The method of developing the complex stress tensor by basic states for the construction solutions of spatial boundary problems of the linear elasticity theory

• Autorzy: Pabyrivskyi, Viktor , Pukach, Petro , Pabyrivskyi, Volodymyr
• Języki publikacji: EN

Abstrakty

EN

The apparatus of holomorphic functions of many complex variables is applied to solving spatial boundary value problems of the linear theory of elasticity. The construction of the solution of the boundary value problem is based on the representation of the displacement vector in the form of J. Dougall through spatial harmonic potentials. The transition from spatial harmonic potentials to holomorphic functions of two complex variables z1, z2 was carried out and a boundary value problem for the above functions was formulated. By presenting these holomorphic functions in the form of homogeneous polynomials of order k relative to complex variables z1 , z2 , solutions were constructed by the method of development of the complex tensor of stresses by basic states. The application of this technique is illustrated in the examples of marginal problems, the real components of solutions that correspond to the solutions of Grashof’s problem for an elastic beam. Imaginary components of exact analytical solutions are obtained and corresponding structures of external load vectors for elastic beams of complex cross-section are constructed.

Słowa kluczowe

PL

trójwymiarowa teoria sprężystości; równanie Lamego; tensor naprężenia; przemieszczenie; wektor; zmienne zespolone; funkcja holomorficzna

EN

three-dimensional theory of elasticity; Lamé equation; stress tensor; complex variables; holomorphic function; displacement vectors

• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 2
• Strony: 66--78
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Pabyrivskyi, Viktor

• Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine,

autor

Pukach, Petro

• Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine,

autor

Pabyrivskyi, Volodymyr

• Institute of Computer Science and Information Technologies, Lviv Polytechnic National University, Lviv, Ukraine,

Bibliografia

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• 2. Solyaev, Y.O., & Korolenko, V.A. (2023). Application of Papkovich-Neuber general solution for crack problems in strain gradient elasticity. Lobachevskii Journal of Mathematics, 44, 2469-2479. DOI: 10.1134/S1995080223060434.
• 3. Solyaev, Y.O. (2022). Complete general solutions for equilibrium equations of isotropic strain gradient elasticity. DOI: 10.48550/arXiv.2207.08863.
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• 13. Onopriienko, O., Loboda, V., Sheveleva, A., & Lapusta, Y. (2018). An interface crack with mixed electro-magnetic conditions at it faces in a piezoelectric/piezomagnetic bimaterial under antiplane mechanical and in-plane electric loadings. Acta Mechanica et Automatica, 12(4), 301-310. DOI: 10.2478/ama-2018-0046.
• 14. Matysiak, S.J., Kulchytsky-Zhygailo, R., & Petrowski, D.M. (2018). Stress distribution in an elastic layer resting on a Winkler foundation with an emptiness. Bulletin of the Polish Academy of Sciences: Technical Sciences, 66(53), 721-727. DOI: 10.24425/125339.
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Identyfikatory

DOI

10.17512/jamcm.2024.2.06