Representation of solutions to the plane elasticity problems for a rectangular domain via Vihak’s functions

Токовий, Ю. В., Юзв’як, М. Й., Ясінський, А. В. (2021). Representation of solutions to the plane elasticity problems for a rectangular domain via Vihak’s functions. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(3), 123–126. https://doi.org/10.17721/1812-5409.2021/3.24

The paper presents the generalization of the direct integration method for the governing equations of the basic elasticity problems for the bounded domains with corner points. An important stage in the realization of the method is the representation of the unknown stress-tensor components via the key functions. The selection of these functions is motivated by some specific features of the problems and thus was regarded as a weakest part of the solution algorithm. Herein, we suggest an universal approach for the selection of the key functions, which we started to call the Vihak functions (to honor Prof. Vasyl M. Vihak, the founder and developer of the direct integration method) by using the integral relationships derived from the equilibrium equations. The approach is illustrated by the solution of a plane elasticity problem for an elastic rectangle. The relationship between Vihak’s function for the considered problem and the classical biharmonic Airy stress function is shown.
Pages of the article in the issue: 123 - 126
Language of the article: Ukrainian