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Modified trapezoidal quadratures and accurate potential evaluation for numerical solutions of S.I.E's on the unit circle
Author(s) -
Theotokoglou E. N.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260914
Subject(s) - mathematics , gravitational singularity , mathematical analysis , unit circle , singular integral , integral equation , point (geometry) , plane (geometry) , complex plane , singular point of a curve , elasticity (physics) , function (biology) , dislocation , geometry , physics , condensed matter physics , evolutionary biology , biology , thermodynamics
Abstract Plane elasticity problems that can be reduced to singular integral equations over the unit circle are considered, the method of using a dislocation density function ω(σ) is adopted. First, the trapezoidal approximation is modified for the evaluation of the contour integral ∮ y [ω(σ)/(σ – z )]dσ at the complex field point z ; extra correction terms for known singularities of ω( z ) can easily be determined from the error expression. Based on the quadratures obtained, expressions for the accurate evaluation of the potentials are derived using their analyticity properties. The numerical techniques proposed are used for the solution of the problem of an infinite plate weakened by a circular hole and subjected to a dislocation.