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Hypersingular integrals in boundary element fracture analysis. (English) Zbl 0717.73081
Summary: A new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multidomain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three- dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single-domain boundary element analysis are also presented.
74S15Boundary element methods in solid mechanics
74R99Fracture and damage
45E99Singular integral equations