Treatment of corner node problems and its singularity

Abstract

In boundary element analyses, special treatments have to be applied at geometric corner nodes in order to achieve a higher accuracy of the boundary element results. This paper first reviews the existing methods in the treatment of corner node problems, and then proposes the boundary point element method, which possesses continuous boundary displacements and discontinuous tractions at the geometric corners. A way to deal with the singularity that occurs when displacements are prescribed at both nodes of a boundary point element is also presented. Numerical analyses of various typical examples are carried out using different treatments for the corner node problems and their performances are compared. It is shown that the boundary point element method is an accurate and effective approach in treating the problems.