Free Vibration and Static Behavior of Bio-Inspired Helicoidal Composite Spherical Caps on Elastic Foundations Applying a 3D Finite Element Method

Spherical caps exploit their intrinsic curvature to achieve efficient stress distribution, delivering exceptional strength-to-weight ratios. This advantage renders them indispensable for aerospace systems, pressurized containers, architectural domes, and structures operating in extreme environments, such as deep-sea or nuclear containment. Their superior load-bearing capacity enables diverse applications, including satellite casings and high-pressure vessels. Meticulous optimization of geometric parameters and material selection ensures robustness in demanding scenarios. Given their significance, this study examines the natural frequency and static response of bio-inspired helicoidally laminated carbon fiber–reinforced polymer matrix composite spherical panels surrounded by Winkler elastic foundation support. Utilizing a 3D elasticity approach and the finite element method (FEM), the governing equations of motion are derived via Hamilton’s Principle. The study compares five helicoidal stacking configurations—recursive, exponential, linear, semicircular, and Fibonacci—with traditional laminate designs, including cross-ply, quasi-isotropic, and unidirectional arrangements. Parametric analyses explore the influence of lamination patterns, number of plies, panel thickness, support rigidity, polar angles, and edge constraints on natural frequencies, static deflections, and stress distributions. The analysis reveals that the quasi-isotropic (QI) laminate configuration yields optimal vibrational performance, attaining the highest fundamental frequency. In contrast, the cross-ply (CP) laminate demonstrates marginally best static performance, exhibiting minimal deflection. The unidirectional (UD) laminate consistently shows the poorest performance across both static and dynamic metrics. These investigations reveal stress transfer mechanisms across layers and elucidate vibration and bending behaviors in laminated spherical shells. Crucially, the results underscore the ability of helicoidal arrangements in augmenting mechanical and structural performance in engineering applications.