Static and dynamic analysis of curved laminated beams through the position-based finite element formulation
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This paper adresses the static and dynamic analysis of curved laminated beams. To this aim, the position-based finite element formulation 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. 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. Conversely, for the dynamic analysis, a simply supported static scheme is used. An excellent agreement is found with both analytical solutions and Abaqus results.