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A boundary integral equation method for three‐dimensional crack problems in elasticity
Author(s) -
Stephan E. P.,
Wendland W. L.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080140
Subject(s) - mathematics , integral equation , galerkin method , mathematical analysis , jump , traction (geology) , summation equation , boundary element method , electric field integral equation , finite element method , physics , quantum mechanics , geomorphology , thermodynamics , geology
This paper presents a solution procedure for three‐dimensional crack problems via first kind boundary integral equations on the crack surface. The Dirichlet (Neumann) problem is reduced to a system of integral equations for the jump of the traction (of the field) across the crack surface. The calculus of pseudodifferential operators is used to derive existence and regularity of the solutions of the integral equations. With the concept of the principal symbol and the Wiener‐Hopf technique we derive the explicit behavior of the densities of the integral equations near the edge of the crack surface. Based on the detailed regularity results we show how to improve the boundary element Galerkin method for our integral equations. Quasi‐optimal asymptotic estimates for the Galerkin error are given.