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On Hierarchical Models of Elastic Shallow Shells with Voids

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

In the report the three-dimensional system of equations of equilibrium for solids with voids is considered. From this system of equations, using a reduction method of I. Vekua, we receive the equilibrium equations for the shallow shells. Further we consider the case of plates with constant thickness in more detail. Namely, the systems of equations corresponding to approximations N = 0 is written down in a complex form and we express the general solutions of these systems through analytic functions of complex variable and solutions of the Helmholtz equation. The received general representations give the opportunity to solve analytically boundary value problems.

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Acknowledgements

This work is supported by the Ministry of Education and Culture of the Autonomous Republic of Abkhazia.

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Authors and Affiliations

  1. Sokhumi State University, Tbilisi, Georgia

    Bakur Gulua

  2. I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Bakur Gulua

Authors
  1. Bakur Gulua
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Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Gulua, B. (2022). On Hierarchical Models of Elastic Shallow Shells with Voids. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_5

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