The Numerical Models Spectral Phantoms in Solid Mechanics

The report reviews the spectrum distortion problem of the deformations distribution function in the mechanical system in numerical simulations. For example, the beam deflection it is shown that the virtual function spectrum depends essentially on the number and irregularity of the grid nodes location along the beam model. It discusses computational validation of such distortions and the results of their mathematical modeling. It is shown that the use of Fourier transform for mathematical models verification can provide a mathematically correct formulation of the evaluating distortion task of the real spectrum. This conclusion for the quasi-static case allows authors to assert that in the dynamic case, the distortion spectrum will have an unacceptable value. The illustrations in the report presents a distorted spectrum distribution function of the beam deflection for different values of the density simulation grid and for the case with non-uniform grid. It is shown that the distortion of the amplitude spectrum can reach over 75%, while the distortion of the phase spectrum - 1800.