2. Reference solution: modeling A

2.1. Calculation method used for the reference solution

The method used here is the so-called time-frequency method [bib1] where after a first linear step resolved in frequency after a Fourier transformation of the transient excitations and then a general return in time of all the result obtained by inverse Fourier transformation, the complement of internal nodal forces due to the non-linearity of the detachment calculated over the entire time range is estimated. A new linear frequency resolution is then carried out in a new step after Fourier transformation of this complement added to the initial transient excitations. The solution obtained generates a new complement of non-linear internal nodal forces and so on. The iterative process is stopped when a norm on the time window of the difference in displacements between 2 successive steps becomes less than a user criterion value.

There is also a purely transitory variant of this method [bib2] where the complement of non-linear internal nodal forces is resolved only transiently without frequency feedback.

2.2. Benchmark results

As reference results, the maxima of horizontal and vertical displacements recorded during 2 stages of the dynamic calculation are taken at the upper left end of the plate at point \(P3\) (cf.).

2.3. Complementary validation of REST_SPEC_TEMP

The REST_SPEC_TEMP operator is based on a Fortran version of the FFT algorithm. It is relevant to check that we find the same result with CALC_FONCTION’s FFT (python). To do this, we will compare the evolution of the following displacement \(X\) and \(Y\) from point \(\mathit{P3}\). The absolute difference between the two methods should be negligible (in the order of numerical precision).