Vibration and buckling analysis of laminated and bio-inspired helicoidal composite curved beams

A comprehensive investigation into the vibration and buckling behaviours of laminated composite and bio-inspired helicoidal composite curved beams is presented. The analysis employs classical, first-order, higher-order, and quasi-3D beam theories to evaluate their accuracy and applicability to curved geometries. A two-node finite element model satisfying the C 1 continuity condition is developed to capture shear deformation and thickness stretching effects. Numerical studies demonstrate that the present formulation is highly accurate and efficient. The results reveal that the fundamental frequencies and critical buckling loads are more sensitive to slenderness ratios than to curvature with clamped–clamped beams showing the strongest dependency and clamped–free beams being the least affected. Increasing fiber orientation angle reduces both frequency and buckling load, with a sharper decline in anti-symmetric lay-ups compared to symmetric ones. For bio-inspired curved beams, helicoidal-recursive, helicoidal-exponential, and linear-helicoidal types with smaller fiber angles exhibit the highest stiffness and stability, while the helicoidal-semicircular type performs best at larger angles. These findings underline the necessity of advanced beam theories for accurate prediction and provide benchmark results and design insights for the development of high-performance composite curved beams.