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New identities for fundamental solutions and their applications to non-singular boundary element formulations. (English) Zbl 0969.74073
Summary: Based on a general operational approach, we establish two new integral identities for the fundamental solutions of potential and elastostatic problems. Non-singular forms of the conventional boundary integral equations (BIEs) are derived by employing these two identities for fundamental solutions, and by using the two-term subtraction technique. Both the strongly (Cauchy type) and weakly singular integrals existing in the conventional BIEs are removed from the BIE formulation. The existence of non-singular forms of conventional BIEs raises new questions about the smoothness requirement in the boundary element method, since the two-term subtraction requires, theoretically, \(C^1\) continuity of the density function, rather than the \(C^0\) continuity as required by the original singular or weakly singular forms of conventional BIEs. Implication of the non-singular BIEs on the smoothness requirement are discussed in this paper.

74S15 Boundary element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
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