Open AccessAn Analytical Method for Plane Elasticity Problems Involving Circular Boundaries
Author(s) -
Zhizhen Jiang,
Rui Zhang,
Shuxi Gong,
Jiahui Hou,
Xiaoqing Jin
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2002/1/012028
Subject(s) - elasticity (physics) , fourier series , polar coordinate system , stress field , fourier transform , mathematical analysis , mathematics , plane (geometry) , geometry , physics , structural engineering , finite element method , engineering , thermodynamics
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.