Perturbation method in the problem on a nearly circular hole in an elastic plane.

E.A. Bashkankova, A.B. Vakaeva, M.A. Grekov

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9 Citations (Scopus)

Abstract

The perturbationmethod is used to construct the solution of the plane elasticity problem for a plane with a curvilinear nearly circular hole. An algorithm for calculating any approximation represented as a Cauchy type integral depending on all preceding approximations is given. The complex potentials of the first approximation are obtained for an elliptic hole and a curvilinear hole whose boundary deviates from the unit circle in the radial direction according to the cosine law. An example of elliptic hole is used to analyze the error in the first approximation of the stress concentration factor by comparing it with the exact solution. The influence of the hole shape on the distribution of circular stresses on the boundary is studied.
Original languageEnglish
Pages (from-to)198-207
JournalMechanics of Solids
Volume50
Issue number2
DOIs
Publication statusPublished - 2015

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Stress concentration
Elasticity
perturbation
approximation
stress concentration
elastic properties

Cite this

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abstract = "The perturbationmethod is used to construct the solution of the plane elasticity problem for a plane with a curvilinear nearly circular hole. An algorithm for calculating any approximation represented as a Cauchy type integral depending on all preceding approximations is given. The complex potentials of the first approximation are obtained for an elliptic hole and a curvilinear hole whose boundary deviates from the unit circle in the radial direction according to the cosine law. An example of elliptic hole is used to analyze the error in the first approximation of the stress concentration factor by comparing it with the exact solution. The influence of the hole shape on the distribution of circular stresses on the boundary is studied.",
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AU - Grekov, M.A.

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AB - The perturbationmethod is used to construct the solution of the plane elasticity problem for a plane with a curvilinear nearly circular hole. An algorithm for calculating any approximation represented as a Cauchy type integral depending on all preceding approximations is given. The complex potentials of the first approximation are obtained for an elliptic hole and a curvilinear hole whose boundary deviates from the unit circle in the radial direction according to the cosine law. An example of elliptic hole is used to analyze the error in the first approximation of the stress concentration factor by comparing it with the exact solution. The influence of the hole shape on the distribution of circular stresses on the boundary is studied.

KW - perturbation method

KW - plane problem

KW - curvilinear hole

KW - stress concentration

U2 - 10.3103/S0025654415020090

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