Application of relations of singularity intensities of tangent derivatives of boundary displacements and tractions to BEM

In order to obtain a highly accurate numerical solution for a two-dimensional elasticity problem with singular boundary conditions on the smooth surface of an elastic body by boundary element method (BEM), the continuous or the singular requirements of the boundary field variables and their derivatives at element intersections have to be satisfied. The singularity intensities of the unknown boundary field variables have been determined through the theoretical relations of singularity intensities of tangent derivatives of boundary displacements and tractions, a priori. The continuous or singular requirements of boundary field variables and their derivatives at element intersections are automatically satisfied by using single node quadratic element (SNQE) developed in this paper. An example problem with singular boundary conditions on the surface of a semi-infinite-plane is numerically studied by BEM by using traditional three-nodes isoparametric elements and SNQEs. Numerical results show that the computation precisions at singular boundary points are greatly increased by using SNQEs.