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Flux and traction boundary elements without hypersingular or strongly singular integrals. (English) Zbl 0987.74074
The paper deals with a boundary element formulation based on the traction elasticity boundary integral equation (potential derivative for Laplace’s problem). The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require any change of coordinates, and the resulting integrals can be numerically evaluated in a simple and efficient way. The formulation presented is completely general and valid for arbitrary shaped open or closed boundaries. The authors give analytical expressions for all the required hypersingular or strongly singular integrals. To fulfill the continuity requirement over the primary density, a simple boundary element discretization is adopted: continuous elements are used, whereas the collocation points are shifted towards the interior of the elements.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74B05 Classical linear elasticity
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