An Isoparametric Finite Element With Nodal Derivatives

Abstract

A finite element using the nodal point values of the first partial derivatives of the unknown function with respect to the coordinates to increase the order of the resulting interpolating polynomial is formulated as an isoparametric element. The shape functions in local coordinates are given and then to satisfy requirements for the transformation of derivatives are modified for use with the global coordinates. Examples of a cantilever beam, a curved cantilever beam, and a flat bar with a hole demonstrate the high-order capabilities of the element. The advantages of the element over other isoparametric elements are discussed.