Abstract
The interfacial singularity of O(r^<-0>)〜O(r^<-1/2>) occurs at an interfacial edge in a dissimilar material. Its order depends on the combination of the constituents of the dissimilar material. Special shape functions have been proposed for such singularity by Akin (Int. J. Num. Meth. Engng., 10(1976), pp.1749-1759.) and by adopting them to the isoparametric element the stress fields occured in a dissimilar material has been analyzed by Wang et al. In our research, the one-dimensional superparametric element whose shape function is Akin's one is examined for various mapping functions in the so-called Serendipity family. Our one-dimensional element has a singularity of either O(r^<-p>) or O(r^<(p+1)/2>) according to the choice of the location of mide-side node. For the two-dimensional element, the shape function which satisfies two necessary conditions is developed on the basis of Akin's method. Moreover, one of the edge of such an element is collapsed to a point and mid-side nodes of the element are moved to designed sites on another edges. Consequently, we can see that the new two-dimensional singular element has a singularity of O(r^<-p>).
