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Summary: Generation of shape functions for straight beam elements
Charles E. Augarde *
Department of Engineering Science, University of Oxford, Parks Road, Oxford, U.K.
Received 17 June 1997; received in revised form 14 February 1998
Abstract
Straight beam ®nite elements with greater than two nodes are used for edge stiening in plane stress analyses and
elsewhere. It is often necessary to match the number of nodes on the edge stiener to the number on a whole plane
stress element side. Beam elements employ shape functions which are recognised to be level one Hermitian
polynomials. An alternative to the commonly adopted method for determining these shape functions is given in this
note, using a formula widely reported in mathematical texts which has hitherto not been applied to this task in the
®nite element literature. The procedure derives shape functions for beams entirely from the set of Lagrangian
interpolating polynomials. Examples are given for the derivation of functions for a three and four-noded beam
element. # 1998 Elsevier Science Ltd. All rights reserved.
Keywords: Finite elements; Beams; Hermitian interpolation; Shape functions
1. Introduction
Analysis of structures using the ®nite element
method is well established. Many formulations exist
for complex elements but simple elements remain pop-
ular since they are usually well-tested and easy to im-
plement into an analysis program. Two-dimensional
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