Shock and Vibration

Shock and Vibration / 2012 / Article

Open Access

Volume 19 |Article ID 786191 | 18 pages | https://doi.org/10.3233/SAV-2011-0623

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

Received03 Jul 2010
Revised20 Oct 2010

Abstract

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.

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.


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