A Galerkin boundary integral method for multiple circular elastic inclusions

Sofia Mogilevskaya; Steven L Crouch

doi:10.1002/nme.243

A Galerkin boundary integral method for multiple circular elastic inclusions

Sofia Mogilevskaya, Steven L Crouch

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss-Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach.

Original language	English (US)
Pages (from-to)	1069-1106
Number of pages	38
Journal	International Journal for Numerical Methods in Engineering
Volume	52
Issue number	10
DOIs	https://doi.org/10.1002/nme.243
State	Published - Dec 10 2001

Keywords

Complex hypersingular integral equation
Elasticity
Galerkin method
Multiple circular inclusions

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N2 - The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss-Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach.

AB - The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss-Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach.

KW - Complex hypersingular integral equation

KW - Elasticity

KW - Galerkin method

KW - Multiple circular inclusions

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