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Bibliographic description:
Kravchuk A. S.
,
Kravchuk A. I.
EFFICIENT DYNAMIC EQUATION FOR COMPOSITIONAL MEAN ISOTROPIC ELASTIC BODY // BSU bulletin. Mathematics, Informatics. - 2018. №2. . - С. 63-76.
Title:
EFFICIENT DYNAMIC EQUATION FOR COMPOSITIONAL MEAN ISOTROPIC ELASTIC BODY
Financing:
Codes:
DOI: 10.18101/2304-5728-2018-2-63-76UDK: 539
Annotation:
The article presents effective dynamic equations for mean isotropic solid in stresses and displacements. We have established that the structure of equations in both cases is completely preserved as in the homogeneous case within the accuracy of re- placement of deformations, stresses and displacements by average values in repre- sentative volume of the composite solid. At the same time, it is necessary to use the previously obtained average Kravchuk — Tarasyuk values of Young's modulus, Poisson's ratio, shear modulus as average elastic characteristics. The equations are obtained in the existence of a connection between the effective values of the elastic- ity modulus, Poisson's ratio, the shear modulus of a similar well-known coupling for the coefficients of a body from one homogeneous material. Since this connec- tion is approximate even in the homogeneous case, this has little effect on the accu- racy of the equations obtained. Effective values of the propagation velocities of various types waves in a composite in average isotropic medium are obtained. The results of these studies allow solving dynamic problems for solid composite bodies using standard finite element support, for example ANSYS. The data obtained in our research allow us to recommend using not only the average for Kravchuk — Tarasyuk elastic parameters, but also the average density of the composite solid, also calculated in Kravchuk — Tarasyuk approximation as the effective characteris- tics of solids.
Keywords:
discrete random variable; concentration of components; average values according to Kravchuk — Tarasyuk, Beltrami — Mitchell equations, Lamé equa- tions.
List of references:
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