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Antiplane strain of a body undergoing large-rotations

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Antiplane strain of a cylindrical elastic body undergoing large rotations under surface load in the absence of body loads is studied. The form of the elastic potential corresponding to this strain is found. The stresses, the strains, and the displacement are expressed in terms of pressure and two independent strains and the pressure is expressed in terms of the linear strain invariant. For the strains and displacement, nonlinear boundary-value problems are formulated and their ellipticity conditions are given. The linear problem for the displacement is obtained by transformation of variables. An example of determining the displacement is considered.

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References

  1. V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad (1958).

    Google Scholar 

  2. J. N. Sneddon and D. S. Berry, The Classical Theory of Elasticity, Springer-Verlag, Berlin (1958).

    Google Scholar 

  3. A. I. Lur’e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  4. Yu. N. Rabotnov, Mechanics of Deformable Solids [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  5. V. D. Bondar’, “Modeling of Nonlinear Antiplane Strain of a Cylindrical Body,” J. Appl. Mech. Tech. Phys., 46, No. 4, 539–548 (2005).

    Article  Google Scholar 

  6. N. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  7. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw–Hill Company, New York (1968).

  8. A. D. Polyanin, Nonlinear Equations of Mathematical Physics: Handbook [in Russian], Fizmatgiz, Moscow (2002).

    Google Scholar 

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, 630090

    V. D. Bondar’

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  1. V. D. Bondar’
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 191–198, May–June, 2007.

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Bondar’, V.D. Antiplane strain of a body undergoing large-rotations. J Appl Mech Tech Phys 48, 460–466 (2007). https://doi.org/10.1007/s10808-007-0057-0

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  • DOI: https://doi.org/10.1007/s10808-007-0057-0

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