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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2001, Volume 42, Issue 4, Pages 145–154 (Mi pmtf2805)  
This article is cited in 6 scientific papers (total in 6 papers)

Exact analytical solution of the Kirsch problem within the framework of the cosserat continuum and pseudocontinuum

M. A. Kulesh, V. P. Matveenko, I. N. Shardakov

Institute of Mechanics of Continuous Media, Ural Division, Russian Academy of Sciences, Perm', 614013
Full-text PDF (247 kB) Citations (6)
Abstract: The Kirsch problem of one-sided tension of a plate with a circular hole is considered within the framework of the nonsymmetric theory of elasticity under the assumption that material deformation is described not only by the displacement vector but also by the rotation vector. The general analytical solution of this problem is expressed in terms of the Bessel functions. The resulting solution is compared with the corresponding solutions for a symmetric medium and Cosserat pseudomedium. A macroparameter characterizing the distortion of the boundary of the circular hole upon deformation is introduced.
Received: 26.12.2000
English version:
Journal of Applied Mechanics and Technical Physics, 2001, Volume 42, Issue 4, Pages 687–695
DOI: https://doi.org/10.1023/A:1019216117018
Bibliographic databases:
Document Type: Article
UDC: 539.3.01
Language: Russian
Citation: M. A. Kulesh, V. P. Matveenko, I. N. Shardakov, “Exact analytical solution of the Kirsch problem within the framework of the cosserat continuum and pseudocontinuum”, Prikl. Mekh. Tekh. Fiz., 42:4 (2001), 145–154; J. Appl. Mech. Tech. Phys., 42:4 (2001), 687–695
Citation in format AMSBIB
\Bibitem{KulMatSha01}
\by M.~A.~Kulesh, V.~P.~Matveenko, I.~N.~Shardakov
\paper Exact analytical solution of the Kirsch problem within the framework of the cosserat continuum and pseudocontinuum
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2001
\vol 42
\issue 4
\pages 145--154
\mathnet{http://mi.mathnet.ru/pmtf2805}
\elib{https://elibrary.ru/item.asp?id=17266369}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2001
\vol 42
\issue 4
\pages 687--695
\crossref{https://doi.org/10.1023/A:1019216117018}
Linking options:
  • https://www.mathnet.ru/eng/pmtf2805
  • https://www.mathnet.ru/eng/pmtf/v42/i4/p145
    • This publication is cited in the following 6 articles:
    1. S. V. Lavrikov, “Development of Mathematical Modeling Methods and Solution of Present-Day Problems in Geomechanics at the Institute of Mining SB RAS”, J Min Sci, 60:4 (2024), 533  crossref
    2. Hassam Khan, Ionel-Dumitrel Ghiba, Angela Madeo, Patrizio Neff, “Existence and uniqueness of Rayleigh waves in isotropic elastic Cosserat materials and algorithmic aspects”, Wave Motion, 110 (2022), 102898  crossref
    3. M. E. Frolov, “Reliable a Posteriori Error Estimation for Cosserat Elasticity in 3D”, Lobachevskii J Math, 42:1 (2021), 96  crossref
    4. Stephen Tyznik, Jacob Notbohm, “Length scale dependent elasticity in random three-dimensional fiber networks”, Mechanics of Materials, 138 (2019), 103155  crossref
    5. V.V. Korepanov, M.A. Kulesh, V.P. Matveenko, I.N. Shardakov, “Analytical and numerical solutions for static and dynamic problems of the asymmetric theory of elasticity”, Physical Mesomechanics, 10:5-6 (2007), 281  crossref
    6. M.A. Kulesh, V.P. Matveenko, I.N. Shardakov, “Parametric analysis of analytical solutions to one‐ and two‐dimensional problems in couple‐stress theory of elasticity”, Z Angew Math Mech, 83:4 (2003), 238  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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