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Variational Statements and Discretization of the Boundary-Value Problem of Elasticity Where Stress at the Boundary is Known

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Abstract

The equations of elastic equilibrium of bodies in displacements with the stresses specified at the surface of the body are considered. Such a problem does not have a unique solution in the whole space of vector functions where it exists. Two variational problems for the considered static problem of the theory of elasticity with a unique solution in the whole space are proposed and investigated. The mathematical apparatus of the study is one of the variants of the Korn inequality that is proved in the paper. Discretization of these variational problems by the finite-element method and convergence of discrete solutions is considered.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    N. A. Vareniuk, E. F. Galba & I. V. Sergienko

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  1. N. A. Vareniuk
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  2. E. F. Galba
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  3. I. V. Sergienko
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Correspondence to N. A. Vareniuk.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2020, pp. 46–60.

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Vareniuk, N.A., Galba, E.F. & Sergienko, I.V. Variational Statements and Discretization of the Boundary-Value Problem of Elasticity Where Stress at the Boundary is Known. Cybern Syst Anal 56, 900–912 (2020). https://doi.org/10.1007/s10559-020-00310-0

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  • DOI: https://doi.org/10.1007/s10559-020-00310-0

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