An Integration Technique in Burnett Infinite Element

Burnett element [1] has been regarded as the most important contribution to infinite element method. It comprises two principal features: one is the use of confocal ellipsoidal coordinate system; another is the exact multi-pole expansion in the newly defined “radial” direction. The former leads in effect to a quasi one-dimensional problem from the infinite point of view, and thereby makes the latter be possibly carried out. However, in evaluating the system matrices, undefined integrals are involved. Hence, the resulting “stiffness”, “damping” and “mass” matrices don’t have definite physical significance. The potential disadvantage is that this efficient element cannot be directly used to solve transient problems. In this paper, presentation of the theory of multi-pole expansion used in Burnett element is changed in form and the shape functions are subsequently expressed in terms of local coordinates by using the infinite-to-finite geometry mapping. In addition to the use of Astley type weighting functions [2] and to the modification of the weighting factor, the system matrices of Burnett infinite element are eventually bounded and integrated term by term using Gauss rules.