A boundary integral equation method for three-dimensional crack problems in elasticity. (English) Zbl 0608.73097

The author has developed an exact solution procedure for both the Dirichlet and Neumann 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 existence and regularity of the solutions of the integral equations are derived using the calculus of pseudo-differential operators. The explicit behaviour of the densities of the integral equations near the edge of the crack surface is discussed using the concept of the principal symbol and the Wiener-Hopf technique. Based on the detailed regularity results the author shows how to improve the boundary element Galerkin method for the integral equations. Quasi-optimal asymptotic estimates for the Galerkin error are given.
Reviewer: P.Narain


74R05 Brittle damage
65R20 Numerical methods for integral equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
47Gxx Integral, integro-differential, and pseudodifferential operators
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