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Modeling of multilayer thin bodies

  • Mikhail NikabadzeEmail author
  • Armine Ulukhanyan
Original Article
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Abstract

In this work, we considered the new parametrization of a multilayer thin domain. In particular, in contrast to classic approaches, we used several base surfaces and an analytic method with the application of orthogonal polynomial systems. We gave the vector parametric equation of each layer and the system of vector parametric equations of a multilayer thin domain and introduced the geometric characteristics for the proposed parametrization. We also derived the expressions for the transfer components of the second-rank identity tensor and the relations connecting the various families of bases and presented some differential operators, the system of equations of motion, the heat flow equation, the constitutive relations of the theory of the micropolar elasticity, and the Fourier heat conduction law under this parametrization of the thin-body domain. Finally, we gave the classification and statements of boundary value problems in the theory of thin bodies.

Keywords

New parametrization Multilayer thin body Legendre polynomials Micropolar theory 

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Notes

Acknowledgements

This work was supported by the Shota Rustaveli National Science Foundation (Project No. DI-2016-41) and the Russian Foundation for Basic Research (Project No. 18–29–10085–mk).

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Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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