A Finite Circular Arch Element Based on Trigonometric Shape Functions

Saffari, H.; Tabatabaei, R.

doi:https://doi.org/10.1155/2007/78507

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2007 | Article ID 078507 | https://doi.org/10.1155/2007/78507

A Finite Circular Arch Element Based on Trigonometric Shape Functions

H. Saffari¹and R. Tabatabaei²

Academic Editor: Jan Awrejcewicz

Received27 Aug 2006

Accepted26 Feb 2007

Published14 May 2007

Abstract

The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.

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Copyright

Copyright © 2007 H. Saffari and R. Tabatabaei. 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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