The Treatment of Singularities and the Application of the Overhauser C⁽¹⁾ Continuous Quadrilateral Boundary Element to Three Dimensional Elastostatics

Summary

This paper is concerned with two topics of key importance in the implimentation of the Boundary Element Method; firstly the integration of the singular kernels encountered in a collocation procedure and secondly, the interpolation of the unknown functions over the element surface and the interpolation of the element surface itself.

For kernel integration, some results are presented which combine the method of singularity subtraction and Taylor expansion with the triangle to square regularising transformation method.

For function and surface interpolation, a C⁽¹⁾ continuous quadrilateral element, the Overhauser element, is described, including its degenerate forms which allow it to be applied to bodies, such as cubes, which are not themselves C 1 continuous. Such an element provides an alternative to the use of splines but still uses only nodal values. Results are given of its application to two elastostatic problems.