Techniques for developing ‘special’ finite element shape functions with particular reference to singularities

Abstract

Abstract A concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions. Based on special one‐dimensional interpolatory schemes derived via the algorithm, a variety of two‐ and three‐dimensional interpolatory schemes are developed which are useful for modelling singular behaviour. The methodology presented is general and may be fruitfully applied to the development of ‘special’ finite element shape functions for a variety of other situations.