4. Solving with Aster

Once the load has been broken down into Fourier harmonics, the harmonics being decoupled from each other (with different Fourier numbers), it is necessary to assemble and solve as many linear systems as there are harmonics.

In addition, since the material is assumed to be non-anisotropic, for the same harmonic number, the symmetric and antisymmetric modes are decoupled. We will therefore have to do as many resolutions (with the corresponding load) as there are different couples (harmonic, mode).

The layout in*Code_Aster* is different depending on whether the phenomenon is thermal or mechanical.

4.1. Thermal

In thermal engineering, there is no global control allowing several harmonics to be calculated directly. We must therefore proceed harmonic by harmonic. In addition, matrix calculations and elementary second members can only be done with the CALC_MATR_ELEM and CALC_VECT_ELEM commands (and not with the THER_LINEAIRE command).

Fourier mode is to be introduced in CALC_MATR_ELEM with the simple keyword MODE_FOURIER. The type of the harmonic is not necessary, the matrices (and vectors) being independent of the type. The type is only taken into account during Fourier recombination.

It is important to assemble the matrices and vectors corresponding to the different harmonics with the same numbering in order to be able to recombine the result fields. The operator NUME_DDL which constructs the numbering is therefore used once for the first harmonic, the numbering thus created being reused for all the other harmonics. This is possible if we have differentiated Dirichlet loads from the loads themselves (see example [§6.1]).

4.2. Mechanics

The command to process multiple harmonics is MACRO_ELAS_MULT [U4.51.02]. In this macro, harmonics are considered as load cases and so we do as many resolutions as there are harmonics. As in thermics, it is necessary to differentiate between Dirichlet loads, which must be identical for all harmonics, from the loads themselves, which can vary.

We get a data structure RESULTAT containing all the fields corresponding to the calculated harmonics (see example [§6.2]).