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Numerical resolution of the boundary integral equations for elastic scattering by a plane crack
Author(s) -
Alves Carlos,
Duong Tuong Ha
Publication year - 1995
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.1620381404
Subject(s) - integral equation , mathematical analysis , mathematics , singularity , boundary element method , scattering , collocation (remote sensing) , boundary value problem , plane (geometry) , displacement field , finite element method , geometry , physics , optics , computer science , machine learning , thermodynamics
The problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. A collocation method is often used to solve that equation, but here we will use a variational method, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical tests were made with circular and elliptical cracks, but this method can be extended to other shapes, with the same convergence profiles. Extensive results are given concerning the crack opening displacement, the scattering cross‐section, the back‐scattered amplitude and far‐field patterns.