Developing a Formulation Based upon Curvature for  Analysis of Nonprismatic Curved Beams

Saffari, H.; Fadaee, M. J.; Tabatabaei, R.

doi:https://doi.org/10.1155/2007/46215

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2007 | Article ID 046215 | https://doi.org/10.1155/2007/46215

Developing a Formulation Based upon Curvature for Analysis of Nonprismatic Curved Beams

H. Saffari,¹M. J. Fadaee,¹and R. Tabatabaei¹

Academic Editor: James Richard Barber

Received09 Jan 2007

Accepted26 Mar 2007

Published04 Jul 2007

Abstract

A new element with three nodal curvatures has been considered for analysis of the nonprismatic curved beams by finite element method. In the formulation developed, the force-curvature relationships in polar coordinate system have been obtained first, then the curvature of the element has been assumed to have a second-order polynomial function form and the radial, tangential displacements, and rotation of the cross section have been found as a function of the curvature accounting for the effects of the cross section variation. Moreover, the relationship between nodal curvatures and nodal deformations has been calculated and used for determining the deformations in terms of curvature at an arbitrary point. The total potential energy has been calculated accounting for bending, shear, and tangential deformations. Invoking the stationary condition of the system, the force-deformation relationship for the element has been obtained. Using this relationship, the stiffness matrix and the equivalent fixed loads applying at the nodes have been computed. The results obtained have been compared with the results of some other references through several numerical examples. The comparison indicates that the present formulation has enough accuracy in analysis of thin and thick nonprismatic curved beams.

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Copyright

Copyright © 2007 H. Saffari et al. 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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