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Monogenic functions in commutative complex algebras of the second rank and the Lamé equilibrium system for some class of plane orthotropy

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Abstract

We consider a class of plane orthotropic deformations of the form εx = σx + a12σy, γxy = 2(p − a12)Txy, εy = a12σx + σy, where σx, Txy, σy and\( {\upvarepsilon}_x\frac{\upgamma_{xy}}{2},{\upvarepsilon}_Y \) are components of the stress tensor and the deformation tensor, respectively, real parameters p and a12 satisfy the inequalities: -1 < p < 1, -1 < a12 < p. A class of solutions of the Lamé equilibrium system for displacements is built in the form of linear combinations of components of “analytic” functions which take values in commutative and associative two-dimensional algebras with unity over the field of complex numbers.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Serhii V. Gryshchuk

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  1. Serhii V. Gryshchuk
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Correspondence to Serhii V. Gryshchuk.

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The article is dedicated to the memory of Professor Bohdan Bojarski

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 3, pp. 345–356 July–September, 2019.

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Gryshchuk, S.V. Monogenic functions in commutative complex algebras of the second rank and the Lamé equilibrium system for some class of plane orthotropy. J Math Sci 246, 30–38 (2020). https://doi.org/10.1007/s10958-020-04720-5

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  • DOI: https://doi.org/10.1007/s10958-020-04720-5

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