This paper focuses on the implementation of the MLPG formulation for layered plates. For this purpose implementaton of homogenization theory was required and analyses were performed in order to obtain homogenized material properties of composite plates. Software for homogenization of material properties uses direct homogenization method that is based on volume average of stresses in the representative volume element (RVE). Homogenization is performed by linking MATLAB and ANSYS software. Obtained data are used in analyses carried out in own software which is based on the MLPG method. Strain, stress and displacement fields were evaluated. Results obtained by MLPG were compared with those obtained by FEM programs ANSYS and ABAQUS. and Obsahuje seznam literatury
By rneans of correlation analysis, resonance interaction between Uranian rings and new satellites predicted earlier, is proved, Instability of circular rings relative to the disturbance with the azimuthal number m =1 is shown; it may be the cause of the ring’s eccentricity. This justifies the authors' hypothesis that the formation of eccentric rings of the protodisk around Uranus ia due to unknown Uranian satellites, There is no longer necessity for the hypothesis of the existence of "shepherd"-satellites in Uranian rings which have not been discovered by Voyager-2. A new - accretion instability of the protodisk is described which may háve served as a generator of the birth of a large-scale structure of Saturn’s rings, The discovery of the instability makes it possible to understand the origin of the hierarchic structure of Saturn’s rings, since the mechanisms of formation of narrow ringlets were investigated earlier.
This paper is closely related to an earlier paper of the author and W. Narkiewicz (cf. [7]) and to some papers concerning ratio sets of positive integers (cf. [4], [5], [12], [13], [14]). The paper contains some new results completing results of the mentioned papers. Among other things a characterization of the Steinhaus property of sets of positive integers is given here by using the concept of ratio sets of positive integers.