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Shock and Vibration
Volume 19 (2012), Issue 2, Pages 187-204

Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

Ahmad Shahba,1,2 Reza Attarnejad,1,2 and Mehran Eslaminia3

1School of Civil Engineering, University College of Engineering, University of Tehran, Tehran, Iran
2Centre of Numerical Methods in Engineering, University of Tehran, Iran
3Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC, USA

Received 3 July 2010; Revised 20 October 2010

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.