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Nonsmooth Boundary Value Problems in Theory of Rods, Plates, and Shells

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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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References

  1. 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).

    Article  MathSciNet  Google Scholar 

  2. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North Holland, Amsterdam (1976).

    MATH  Google Scholar 

  3. V. F. Dem’yanov and A. M. Rubinov, Approximation Methods for Solving Extremum Problems [in Russian], Leningr. Univ. Press, Leningr. (1968).

    Google Scholar 

  4. 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).

  5. 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).

    Google Scholar 

  6. A. S. Volmir, Stability of Defomrable Systems [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  7. A. V. Pogorelov, Differential Geometry [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  8. A. V. Pogorelov, Geometric Theory of Stability of Shells [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  9. G. M. Fikhtengol’ts, Course of Differential and Integral Calculus. Vol. 3 [in Russian], Nauka, Moscow (1970).

  10. V. Yu. Andryukova and V. N. Tarasov, “Stability of elastic systems with nonretaining connections” [in Russian], Izv. KOMI Nauchn. Tsentr 3, 12–19 (2013).

    Google Scholar 

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Correspondence to V. N. Tarasov.

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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

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