Static and dynamic analysis of curved laminated beams through the position-based finite element formulation

This paper adresses the static and dynamic analysis of curved laminated beams. To this aim, the position-based finite element formulation proposed by Valvo for isoparametric elements is extended to include rotational degrees of freedom. Accordingly, the nodal positions and rotations in the current configuration are chosen as the main unknowns. A curved laminated beam element is formulated adopting an interpolation scheme based on Hermite polynomials, as proposed by Armero. The general expressions of the secant and tangent stiffness matrices are first obtained for the geometrically nonlinear case and then consistently linearised. For the static analysis, a cantilever circular beam is considered: one end is clamped while the opposite one is free and subjected to an assigned horizontal or vertical load. Conversely, for the dynamic analysis, a simply supported static scheme is used. The free vibration modes are investigated by employing a consistent mass approach. The model is validated in the case of infinitesimal plane displacements, as shown by the excellent agreement with both analytical solutions and Abaqus results. It is our intention to later address the geometrically nonlinear case.