Formulação com dupla reciprocidade hipersingular do método dos elementos de contorno para problemas de potencial escalar bidimensionais

Abstract

The Boundary Element Method Hyper-singular Formulation has been initially evaluated to harmonic and elatostatic problems. Fracture mechanics problems, which require two distinct equations for the same particle at some position, constitute its most common application field actually. This formulation, however, never has been studied when domain loads are present in the potential scalar problem. In this work, the external load term is treated by the Dual Reciprocity Formulation, where the repeated matrices are not the ones with singular integrals, but that with hyper-singular integrals of the formulation cited above. Test examples have been selected to validate the technique, pointing to coherent results by comparing to both Singular Dual Reciprocity Formulation and analytical calculations. The results show that the potential derivatives are better determinated, by the studied formulation, than the potential itself. However, there is no sufficient evidence to confirm the idea that the hyper-singular boundary integral equation works better when high potential gradients are involved.