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Boundary Value Problems of the Plane Theory of Elasticity for Materials with Voids

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Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 334))

Abstract

The present paper deals with plane strain problem for linear elastic materials with voids. In the spirit of N.I. Muskhelishvili the governing system of equations of the plane strain is rewritten in the complex form and its general solution is represented by means of two analytic functions of the complex variable and a solution of the Helmholtz equation. The constructed general solution enables us to solve analytically a problem for a circle and a problem for the plane with a circular hole.

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Author information

Authors and Affiliations

  1. Sokhumi State University, 61 Politkovskaya Street, 0186, Tbilisi, Georgia

    Bakur Gulua

  2. Faculty of Exact and Natural Sciences of I. Javakhishvili Tbilisi State University, 2 University Street, 0186, Tbilisi, Georgia

    Bakur Gulua

  3. I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University, 2 University Street, 0186, Tbilisi, Georgia

    Roman Janjgava

  4. Georgian National University SEU, 9 Tsinandali Str, 0144, Tbilisi, Georgia

    Roman Janjgava

Authors
  1. Bakur Gulua
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  2. Roman Janjgava
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Correspondence to Bakur Gulua .

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Editors and Affiliations

  1. I.Vekua Institute of Applied Mathematics & Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    George Jaiani

  2. Georgian Technical University, Tbilisi, Georgia

    David Natroshvili

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Gulua, B., Janjgava, R. (2020). Boundary Value Problems of the Plane Theory of Elasticity for Materials with Voids. In: Jaiani, G., Natroshvili, D. (eds) Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol 334. Springer, Cham. https://doi.org/10.1007/978-3-030-56356-1_13

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