Strong and weak form solutions of curved beams via Carrera's unified formulation

In this article, the mechanical behavior of three-dimensional curved beams is investigated through closed-form solution as well as one-dimensional finite elements based on Carrera's Unified Formulation (CUF). CUF is a hierarchical formulation in which the approximation order of the displacement field is a free parameter of the analysis. Therefore, refined models accounting for higher-order effects such as shear deformation and local warping can be obtained with no need for ad hoc formulations. The principle of virtual displacements (PVD) is used in order to derive both strong and weak formulations. For the latter, locking phenomena typical of curved finite elements are tackled by means of a Mixed Interpolation of Tensorial Components (MITC). Numerical results for different boundary conditions and loading configurations are investigated and validated towards elasticity solutions and commercial software finite elements showing that the proposed formulation can lead to an accurate evaluation of the displacement and stress fields with reduced computational costs.