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Antiplane Shear Deformation of Elastic Cylinders in Contact with a Rigid Foundation

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Variational and Monotonicity Methods in Nonsmooth Analysis

Part of the book series: Frontiers in Mathematics ((FM))

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Abstract

We analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation, for static processes, under the small deformations hypothesis. Using the KKM lemma due to Fan (see Corollary D.1), we prove that the model has at least one weak solution. Moreover, we present several examples of constitutive laws and friction laws for which our theoretical results are valid.

Finally, we comment on the conditions which guarantee the uniqueness of solution.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University Politehnica of Bucharest, Bucharest, Romania

    Nicuşor Costea

  2. Department of Economics, Babeș-Bolyai University, Cluj-Napoca, Hungary

    Alexandru Kristály

  3. Institute of Applied Mathematics, Óbuda University, Budapest, Hungary

    Alexandru Kristály

  4. Department of Mathematics, Babeș-Bolyai University, Cluj-Napoca, Romania

    Csaba Varga

Authors
  1. Nicuşor Costea
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  2. Alexandru Kristály
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  3. Csaba Varga
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Costea, N., Kristály, A., Varga, C. (2021). Antiplane Shear Deformation of Elastic Cylinders in Contact with a Rigid Foundation. In: Variational and Monotonicity Methods in Nonsmooth Analysis. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-81671-1_11

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