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

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