Dealing with corners and changing geometry

Abstract

The multi-region method outlined in the previous chapter works well if interfaces between regions are smooth, i.e. where interface points have a unique tangent. If the boundary is not smooth but has corners and edges, i.e. the outward normals are different at elements adjacent to the node, then the normal flow or normal tractions are also different on each side. Such a case would arise, for example, if the shape of the inclusion in the example of the previous chapter is square (Figure 12.1) instead of circular. In this case, two values of normal flow or two sets of traction vectors would have to be computed at the corner node instead of one. However, the integral equations allow the computation at a node of only one value of t for potential problems and one vector of t for elasticity problems.