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Investigation of stress-strain state of an incompressible elliptic cylinder with a hole

Natela Zirakashvili

Vol. 17 (2022), No. 4, 297–318
Abstract

The paper studies the elastic equilibrium of a homogeneous isotropic incompressible elliptic cylinder with a hole, when normal or tangential stresses are applied on its internal and external surfaces. The cylinder is in a state of plane deformation. Thus, the boundary value problems are set and solved for an incompressible confocal elliptic ring in an elliptic coordinate system. The boundary value problems for a confocal elliptic ring are given with the superposition of the internal and external problems of an ellipse. For incompressible bodies, equilibrium equations and Hooke’s law are written in the elliptic coordinate system, boundary value problems are set and solutions are presented with two harmonic functions, which are obtained by a method of separation of variables. Two test problems for a confocal elliptic semiring are solved and the graphs relevant to the numerical values are drafted. One problem concerns the change in the deformed state of the incompressible confocal elliptic semiring in relation with the change in the axes of the elliptical hole, while in the second problem the deformation process of the rubber shaft with the elliptical hole is investigated.

Keywords
incompressible elliptic cylinder, elliptic coordinates, separation of variables, harmonic function, homogeneous isotropic body
Milestones
Received: 20 August 2021
Revised: 28 January 2022
Accepted: 13 March 2022
Published: 18 February 2023
Authors
Natela Zirakashvili
Ilia Vekua Institute of Applied Mathematics
Ivane Javakhishvili Tbilisi State University
Tbilisi
Georgia