We study the stability of elastic systems with one-sided constraints on displacements. We analytically solve the contact problem for rods and propose a new method for solving contact problems with a free boundary. We present numerical results concerning the stability of elastic systems with one-sided constraints on displacements. Bibliography: 10 titles.
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E. I. Mikhajlovskii and V. N. Tarasov, “The convergence of the method of generalized reaction in contact problems with a free boundary” [in Russian], Prikl. Mat. Mekh. 57, No. 1, 128–136 (1993); English transl.: J. Appl. Math. Mech. 57, No. 1, 147–157 (1993).
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North Holland, Amsterdam (1976).
V. F. Dem’yanov and A. M. Rubinov, Approximation Methods for Solving Extremum Problems [in Russian], Leningr. Univ. Press, Leningr. (1968).
V. N. Tarasov, Optimization Methods in the Study of Constructive-Nonlinear Problems of Mechanics of Elastic Systems [in Russian], Komi Sci. Center Ural Branch RAS, Syktyvkar (2013).
V. N. Tarasov, “On stability of elastic systems under one-sided constraints on displacements” [in Russian], Trudy IMM, Ekaterinburg 11, No. 1, 177–188 (2005).
A. S. Volmir, Stability of Defomrable Systems [in Russian], Nauka, Moscow (1967).
A. V. Pogorelov, Differential Geometry [in Russian], Nauka, Moscow (1974).
A. V. Pogorelov, Geometric Theory of Stability of Shells [in Russian], Nauka, Moscow (1966).
G. M. Fikhtengol’ts, Course of Differential and Integral Calculus. Vol. 3 [in Russian], Nauka, Moscow (1970).
V. Yu. Andryukova and V. N. Tarasov, “Stability of elastic systems with nonretaining connections” [in Russian], Izv. KOMI Nauchn. Tsentr 3, 12–19 (2013).
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Translated from Problemy Matematicheskogo Analiza 77, December 2014, pp. 163-186.
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Tarasov, V.N. Nonsmooth Boundary Value Problems in Theory of Rods, Plates, and Shells. J Math Sci 205, 308–334 (2015). https://doi.org/10.1007/s10958-015-2250-7
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DOI: https://doi.org/10.1007/s10958-015-2250-7