Determination of non-axisymmetric stresses in the bodies of revolution based on regulized intergral equations

A solution to the 3D elasticity theory problem in the form of a Fourier series expansion by an angular coordinate, the coefficients of which are determined from the system of one-dimensional integral equations, is constructed. The relation for determining the kernels of these equations for harmonics...

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Bibliographic Details
Published in:European journal of mechanics, A, Solids Vol. 87; p. 104218
Main Authors: Maksymovych, Olesya, Solyar, Tetyana
Format: Journal Article
Language:English
Published: Berlin Elsevier Masson SAS 01.05.2021
Elsevier BV
Subjects:
Algorithms
Bodies of revolution
Cartesian coordinates
Elasticity
Fourier series
Integral equations
Kernels
Non-axisymmetric problem
Numerical analysis
Regularization
Reliability analysis
Rotating bodies
Series expansion
Stress concentration
Stresses
Tensors
Stresses
Bodies of revolution
Non-axisymmetric problem
Integral equations
ISSN:0997-7538, 1873-7285
Online Access:Get full text
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Summary:A solution to the 3D elasticity theory problem in the form of a Fourier series expansion by an angular coordinate, the coefficients of which are determined from the system of one-dimensional integral equations, is constructed. The relation for determining the kernels of these equations for harmonics of arbitrary order is written in analytical form. The regularization of the obtained equations is carried out. For this purpose, the kernels of the equations are represented as the sum of regular functions and singular components, which are determined through the kernels of the plane problem of the elasticity theory in the Cartesian coordinate system. In the stress tensor, the components that contain logarithmic functions as multiplier, are additionally highlighted. The test calculations are performed, which confirm the reliability of the analytically obtained relations and integral equations built on their basis. Testing of the developed numerical algorithm for solving integral equations is carried out and examples of calculation of non-axisymmetric stress concentration near cavities in bodies of various shapes are resulted. The obtained results allow to expand the application of boundary elements method to study of practically important non-axisymmetric problems for the bodies of rotation. •Kernels of integral equations for arbitrary members of the Fourier series are found explicitly.•In this case the Kelvin matrix and the stress tensor are given.•Explicit relations for the kernels of equations allowed us to extract singular components.•On the basis of the established singular components the regularization of integral equations is carried out.•Stress concentration near cavities of various shapes under one-sided tension of bodies is investigated.
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ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2021.104218