6. Modeling A

6.1. Characteristics of modeling

In this modeling, the dynamic problem is solved in a linear calculation loop where the complement of nodal forces due to the nonlinearity of the detachment is recalculated each time over the entire time range. We use either a harmonic calculation with a frequency evolution and time feedback by Fourier transform in the classical time-frequency method, or a transient calculation on a physical basis with an alternative strictly temporal method.

6.2. Characteristics of the mesh

The model is composed of 55 nodes (285 ddls), 42 elements (32 plate elements DKT and 10 discrete elements DIS_T).

6.3. Calculation parameters

Each dynamic transient calculation is carried out over an interval of \(5s\) by time steps of \(0.005s\) archived every 2 steps. Each harmonic calculation is carried out with a step of \(1/20.48\mathrm{Hz}\) which makes it possible to restore a time window of \(20.48s\) sufficient to correctly calculate the FFT of the force of gravity constant over time; the maximum calculation frequency is equal to \(25\mathrm{Hz}\) and the extended one is \(50\mathrm{Hz}\) in order to obtain a time step of \(0.01s\) in the time window restored by FFT.

6.4. Tested sizes and results

Identification	Transition	Harmonic	Difference
\(\mathrm{P3}\) — \(\mathrm{DX}\) (2.33 s) iter=1	-4.58502E-2	-4.58588E-2	0.019%
\(\mathrm{P3}\) — \(\mathrm{DY}\) (2.33 s) iter=1	5.67299E-3	5.67541E-3	0.043%
\(\mathrm{P3}\) — \(\mathrm{DX}\) (2.34 s) iter=2	-4.82202E-2	-4.82436E-2	0.048%
\(\mathrm{P3}\) — \(\mathrm{DY}\) (2.34 s) iter=2	6.55566E-3	6.54736E-3	0.127%

Comparison of FFT fortran (REST_SPEC_TEMP) and FFT python (CALC_FONCTION):

Identification	REST_SPEC_TEMP	CALC_FONCTION	Absolute variance
\(\mathrm{P3}\) — \(\mathrm{DX}\) (2.34 s) iter=2	-4.82202E-2	-4.82202E-2	2.5673907444E-16
\(\mathrm{P3}\) — \(\mathrm{DY}\) (2.34 s) iter=2	6.55566E-3	6.55566E-3	-7.4593109467E-17