1. Generalities#

The static substructure implemented in Aster can be used in linear mechanics and in nonlinear mechanics on linear parts of a model. In principle, it can be done at several levels: a substructure can contain other substructures at a lower level. All types of elements of the « MECANIQUE » phenomenon are accepted as well as all the loads supported by these elements.

The substructuring is currently implemented as part of the ordinary orders [U4.4‑] and [U4.5-]. However, it is not implemented as part of global orders: MECA_STATIQUE, CALC_CHAMP, POST_ELEM,…

An exception exists: commands STAT_NON_LINE and DYNA_NON_LINE accept static macro elements (see [§2]).

Static substructuring consists in statically « condensing » the problem to be treated: a certain number of (internal) unknowns are eliminated. There are then fewer so-called « external » unknowns.

It is a method that reduces the size of the problem. We can therefore expect gains in CPU time and disk occupancy. This static condensation naturally applies to the stiffness and mass matrix and to the second members representing the various loads. In this case, the condensation method can be interpreted algebraically as a resolution of the linear system by the « elimination » method. The solution of a linear static problem is therefore not modified by substructuring. On the other hand, it is possible to statically condense the mass matrix (Guyan condensation) but in this case the search for the natural modes of the condensed structure is altered by the substructuration method (see for example IMBERT [bib1]). There are other substructuring methods for dynamics problems in Aster [U4.55].

The theoretical principles of static substructuring are well explained in the book by IMBERT [bib1] and the manuals PERMAS [bib2].

The use of static substructuring in nonlinear situations is discussed in a separate first chapter.

In the rest of this document, these theoretical principles will be assumed to be known and only the « user » aspects will be considered. To do this, we will use an example a lot: test case SSLP100 from the Aster validation manual. Through this test case, we tried to illustrate a large number of possibilities of the software, by deliberately complicating the test:

  • substructuring at several levels (2),

  • use of a macro-element to generate several substructures by successive rotations,

  • boundary conditions and multi-level loads,

  • mixture of substructures and ordinary finite elements,

  • « follower » loading or not.

The command file for this test case whose lines have been numbered is given in the appendix to this document. When we want to refer to line n of this file, we will write {line n}.