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Doklady Physics

, Volume 63, Issue 4, pp 161–164 | Cite as

Semi-Inverse Solution of a Pure Beam Bending Problem in Gradient Elasticity Theory: The Absence of Scale Effects

  • E. V. Lomakin
  • S. A. Lurie
  • L. N. Rabinskiy
  • Y. O. Solyaev
Mechanics
  • 17 Downloads

Abstract

The semi-inverse solutions of pure beam bending problems within the three-dimensional formulation of gradient elasticity theory as exact tests for the problem of estimating the efficient bending stiffness of so-called scale-dependent thin beams and plates due to the necessity of modeling sensing devices are presented. It is shown that the solutions within the gradient elasticity theory give classic beam bending stiffnesses and demonstrate the invalidity of the widespread results and estimates obtained in the past 15 years during study of scale effects within the gradient beam theories, according to which the relative bending stiffness grows by a hyperbolic law with decreasing thickness.

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References

  1. 1.
    R. D. Mindlin, Arch. Ration. Mech. Anal. 16 (1), 51 (1964).CrossRefGoogle Scholar
  2. 2.
    E. C. Aifantis, Int. J. Eng. Sci. 30 (10), 1279 (1992).CrossRefGoogle Scholar
  3. 3.
    D. C. C. Lam, F. Yang, A. C. M. Chonga, J. Wang, and P. Tong, J. Mech. Phys. Solids 51 (8), 1477 (2003).ADSCrossRefGoogle Scholar
  4. 4.
    A. A. Gusev and S. A. Lurie, Math. Mech. Solids 22 (4), 683 (2017).MathSciNetCrossRefGoogle Scholar
  5. 5.
    X. F. Li, B. L. Wang, and K. Y. Lee, J. Appl. Phys. 105 (7), 074306 (2009).ADSCrossRefGoogle Scholar
  6. 6.
    S. K. Park and X.-L. Gao, J. Micromech. Microeng. 16 (11), 2355 (2006).ADSCrossRefGoogle Scholar
  7. 7.
    X. Liang, S. Hu, and S. Shen, Compos. Struct. 111, 317 (2014).CrossRefGoogle Scholar
  8. 8.
    X.-L. Gao and S. K. Park, Int. J. Solids Struct. 44 (22), 7486 (2007).CrossRefGoogle Scholar
  9. 9.
    S. A. Lurie, E. L. Kuznetsova, L. N. Rabinskiy, and E. I. Popova, Mech. Solids 50 (2), 135 (2015).ADSCrossRefGoogle Scholar
  10. 10.
    S. A. Lurie, D. B. Volkov-Bogorodskiy, P. A. Belov, and E. D. Lykosova, Int. J. Nanomech. Sci. Technol. 7 (4), 261 (2016).CrossRefGoogle Scholar
  11. 11.
    S. Lurie, Yu. Solyaev, A. Volkov, and D. Volkov-Bogorodskiy, Math. Mech. Solids. https://doi.org/10.1177/1081286517691570
  12. 12.
    S. C. Cowin and J. W. Nunziato, J. Elasticity 13 (2), 125 (1983).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • E. V. Lomakin
    • 1
    • 3
  • S. A. Lurie
    • 2
    • 3
  • L. N. Rabinskiy
    • 3
  • Y. O. Solyaev
    • 2
    • 3
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Institute of Applied MechanicsRussian Academy of SciencesMoscowRussia
  3. 3.Moscow Aviation Institute (National Research University)MoscowRussia

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