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IssuesArchive of Issues2008-2pp.218-224

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V. V. Korepanov, V. P. Matveenko, and I. N. Shardakov, "Numerical study of two-dimensional problems of nonsymmetric elasticity," Mech. Solids. 43 (2), 218-224 (2008)
Year 2008 Volume 43 Number 2 Pages 218-224
DOI 10.3103/S0025654408020064
Title Numerical study of two-dimensional problems of nonsymmetric elasticity
Author(s) V. V. Korepanov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, kvv@icmm.ru)
V. P. Matveenko (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, mvp@icmm.ru)
I. N. Shardakov (Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Ul. Akad. Koroleva 1, Perm, 614013, Russia, shardakov@icmm.ru)
Abstract We consider the algorithm of the finite element method for solving two-dimensional problems of nonsymmetric elasticity. We discuss the possibilities of the algorithm and its efficiency by comparing the numerical results with the well-known analytic solutions. We present the results obtained by solving the problem of tension of a plate weakened by a series of holes and the problem of tension for a plate with a central crack. The numerical results thus obtained are considered as an addition to the analytic solutions in the context of experimental justification of couple-stress effects arising under deformation of elastic materials and in the context of solving the identification problem for mechanical constants in nonsymmetric elasticity.
References
1.  W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1975).
2.  V. A. Pal'mov, "Fundamental Equations of the Theory of Asymmetric Elasticity," "Fundamental Equations of the Theory of Nonsymmetric Elasticity," Prikl. Mat. Mekh. 28 (3), 401-408 (1964) [J. Appl. Math. Mech. (Engl. Transl.) 28 (3), 496-505 (1964)].
3.  A. C. Eringen, Micropolar Field Theories, Vol. II: Failure, Ed. by G. Liboviz (Mir, Moscow, 1975), pp. 647-751 [in Russian].
4.  R. D. Gauthier and W. E. Jahsman, "A Quest for Micropolar Elastic Constants," Trans. ASME Ser. E. J. Appl. Mech. 42 (2), 369-374 (1975).
5.  R. S. Lakes, "Experimental Methods for Study of Cosserat Elastic Solids and Other Generalized Continua," in Continuum Models for Materials with Micro-Structure, Ed. by H. Muhlhaus (Wiley, New York, 1995), pp. 1-22.
6.  R. D. Mindlin, "Influence of Couple-Stress on Stress Concentrations, Experim. Mech. 3 (1), 1-7 (1963).
7.  V. A. Pal'mov, "The Plane Problem in the Theory of Nonsymmetrical Elasticity," Prikl. Mat. Mekh. 28 (6), 1117-1120 (1964) [J. Appl. Math. Mech. (Engl. Transl.) 28 (6), 1341-1345 (1964)].
8.  M. Onami, S. Ivasimidzu, K. Genka, et al., Introduction to Micromechanics (Metallurgiya, Moscow, 1987) [in Russian].
9.  W. T. Koiter, "Couple-Stress in the Theory of Elasticity," Proc. Könicl. Acad. Wet. B67 (17), 89-112 (1964).
10.  E. Kröner, "On the Physical Reality of Torque Stresses in Continuum Mechanics," Intern. J. Eng. Sci. 1 (2), 261-278 (1963).
11.  M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, "Construction of Analytical Solutions of Some Two-Dimensional Problems in the Moment Theory of Elasticity," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 69-82 (2002) [Mech. Solids (Engl. Transl.) 37 (5), 56-67 (2002)].
12.  M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, "Parametric Analysis of Analytical Solution to One- and Two-Dimensional Problems in Couple-Stress Theory of Elasticity," ZAMM 83 (4), 238-248 (2003).
13.  S. Nakamura, R. L. Benedict, and R. S. Lakes, "Finite Element Method for Orthotropic Micropolar Elasticity," Intern. J. Eng. Sci 22 (3), 319-330 (1984).
14.  S. Nakamura and R. S. Lakes, "Finite Element Analysis of Stress Concentration around a Blunt Crack in a Cosserat Elastic Solid," Comput. Methods in Appl. Mech. and Eng. 66 (3), 257-266 (1988).
15.  O. C. Zienkiewicz, Finite Element Method in Engineering Science (McGraw-Hill Education, London, 1971; Mir, Moscow, 1975).
Received 28 August 2005
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