Transition elements based on transfinite interpolation

Abstract

In this study the transfinite interpolation methodology, a 'blending-function' method in particular, is utilized for the formulation of transition elements. The method offers a formal way of meeting continuity requirements in a transition element. Element shape functions are derived by blending the continuity requirements of individual boundary segments. The blending directions are naturally orthogonal in rectangular domains therefore interpolation of the boundaries over rectangular 2D and 3D elements can be performed with minimal effort. In triangular domains, however, the choice of blending directions and interpolants is not straightforward. For that reason, two interpolation techniques are proposed for blending of the boundaries of triangular domains. A series of transition elements of various classes compatible with elements of different orders and dimensions is developed and the full potential of the transfinite interpolation, as it applies to element formulation, is explored.