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IssuesArchive of Issues2009-5pp.776-780

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S.E. Omarov, "Determining the Material Constant in the Equilibrium Problem for an Infinite Elastic Plane Weakened by a Circular Hole," Mech. Solids. 44 (5), 776-780 (2009)
Year 2009 Volume 44 Number 5 Pages 776-780
DOI 10.3103/S002565440905015X
Title Determining the Material Constant in the Equilibrium Problem for an Infinite Elastic Plane Weakened by a Circular Hole
Author(s) S.E. Omarov (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia)
Abstract The averaging method is used to determine the material functions of the linear Cosserat theory of elasticity. The proposed method is used to find the material constant in the equilibrium problem for an infinite plane weakened by a circular hole.
Keywords Cosserat elasticity, material function, averaging, composite
References
1.  W. Voigt, "Theoretische Studient über die Elasticitats Verhältnisse der Kristalle," Abhandl. Ges. Wiss. Gottingen 3, 100 (1887).
2.  E. F. Cosserat and F. F. Cosserat, Theorie des Corps Deformbles (Hermann, Paris, 1909).
3.  W. Weitzman, "Influence of the Couple Stress on the Stress Concentration near a Circular Inclusion in a Uniaxial Torsion Field," Trudy Amer. Obshch. Inzhen.-Mekh. Prikl. Mekh. 32 (2), 193-197 (1965).
4.  R. D. Mindlin, "Influence of Couple Stresses on Stress Concentration," Exp. Mech. 3, 1-7 (1963) [Mekhanika. Period. Sb. Perev. Inostr. Statey (Russ. Transl.), No. 4, 115-128 (1964].
5.  Yu. N. Nemish, "Plane Problem of the Couple Stress Theory of Elasticity for a Domain with a Circular Hole," Prikl. Mekh. 1 (5), 52-59 (1965).
6.  E. L. Aero and E. V. Kuvshinskii, "Fundamental Equations of the Theory of Elastic Media With Rotationally Interacting Particles," Fiz. Tverd. Tela 2 (7), 1399-1409 (1960) [Sov. Phys. Solid State (Engl. Transl.) 2, 1272-1281 (1961)].
7.  E. V. Kuvshinskii and E. L. Aero, "Continuum Theory of Asymmetric Elasticity - the Problem of Internal Rotation," Fiz. Tverd. Tela 5 (9), 2591-2598 (1963) [Sov. Phys. Solid State (Engl. Transl.) 5, 1892-1897 (1964)].
8.  V. A. Pal'mov, "Fundamental Equations of the Theory of Asymmetric Elasticity," Prikl. Mat. Mekh. 28 (3), 401-408 (1964) [J. Appl. Math. Mech. (Engl. Transl.) 28 (3), 496-505 (1964)].
9.  W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1975).
10.  G. N. Savin, Foundations of the Plane Problem of the Couple Stress Theory of Elasticity (Izd-vo Kiev. Univ., Kiev, 1965) [in Russian].
11.  O. Hoffman, "On Bending of Thin Elastic Plates in the Presence of Couple Stress," Trudy Amer. Obshch. Inzhen.-Mekh. Prikl. Mekh. 31 (4), 149-150 (1964).
12.  H. Schaefer, "Versuch einer Elastisitätstheorie des Zweidimensionalen ebenen Cosserat-Kontinuums," in Miszellaneen Angewandten Mechanik (Akademie-Verlag, Berlin, 1962), pp. 277-292 [in German].
13.  B. E. Pobedrya and S. E. Omarov, "Constitutive Relations of Couple Stress Theory of Elasticity," Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 3, 56-58 (2007) [Moscow Univ. Math. Bull. (Engl. Transl.)].
14.  B. E. Pobedrya, Mechanics of Composite Materials (Izd-vo MGU, Moscow, 1984) [in Russian].
15.  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)].
16.  S. P. Timoshenko and J. N. Goodyear, Theory of Elasticity (McGraw-Hill, New York, 1951; Nauka, Moscow, 1975).
Received 18 October 2007
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