Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 46215, 19 pages
Developing a Formulation Based upon Curvature for Analysis of Nonprismatic Curved Beams
Department of Civil Engineering, Kerman University, P.O. Box 76169-133, Kerman, Iran
Received 9 January 2007; Accepted 26 March 2007
Academic Editor: James Richard Barber
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.
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.