Buckling Characteristics of Bio-Inspired Helicoidal Laminated Composite Spherical Shells Under External Normal and Torsional Loads Subjected to Elastic Support

Spherical shells exhibit superior strength-to-geometry efficiency, making them ideal for industrial applications such as fluid storage tanks, architectural domes, naval vehicles, nuclear containment systems, and aeronautical and aerospace components. Given their critical role, careful attention to the design parameters and engineering constraints is essential. The present paper investigates the buckling responses of bio-inspired helicoidal laminated composite spherical shells under normal and torsional loading, including the effects of a Winkler elastic medium. The pre-buckling equilibrium equations are derived using linear three-dimensional (3D) elasticity theory and the principle of virtual work, solved via the classical finite element method (FEM). The buckling load is computed using a nonlinear Green strain formulation and a generalized geometric stiffness approach. The shell material employed in this study is a T300/5208 graphite/epoxy carbon fiber-reinforced polymer (CFRP) composite. Multiple helicoidal stacking sequences—linear, Fibonacci, recursive, exponential, and semicircular—are analyzed and benchmarked against traditional unidirectional, cross-ply, and quasi-isotropic layups. Parametric studies assess the effects of the normal/torsional loads, lamination schemes, ply counts, polar angles, shell thickness, elastic support, and boundary constraints on the buckling performance. The results indicate that quasi-isotropic (QI) laminate configurations exhibit superior buckling resistance compared to all the other layup arrangements, whereas unidirectional (UD) and cross-ply (CP) laminates show the least structural efficiency under normal- and torsional-loading conditions, respectively. Furthermore, this study underscores the efficacy of bio-inspired helicoidal stacking sequences in improving the mechanical performance of thin-walled composite spherical shells, exhibiting significant advantages over conventional laminate configurations. These benefits make helicoidal architectures particularly well-suited for weight-critical, high-performance applications in aerospace, marine, and biomedical engineering, where structural efficiency, damage tolerance, and reliability are paramount.