4. Implementation of the calculation#

4.1. Calculation of static and dynamic stresses#

The estimation of the admissible vibration level requires the prior calculation of the static and dynamic stresses:

  • the result corresponding to static loading (centrifugal force, pressure,…) can be calculated with MECA_STATIQUE or STAT_NON_LINE. A single time step must be present in the result data structure. The calculation of the \({\sigma }_{\mathrm{stat}}\) constraints from the displacement field is done using the CALC_CHAMP command (option SIEQ_ELGA or SIEQ_ELNO depending on whether you want to calculate the damage to the nodes or to the Gauss points).

  • The calculation of the \(N\) natural modes considered can be done with the CALC_MODES command. The calculation of the modal constraints \({\sigma }_{\mathrm{mod}}^{i}\) is done using the CALC_CHAMP command (option SIEQ_ELGA or SIEQ_ELNO depending on whether you want to calculate the damage at the nodes or at the Gauss points).

4.2. Definition of material properties#

Two material parameters are required for the calculation:

  • the value of the breaking limit of material \({S}_{u}\). This parameter must be entered in the operator DEFI_MATERIAU [U4.43.01] (keyword factor RCCM, operand Su).

  • the endurance limit of material \({S}_{l}\). This parameter corresponds to the first point of the Wöhler curve (operator DEFI_MATERIAU, keyword FATIGUE, operand WOHLER).

4.3. Call to CALC_FATIGUE#

The use of CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_VIBR”) requires the following parameters to be filled in:

  • static and modal constraints previously calculated;

  • material properties;

  • the list of modes to consider (NUME_MODE) and their relative weight (FACT_PARTICI), corresponding to the coefficients \({({\beta }_{i})}_{1\le i\le N}\);

  • the choice of the method of taking into account the average constraints (Gerber or Goodman: operand CORR_SIGM_MOYE);

  • the choice of the place to calculate the damage: at the nodes (OPTION =” DOMA_ELNO_SIGM “) or at the Gauss points (OPTION =” DOMA_ELGA_SIGM”).

4.4. Interpreting the results#

At the output of operator CALC_FATIGUE, we have a field (at nodes or at Gauss points) with the admissible value of \(\alpha\): the areas where \(\alpha\) is the weakest correspond to the zones that limit the life of the structure.

To pass from the coefficient \(\alpha\) to the admissible vibration amplitude, an additional operation is required. For example, suppose we are interested in the magnitude of the movements at a given point, which we will write \(\partial \tilde{u}\). This point may correspond, for example, to the position of a sensor, or to the zone of maximum vibration amplitude.

Note \({\tilde{u}}_{\mathrm{mod}}^{i}\) the movement to the point of interest associated with mode i. The admissible vibration amplitude at the point of interest is then:

\(\partial \tilde{u}=\mathrm{min}(\alpha )\sum _{i=1}^{N}{\beta }_{i}{\tilde{u}}_{\mathrm{mod}}^{i}\)

This calculation is illustrated in the example below.

The minimum value of \(\alpha\) can be obtained in three different ways:

  • or by subcontracting the result field in Aster (POST_RELEVE_T, OPERATION =” EXTREMA “);

  • or by viewing the result field;

  • or in the message file. The information is printed as follows:

Maximum vibration amplitude allowed by the structure: 1.318438

4.5. Notes and tips#

A few remarks can be made about this feature:

  • The result of the calculation is necessarily very sensitive to the quality of the stress calculation. The user must therefore ensure that the fineness of his mesh is sufficient. The use of quadratic elements is essential.

  • Likewise, it is advisable to do the calculation at Gauss points, as interpolation for the passage Gauss points - knots being a source of imprecision.

  • Critical areas most often correspond to geometric singularities. The user will have to check whether the singularity corresponds to a physical reality or to a discretization that is too crude. Note that the use of remeshing (Homard software, operator MACR_ADAP_MAIL) does not make it possible to converge on a stable non-zero solution if the initial geometry is discretized too roughly.