An Isoparametric Finite Element With Nodal Derivatives

[+] Author and Article Information
W. D. Webster

Department of Mechanical Engineering, General Motors Institute, 1700 W. Third Avenue, Flint, Mich. 48502

J. Appl. Mech 48(1), 64-68 (Mar 01, 1981) (5 pages) doi:10.1115/1.3157593 History: Received December 01, 1979; Revised May 01, 1980; Online July 21, 2009


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.

Copyright © 1981 by ASME
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