3. Operands#

3.1. Operands TABL_POST_ALEA/MOMENT_SPEC_0/MOMENT_SPEC_2/MOMENT_SPEC_4#

These operands make it possible to enter the value of the three spectral moments of order 0, 2 and 4 that may have been determined by the command POST_DYNA_ALEA [U4.84.04].

These values completely characterize the random signal for statistical methods for counting cycles:

  • method for counting stress peaks, which uses 0, 2 and 4,

  • method for counting when a given level has been exceeded, which requires only the data of 0 and 2.

♦/♦ MOMENT_SPEC_0 = 0, [R]

♦ MOMENT_SPEC_2 = 2, [R] ◊ MOMENT_SPEC_4 = 4, [R]

The value of the spectral moment is provided after the corresponding operand.

♦/TABL_POST_ALEA = table, [tabl_post_alea]

Allows you to specify the name of a table created by POST_DYNA_ALEA [U4.84.04], in which values of spectral moments (0, 2, 4) are stored, for various modes or nodes.

The values are read again and an average damage value is calculated for each triplet of spectral moments encountered in the table.

However, since the method for calculating the average damage is only valid for loads that are homogeneous to stresses, an alarm is issued when the calculation of the average damage does not correspond to power spectral densities that are homogeneous to the constraints (DSP_CONT).

3.2. Operand COMPTAGE#

♦ COMPTAGE =

To be able to calculate the damage suffered by a structure, it is first necessary to extract the elementary cycles of the loading history.

/”PIC”,

Allows you to choose the method for counting stress peaks to determine the elementary cycles of random loading [R7.04.02].

/”NIVEAU”,

Allows you to choose the method for counting overruns of a given level to determine the elementary cycles of random loading [R7.04.02].

3.3. Operand DUREE#

◊ DUREE =/duration, [R]

/1. , [DEFAUT]

Allows you to enter the data on the duration of the signal that is involved in the expression of average damage [R7.04.02].

3.4. Operand CORR_KE#

◊ CORR_KE = 'RCCM',

This operand makes it possible to take into account an elasto-plastic concentration coefficient \({K}_{e}\), which is defined by RCC -M as being the ratio between the actual deformation amplitude and the deformation amplitude determined by an elastic analysis.

\(\{\begin{array}{ccccccccc}{K}_{e}& \text{=}& 1& \text{si}& & & \Delta \sigma & \text{<}& 3{S}_{m}\\ {K}_{e}& \text{=}& 1+\frac{(1-n)(\Delta \sigma /3{S}_{m}-1)}{n(m-1)}& \text{si}& 3{S}_{m}& \text{<}& \Delta \sigma & \text{<}& 3m{S}_{m}\\ {K}_{e}& \text{=}& 1& \text{si}& 3m{S}_{m}& \text{<}& \Delta \sigma & & \end{array}\)

where \({S}_{m}\) is the maximum allowable stress, \(n\) and \(m\) are two constants that depend on the material.

The values of \({S}_{m}\), \(n\), and \(m\) are introduced into the operator DEFI_MATERIAU [U4.43.01] under the key word FATIGUE and the operands SM_KE_RCCM, N_ KE_RCCM, and M_, and M_ KE_RCCM.

3.5. Operand DOMMAGE#

♦ DOMMAGE = 'WOHLER',

This operand makes it possible to specify the method for calculating the damage, which in the case of a random type of stress is the Wöhler method.

To calculate the damage, the user must enter into the operator DEFI_MATERIAU [U4.43.01], the Wöhler curve of the material, which can be given in three distinct mathematical forms [R7.04.02]:

  • discretized function point by point (keyword FATIGUE, operand WOHLER),

  • Basquin analytical form (keyword FATIGUE, operands A_ BASQUIN and BETA_BASQUIN),

  • « current zone » form (keyword FATIGUE, operands E_ REFE, E_, A0, A1, A2, A3 and SL and keyword ELAS operand E).

Note on fatigue curves:

For small amplitudes, the problem of extending the fatigue curve may arise: for example, for RCC -M fatigue curves beyond 106 cycles, the corresponding stress, 180 MPa is considered to be the endurance limit, i.e. any stress less than 180 MPa must produce a zero use factor or an infinite number of admissible cycles.

The method adopted here corresponds to this concept of endurance limit: if the stress amplitude is less than the first x-axis of the fatigue curve, then a zero use factor is taken, that is to say an infinite number of admissible cycles.

3.6. Operand MATER#

♦ MATER = subdue,

Allows you to specify the name of the material to be subdued created by DEFI_MATERIAU [U4.43.01].

The material to be subdued must at least contain the definition of the material’s Wöhler curve [R7.04.02].

If it is desired to take into account an elasto-plastic concentration coefficient \({K}_{e}\), it is also necessary to have specified the material data (N, M and SM) necessary for the calculation of \({K}_{e}\).

3.7. Operand TITRE#

◊ TITRE = title,

Title associated with the table.

3.8. Table produced#

The POST_FATI_ALEA operator creates a table, tabl_post_f_alea, which includes 1 parameter: DOMMAGE: value of the average damage over the duration of the signal.

Note:

In the case where the operand TABL_POST_ALEA was used to enter the values of the spectral moments, the value of the average damage over the duration of the signal is stored in the table, for each triplet of spectral moments present in the table.

The command IMPR_TABLE [U4.91.03] allows you to print the table produced.