Abstract
This paper outlines the correct boundary element formulation concerning the fact that arbitrary rigid body displacements, which are inherent to any fundamental solution, should actually have no influence on the accuracy of the final results. A related, and most important, aspect is that, in such an improved formulation, the forces described along the boundary are always in balance, independently of approximation. Implementation of the proposed modifications in the traditional equations, for the sake of achieving spectral consistency of the matrices involved, is always simple and possibly inexpensive, depending on the application. The formulation is generally valid for any static elasticity or potential problem in two or three dimensions, for either finite or infinite domains and considering body forces. It is demonstrated that this formulation yields a constrained equation system, which is mathematically equivalent to the problem proposed and solved by Bott and Duffin (1953) for electrical networks, in the frame of the theory of generalized inverses. The present paper proposes adequately and solves exactly a problem that has been hanging for decades. The author suggests that its main achievements be incorporated into the fundamentals of the boundary element methods.
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Dumont, N. An assessment of the spectral properties of the matrix G used in the boundary element methods. Computational Mechanics 22, 32–41 (1998). https://doi.org/10.1007/s004660050336
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DOI: https://doi.org/10.1007/s004660050336