Dynamics of Strongly Curved Concrete Beams by Isogeometric Finite Elements

The standard finite elements approach for the dynamics of curved beam is usually based on the same energy functional used for straight beam, in other words an energy form that is essentially derived from de Saint-Venant's theory. In case of strongly curved elements this approximation yields to not negligible errors, in particular for stress assessments. For this reason, in this work a different formulation, based on the Winkler's simple kinematic assumptions, is adopted. In this way a non diagonal constitutive matrix is obtained and the computational efficiency of NURBS (Non Uniform Rational B-Splines) shape functions is added to an accurate representation of the constitutive relations. In this paper the natural frequencies and mode shapes of plane curved concrete beams are obtained. Computational cost and results accuracy is assessed with respect to closed form solutions and literature results.