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The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface

Received: 23 September 2016     Accepted: 7 October 2016     Published: 3 November 2016
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Abstract

The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the essential characteristics of the stress-strain state of an anisotropic shell in comparison with isotropic shells. Homogeneous solutions were built here.

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6)
DOI 10.11648/j.sjams.20160406.14
Page(s) 269-275
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Theory of Elasticity, Transversely Isotropic Hollow Cylinder, Side Surface, Mixed Boundary Conditions, Stress-Strain State, Eigenvalues, Transcendental Equation, Anisotropic Shell

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    Magomed Farman Mekhtiyev, Nina Ilyinichna Fomina, Nazaket Boyukaga Mammadova. (2016). The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface. Science Journal of Applied Mathematics and Statistics, 4(6), 269-275. https://doi.org/10.11648/j.sjams.20160406.14

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    ACS Style

    Magomed Farman Mekhtiyev; Nina Ilyinichna Fomina; Nazaket Boyukaga Mammadova. The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface. Sci. J. Appl. Math. Stat. 2016, 4(6), 269-275. doi: 10.11648/j.sjams.20160406.14

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    AMA Style

    Magomed Farman Mekhtiyev, Nina Ilyinichna Fomina, Nazaket Boyukaga Mammadova. The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface. Sci J Appl Math Stat. 2016;4(6):269-275. doi: 10.11648/j.sjams.20160406.14

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  • @article{10.11648/j.sjams.20160406.14,
      author = {Magomed Farman Mekhtiyev and Nina Ilyinichna Fomina and Nazaket Boyukaga Mammadova},
      title = {The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {6},
      pages = {269-275},
      doi = {10.11648/j.sjams.20160406.14},
      url = {https://doi.org/10.11648/j.sjams.20160406.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160406.14},
      abstract = {The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the essential characteristics of the stress-strain state of an anisotropic shell in comparison with isotropic shells. Homogeneous solutions were built here.},
     year = {2016}
    }
    

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    T1  - The Asymptotic Analysis of the Solution of an Elasticity Theory Problem for a Transversely Isotropic Hollow Cylinder with Mixed Boundary Conditions on the Side Surface
    AU  - Magomed Farman Mekhtiyev
    AU  - Nina Ilyinichna Fomina
    AU  - Nazaket Boyukaga Mammadova
    Y1  - 2016/11/03
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    N1  - https://doi.org/10.11648/j.sjams.20160406.14
    DO  - 10.11648/j.sjams.20160406.14
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
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    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20160406.14
    AB  - The problem of elasticity theory for the transversely isotropic hollow cylinder with mixed conditions on the side surface is considered in the paper. Transcendental equations are obtained regarding the eigenvalues of the problem. The roots of the characteristic equations are studied thoroughly. The study of the eigenvalues allowed to establish the essential characteristics of the stress-strain state of an anisotropic shell in comparison with isotropic shells. Homogeneous solutions were built here.
    VL  - 4
    IS  - 6
    ER  - 

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Author Information
  • Department of Applied Mathematics, Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

  • Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku, Azerbaijan

  • Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku, Azerbaijan

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