| Abstract: | A general and efficient technique is developed for the evaluation of the integrals with various orders of singularity, such as occur in the three-dimensional boundary element method (BEM). Generalized (extended) triangle, tetrahedron polar co-ordinate mappings together with two conditions are used to remove the singularity of the integrals, and to evaluate the corresponding non-singular ones in a new numerical space. Triangle and tetrahedron polar co-ordinates in Reference 1 are proved to be a special case of the generalized ones in this paper. With the developed idea, boundary element results converge rapidly towards the analytical solutions for the strongly singular integrals evaluated directly, and the analytical solutions can be gained in principle, even when employing higher order, triangular boundary elements and tetrahedral cells. The generality and practicability of the method are demonstrated in the case of higher order elements, discontinuous elements and large engineering problems. |
