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

Magomed Farman Mekhtiyev; Nina Ilyinichna Fomina; Nazaket Boyukaga Mammadova

doi:doi:10.11648/j.sjams.20160406.14

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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

Magomed Farman Mekhtiyev, Nina Ilyinichna Fomina, Nazaket Boyukaga Mammadova

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6)

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), 2024. 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

References

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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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TY  - JOUR
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
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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
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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
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Author Information

Magomed Farman Mekhtiyev

Department of Applied Mathematics, Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan
Nina Ilyinichna Fomina

Faculty of Applied Mathematics and Cybernetics, Baku State University, Baku, Azerbaijan
Nazaket Boyukaga Mammadova

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

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Plain Text BibTeX RIS

APA Style

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2016
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
SP  - 269
EP  - 275
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  -

Copy | Download