International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies

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:: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies

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ISSN 2228-9860
eISSN 1906-9642
CODEN: ITJEA8


FEATURE PEER-REVIEWED ARTICLE

Vol.12(3) (2021)

  • The Solution of the First Main Problem of the Theory of Elasticity for a Transtropic Body of Revolution

    D.A. Ivanychev (Department of General Mechanics, Lipetsk State Technical University, Lipetsk, RUSSIA),
    E.Yu. Levina (Department of Physics, Bauman Moscow State Technical University, Moscow, RUSSIA),
    E.A. Novikov, M.V. Polikarpov (Department of General Mechanics, Lipetsk State Technical University, Lipetsk, RUSSIA).

    Disciplinary: Engineering Mechanics.

    ➤ FullText

    doi: 10.14456/ITJEMAST.2021.54

    Keywords: Boundary state method; Transverse isotropy; Spatial problems; Axisymmetric problems; Isomorphism of state spaces; Elasticity for anisotropic bodies.

    Abstract
    Based on the method of boundary states, this work investigates the elastic equilibrium of transversely isotropic bodies of revolution under the action of forces applied to the surface of a body. A new method is proposed for the formation of bases of internal and boundary states based on a general solution of plane deformation and formulas for the transition to a spatial axisymmetric state. Isomorphism of state spaces is proved. Isomorphism of spaces allows the search for an internal state to be reduced to the study of boundary states. In the case of the first and second main problems of the theory of elasticity, the problem is reduced to expanding the sought state in a series in terms of the orthonormal elements and finding the Fourier coefficients of this linear combination. Fourier coefficients are quadratures. The first main problem of the theory of elasticity for a transversely isotropic hemisphere with boundary conditions imitating inhomogeneous tension is solved. Verification of the solution is presented and accuracy is assessed. The results are presented graphically.

    Paper ID: 12A3L

    Cite this article:

    Ivanychev, D. A., Levina, E.Yu., Novikov, E.A., Polikarpov, M.V. (2021). The Solution of the First Main Problem of the Theory of Elasticity for a Transtropic Body of Revolution. International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies, 12(3), 12A3L, 1-9. http://doi.org/10.14456/ITJEMAST.2021.54



References

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  2. Ivanychev, D. A. (2019). The method of boundary states in the solution of the second fundamental problem of the theory of anisotropic elasticity with mass forces. Tomsk State University Journal of Mathematics and Mechanics, No. 61, pp. 45-60. DOI 10.17223/19988621/61/5.
  3. Ivanychev, D. A. (2019). The contact problem Solution of the elasticity theory for anisotropic rotation bodies with mass forces. PNRPU Mechanics Bulletin, No. 2, pp. 49-62. DOI: 10.15593/perm.mech/2019.2.05.
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Other issues:
Vol.12(2)(2021)
Vol.12(1)(2021)
Vol.11(16)(2020)
Vol.11(15)(2020)
Vol.11(14)(2020)
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