| The Boundary Element Method (BEM), based on the displacement Boundary Integral Equation (BE), is now well established as an efficient numerical tool for engineering analysis. However, in some linear elastostatic problems, if the distance from an interior point to the surface of the solution domain, or between two points on two parts of the surface close by in a thin, slender body, is relatively small, it will give rise to near singularities of the kernel functions of the BIE as they are singular with respect to this distance. For these problems, the conventional BEM is not well suited as very siginificant mesh refinement becomes necessary. In this study, a self-regularization BEM scheme previously applied in two-dimensional (2D) elastostatics is extended to three dimensions (3D). It is first implemented for the evaluation of the displacements and stresses at an interior point. Several numerical examples are presented to demonstrate the veracity of the scheme, for accurate solutions are obtained even for interior points very close to the surface without using refined mesh. A similar self-regularized traction-BIE extended from the corresponding 2D scheme to the 3D case is then investigated for the thin-body problems. It is not met with success, however, due to the lack of C 1,α continuity across element boundaries. A new self-regularized displacement-BIE which does not require this continuity requirement is developed for treating the thin-body problem. Using this scheme, preliminary tests show that very accurate results can still be obtained for the boundary stresses and displacements even when the cross section of the domain is very thin indeed. More extensive tests will still be necessary to fully establish the general applicability of this new scheme. |
