Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements

Abstract

AbstractThis paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary‐described elements. Two basic procedures are introduced; the first by linear combinations of side‐interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1].The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technology.