Vol. 15, No. 5, 2020

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Approximate conformal mappings and elasticity problems for noncircular tubes

Damir F. Abzalilov, Pyotr N. Ivanshin and Elena A. Shirokova

Vol. 15 (2020), No. 5, 555–564
DOI: 10.2140/jomms.2020.15.555
Abstract

We present a method for analytic stress evaluation in elliptic and oval tubes based on approximate conformal mappings from annuli onto oval and elliptical doubly connected domains. The approximate conformal mapping is realized by the boundary reparametrization method. We also solve two elasticity problems for such tubes.

Keywords
conformal mapping, elasticity theory, stresses
Milestones
Received: 15 March 2018
Revised: 18 July 2018
Accepted: 24 July 2020
Published: 21 November 2020
Authors
Damir F. Abzalilov
N. I. Lobachevsky Institute of Mathematics and Mechanics
Kazan Federal University
Kazan
420008
Russia
Pyotr N. Ivanshin
N. I. Lobachevsky Institute of Mathematics and Mechanics
Kazan Federal University
Kazan
420008
Russia
Elena A. Shirokova
N. I. Lobachevsky Institute of Mathematics and Mechanics
Kazan Federal University
Kazan
420008
Russia