The study of mathematical models of the linear theory of elasticity by presenting the fundamental solution in harmonic potentials

2020;
: pp. 259–268
https://doi.org/10.23939/mmc2020.02.259
Received: January 28, 2020
Revised: May 27, 2020
Accepted: May 30, 2020
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University

In this paper, the approaches to the study of mathematical models of the theory of linear elasticity are developed.  The general formulation of the 3-dimensional problem based on the representation of the fundamental solution in the form of V. P. Revenko in terms of spatial harmonic functions is considered.  The formulation in the harmonic potentials of the 3-dimensional problem of elasticity in a cylindrical coordinate system for bodies bounded by the canonical surface is done.  The boundary-value problems of pure rotation and circular symmetry in harmonic potentials are formulated.  The mentioned approaches make it possible to obtain analytical solutions to these problems and are the theoretical basis for calculating the strength parameters of technical systems in a way of analysis of their mathematical models.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 259–268 (2020)