Commands useful for static substructuring:

  • ASSE_MAILLAGE [U4.12.02]

  • DEFI_GROUP [U4.12.03]

6.1. Operator AFFE_MODELE {line 22}#

Since we want to build a macro-element from polygon ABCD and the mesh ma contains all the elements of IJBCDA, we cannot use the assignment: TOUT: “OUI”.

It is necessary to assign only the mesh group ABCD (grsd2) and do not forget to assign the elements of the AD edge (grma14) because of the pressure load.

6.2. Operator MACR_ELEM_STAT {lines 45-59}#

  • The example illustrates the fact that the macroelement can be defined in several successive steps (use of the MACR_ELEM_STAT operator 3 times: {lines 45, 50 and 56} with the enrichment symbol &).

At the first call, we really define the macro-element:

  • « volume » sound: the mo_1 model

  • its external nodes {line 48}

  • the material field and the kinematic conditions applied to it {line47}.

During the next 2 calls {line 50 and 56}, the data structure of the macro-element is enriched:

  • calculation of the condensed stiffness matrix {line 52}

  • calculation of two « load cases » {lines 53 and 58}.

This possibility of enriching the macro-element makes it possible to « repair an oversight » without starting from scratch:

  • addition of a new load case,

  • calculation of the condensed mass for a Guyan method.

  • Definition of load case 1: CHF1 {line 53}

This load case is a follower (SUIV = “OUI”) because pressure is a loading that always acts according to normal at the edge.

The fact of having specified CHBL_1 as load is useless here because the kinematic conditions are zero DX = 0.0 DY = 0.0 {line 29}.

6.3. Operator DEFI_MAILLAGE {lines 68, 84}#

  • {line 70}: we define a substructure (and the support supermesh) by giving it the same name as the macroelement that is assigned to it. It is not forbidden.

  • {line 74}

All geometrically combined nodes are « unified »:

the CD side of S_1 merges with the \(\mathit{AB}\) side of S_2,

the CD side of S_2 merges with the \(\mathit{AB}\) side of S_3.

  • {line 76}

  • the node C, whose name is N12 in the initial mesh MA, will have the name NN112 in the mesh MA_123,

  • Node E, which is the image of C of the MA mesh in the S_2 substructure, will have the name NN212.

This node E can also be considered as the image of node B in the S_3 substructure so it could have had the name NN310 but the supermesh matching convention [U4.12.04] chooses the first name.

  • {line 77}

Node A (N1), which was named NN11 on line 76, is renamed to N1. The same is true for the nodes N4, N7 and N10.

This renaming is necessary in order to assemble the meshes that will be made {line 125} because this assembly is done by pooling the nodes of the same name.

  • {line 82}

We define the group of nodes GH that will be used {line 107} to define the exterior of the macro-element S_123.

6.4. Operators AFFE_MODELE and AFFE_CHAR_MECA {lines 86, 89}#

  • {line 87}

All MA_123 supermeshes are « activated »: the macro-element S_1 is assigned to them.

  • {line 91}

Node NN33, which is node N3 of the substructure S_3, is subject to a sliding support condition.

6.5. Operator MACR_ELEM_STAT {lines 104, 111}#

  • {line 109}

The kinematic load CHBL_123, which corresponds to the sliding support on GH, is introduced into the macro-element S_123. It is recommended in the notice [U4.44.01] to introduce this condition at the highest level: we could have done it at the global level because GH is part of the exterior of S_123.

  • {line 109}

For the macro-element S_123, the same load case name CHF1 is given as for the macro-element S_1 because the convention for defining a load case leads to the addition of:

  • the loads defined by the keyword CHARGE (here: chbl_123 which is useless because the imposed trips are zero),

  • the load cases that may be present on the substructures included in the model: here chf1 which is present in S_1, S_2, S_3.

6.6. Operator DEFI_MAILLAGE {line 120}#

  • {line 123} the nodes in MAG0 will have the same name as the nodes of the macro-elements used to define it (S_123).

The nodes of MAG0 will therefore be:

side \(\mathit{AB}\): N1, N4, N7, N10

side \(\mathit{GH}\): NN33, NN36, NN39, NN312

Mesh MAG0 contains only one supermesh and no regular mesh.

6.7. Operator ASSE_MAILLAGE {line 125}#

The final (or global) mesh contains:

  • all the QUAD4 cells of the initial MA mesh,

  • the S_123 supermesh of mesh MAG0

The supermesh is connected to mesh QUAD4 thanks to the identity of the names of the nodes N1, N2, N7, N10 in the MA and MAG0 meshes

6.8. Calculation at the global level {lines 129-184}#

  • {line 130} in the global grid, which contains all the cells in ma, we only affect those in quadrilateral \(\mathit{IJBA}\).

  • {line 131} we assign the S_123 substructure; the model therefore contains: a substructure (S_123) and ordinary finite elements (\(\mathit{IJBA}\)).

  • {line 165} do not forget to indicate the load case CHF1 which was defined in line 32 and which passes through the two macro-elements S_1 and S_123 via the name CHF1.

6.9. Operator DEPL_INTERNE#

  • {line 193} U1S_123 is the displacement field on the nodes in model MO_123 (i.e. the nodes in \(\mathit{AB}\), \(\mathit{CD}\), \(\mathit{EF}\), \(\mathit{GH}\)). This travel field corresponds to load case CHF1.

  • {line 199} U1S_2 is the displacement field on the nodes in model MO_1 (i.e. the nodes in \(\mathit{ABCD}\)). It should be noted that the displacement field was requested on the mesh S_2, but there is no « finite element » mesh for this part of the structure.

This is why the field of movement is restored in the « local » coordinate system of the macro-element S_1 (rotation of -45°). This coordinate system is the only one that allows the calculation of constraints using model MO_1.