BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, 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:
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:
Kravchuk A. S., Chigarev A. V. Mekhanika kontaktnogo vzaimodeistviya tel s krugovymi granitsami [Mechanics of Contact Interaction of Bodies with Circular Boundaries]. Minsk: Tekhnoprint Publ., 2000. 196 p.
Zhemochkin B. N. Teoriya uprugosti [Theory of Elasticity]. Moscow: Goss- troiizdat Publ., 1957. 256 p.
Kravchuk A. S., Kravchuk A. I., Tarasyuk I. A. Metodika vychisleniya effektiv- nykh koeffitsientov v uravnenii teploprovodnosti kompozitsionnogo tela [A Technique for Calculating Effective Coefficients in the Equation of Composite Body Thermal Conductivity]. Vestnik SpbGU — Bulletin of St Petersburg State University. 2016. Ser. 4. V. 2 (60). Iss. 4. Pp. 335–341.
Kravchuk A. S., Kravchuk A. I., Popova T. S. Uravnenie diffuzii kompozitsion- noi smesi v kompozitsionnuyu sredu [Equation of Diffusion of a Composite Mixture into a Composite Medium]. Inzhenerno-fizicheskii zhurnal — Engineering and Physics Journal. 2016. V. 89. No. 4. Pp. 1041–1046.
Tarasyuk I. A., Kravchuk A. S. Suzhenie «vilki» v teorii uprugikh strukturno neodnorodnykh v srednem izotropnykh kompozitsionnykh tel bez primeneniya variat- sionnykh printsipov [Restriction of Voigt–Reuss "Bracketing" in the Theory of Elastic Structurally Inhomogeneous Mean Isotropic Composite Bodies without the Use of Variational Principles]. APRIORI. Ser. Natural and Technical Sciences. 2014. No. 3. Available at: http://apriori-journal.ru/seria2/3-2014/tarasyuk-kravchuk.pdf (accessed 05.04.2018).
Tarasyuk I. A., Kravchuk A. S. Vychislenie effektivnykh parametrov uprugosti v srednem izotropnykh kompozitsionnykh tel v sluchae zapisi zakona Guka dlya ten- zora deformatsii po Koshi [Calculation of Effective Elasticity Parameters of Mean Iso- tropic Composite Bodies in the Case of Recording the Hooke Law for the Cauchy Strain Tensor]. APRIORI. Ser. Natural and Technical Sciences. 2015. No. 3. Available at: http://apriori-journal.ru/seria2/3-2015/tarasyuk-kravchuk.pdf (accessed 05.04.2018).
Amenzade Yu. A. Teoriya uprugosti [Theory of Elasticity]. Moscow: Vysshaya shkola Publ., 1976. 272 p.
Sapunov V. T. Prikladnaya teoriya uprugosti [Applied Theory of Elasticity]. Moscow: Moscow Engineering Physics Institute Publ., 2008. Part 1. 232 p.
Kol'skii G. Volny napryazheniya v tverdykh telakh [Waves of Stress in Solids]. Moscow: Izdatel’stvo inostrannoi literatury Publ., 1955. 194 p.
Zhemochkin B. N. Teoriya uprugosti [Theory of Elasticity]. Moscow: Goss- troiizdat Publ., 1957. 256 p.
Kravchuk A. S., Kravchuk A. I., Tarasyuk I. A. Metodika vychisleniya effektiv- nykh koeffitsientov v uravnenii teploprovodnosti kompozitsionnogo tela [A Technique for Calculating Effective Coefficients in the Equation of Composite Body Thermal Conductivity]. Vestnik SpbGU — Bulletin of St Petersburg State University. 2016. Ser. 4. V. 2 (60). Iss. 4. Pp. 335–341.
Kravchuk A. S., Kravchuk A. I., Popova T. S. Uravnenie diffuzii kompozitsion- noi smesi v kompozitsionnuyu sredu [Equation of Diffusion of a Composite Mixture into a Composite Medium]. Inzhenerno-fizicheskii zhurnal — Engineering and Physics Journal. 2016. V. 89. No. 4. Pp. 1041–1046.
Tarasyuk I. A., Kravchuk A. S. Suzhenie «vilki» v teorii uprugikh strukturno neodnorodnykh v srednem izotropnykh kompozitsionnykh tel bez primeneniya variat- sionnykh printsipov [Restriction of Voigt–Reuss "Bracketing" in the Theory of Elastic Structurally Inhomogeneous Mean Isotropic Composite Bodies without the Use of Variational Principles]. APRIORI. Ser. Natural and Technical Sciences. 2014. No. 3. Available at: http://apriori-journal.ru/seria2/3-2014/tarasyuk-kravchuk.pdf (accessed 05.04.2018).
Tarasyuk I. A., Kravchuk A. S. Vychislenie effektivnykh parametrov uprugosti v srednem izotropnykh kompozitsionnykh tel v sluchae zapisi zakona Guka dlya ten- zora deformatsii po Koshi [Calculation of Effective Elasticity Parameters of Mean Iso- tropic Composite Bodies in the Case of Recording the Hooke Law for the Cauchy Strain Tensor]. APRIORI. Ser. Natural and Technical Sciences. 2015. No. 3. Available at: http://apriori-journal.ru/seria2/3-2015/tarasyuk-kravchuk.pdf (accessed 05.04.2018).
Amenzade Yu. A. Teoriya uprugosti [Theory of Elasticity]. Moscow: Vysshaya shkola Publ., 1976. 272 p.
Sapunov V. T. Prikladnaya teoriya uprugosti [Applied Theory of Elasticity]. Moscow: Moscow Engineering Physics Institute Publ., 2008. Part 1. 232 p.
Kol'skii G. Volny napryazheniya v tverdykh telakh [Waves of Stress in Solids]. Moscow: Izdatel’stvo inostrannoi literatury Publ., 1955. 194 p.
Article.pdf