On the refined stress analysis in the applied elasticity problems accounting of gradient effects
- Authors: Lomakin E.V.1,2, Lurie S.A.2,3, Rabinskiy L.N.2, Solyaev Y.O.1,2
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Affiliations:
- Lomonosov Moscow State University
- Moscow Aviation Institute
- Institute of Applied Mechanics of Russian Academy of Sciences
- Issue: Vol 489, No 6 (2019)
- Pages: 585-591
- Section: Mechanics
- URL: https://journals.eco-vector.com/0869-5652/article/view/18861
- DOI: https://doi.org/10.31857/S0869-56524896585-591
- ID: 18861
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Abstract
The paper proposes an extension of the approaches of gradient elasticity of deformable media, which consists in using the fundamental property of solutions of the gradient theory - the smoothing of singular solutions of the classical theory of elasticity, converting them into a regular class not only for the problems of micromechanics, where the length scale parameter is of the order of the material‘s characteristic size, but for “macromechanical” problems. In these problems, the length scale parameter, as a rule, can be found from the macro-experiments or numerical experiments and does note have an extremely small values. It is shown, by attracting numerical three-dimensional modeling, that even one-dimensional gradient solutions make it possible to clarify the stress distribution in the constrained zones of the body and in the area of the loads application. It is shown that additional length scale parameters of the gradient theory are related with specific boundary effects and can be associated with structural geometric parameters and loading conditions that determine the features of the classical three-dimensional solution.
About the authors
E. V. Lomakin
Lomonosov Moscow State University; Moscow Aviation Institute
Author for correspondence.
Email: lomakin@mech.math.msu.su
Corresponding Member of the Russian Academy of Sciences
Russian Federation, 1, Leninskie gory, Moscow, 119991; 4, Volokolamskoe shosse, Moscow,125993S. A. Lurie
Moscow Aviation Institute; Institute of Applied Mechanics of Russian Academy of Sciences
Email: lomakin@mech.math.msu.su
Russian Federation, 4, Volokolamskoe shosse, Moscow,125993; 7, ave., Leningradsky, Russia, Moscow 125040
L. N. Rabinskiy
Moscow Aviation Institute
Email: lomakin@mech.math.msu.su
Russian Federation, 4, Volokolamskoe shosse, Moscow,125993
Y. O. Solyaev
Lomonosov Moscow State University; Moscow Aviation Institute
Email: lomakin@mech.math.msu.su
Russian Federation, 1, Leninskie gory, Moscow, 119991; 4, Volokolamskoe shosse, Moscow,125993
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