An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

Abstract Complex structure with circular boundaries is commonly used in engineering practice, and it is essential to conduct a detailed analysis of the interior stress field of the structure. The Michell stress function is a well-known general solution for plane elasticity problems in the polar coor...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 2002; no. 1; pp. 12028 - 12033
Main Authors Jiang, Zhizhen, Zhang, Rui, Gong, Shiyu, Hou, Jiahui, Jin, Xiaoqing
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.08.2021
Subjects
Boundaries
Elasticity
Exact solutions
Fourier analysis
Fourier series
Mathematical analysis
Polar coordinates
Stress concentration
Stress distribution
Stress functions
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Summary:Abstract Complex structure with circular boundaries is commonly used in engineering practice, and it is essential to conduct a detailed analysis of the interior stress field of the structure. The Michell stress function is a well-known general solution for plane elasticity problems in the polar coordinates, particularly when circular boundaries are involved. This work presents an analytical method with the assistance of the Michell solution, which could be seamlessly combined with Fourier analysis. Using the expansion of Fourier series, problems with arbitrarily distributed loads can be handled via a standard procedure. A complete analytical solution is elaborated for an arbitrarily loaded circular ring, and a classical elastic solution is provided for verification.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2002/1/012028