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Determining elastic and plastic deformation regions in a problem of unixaxial tension of a plate weakened by holes. (English. Russian original) Zbl 1459.74025

J. Appl. Mech. Tech. Phys. 62, No. 1, 157-163 (2021); translation from Prikl. Mekh. Tekh. Fiz. 62, No. 1, 179-186 (2021).
Summary: This paper describes a solution to the problem of determining the elastic and plastic deformation regions arising in a plate that is under tension and weakened by two circular holes in the case of a plane stress state. A method for solving the problem is based on the use of conservation laws.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74K20 Plates
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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References:

[1] B. D. Annin and G. P. Cherepanov, Elastoplastic Problem (Nauka, Novosibirsk, 1983) [in Russian].
[2] N. P. Ostrosablin, “Plastic Zone Around a Round Hole in a Plane with a Nonuniform Basic Stressed State,” Prikl. Mekh. Tekh. Fiz.31 (5), 124-131 (1990) [J. Appl. Mech. Tech. Phys.31 (5), 783-792 (1990)].
[3] V. M. Mirsalimov, “Elastoplastic Tension Problem for a Plate with a Circular Hole with Account for Crack Nucleation in an Elastic Deformation Region,” Prikl. Mekh. Tekh. Fiz. 61 (4), 162-173 (2020) [J. Appl. Mech. Tech. Phys. 61 (4), 641-651 (2020)]. · Zbl 1451.74151
[4] B. D. Annin, “Elastoplastic Stress Distribution in a Plane with a Hole,” Dokl. Akad. Nauk SSSR 184 (2), 315-317 (1969).
[5] N. I. Ostrosablin, Plane Elastic-Plastic Stress Distribution Around Circular Holes (Nauka, Novosibirsk, 1984) [in Russian].
[6] Symmetries and the Conservation Laws of Equations of Mathematical Physics, Ed. by A. M. Vinogradov and I. S. Krasil’shchik (Faktorial Press, Moscow, 2005) [in Russian].
[7] P. P. Kiryakov, S. I. Senashov, and A. N. Yakhno, Using Symmetries and Conservation Laws to Solve Differential Equations (Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2001) [in Russian].
[8] S. I. Senashov, O. V. Gomonova, and A. N. Yakhno,Mathematical Questions of Two-Dimensional Equations of Perfect Plasticity (Reshetnev Siberian State Univ. of Sci. and Technol., Krasnoyarsk, 2012) [in Russian].
[9] S. I. Senashov, O. N. Cherepanova, and A. V. Kondrin, “On Elastoplastic Torsion of a Rod with Multiply Connected Cross-Section,” J. Sib. Federal Univ. Math. Phys. 7(1), 343-351 (2015). · Zbl 07325235
[10] S. I. Senashov and O. V. Gomonova, “Construction of Elastoplastic Boundary in Problem of Tension of a Plate Weakened by Holes,” Int. J. Nonlinear Mech. 108, 7-10 (2019).
[11] L. V. Ovsiannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978; Academic Press, 1982). · Zbl 0485.58002
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