Variable-kinematic finite beam elements for geometrically nonlinear dynamic analyses

This article investigates the dynamic nonlinear response of three-dimensional structures using variable-kinematics finite beam elements obtained with the Carrera Unified Formulation. The formalism enables one to consider the three-dimensional form of displacement–strain relations and constitutive law. The deformation mechanisms and the associated couplings are described consistently with the selected kinematic model. The Hilbert–Hughes–Taylor method and the iterative Newton–Raphson scheme are adopted to solve the motion equations derived in a total Lagrangian scenario. Various models have been obtained by using Taylor- and Lagrange-like expansions. The capabilities of the beam elements are assessed considering isotropic, homogeneous structures with compact and thin-walled sections.