A systematic FEA framework for different complex shell architectures under non-homogeneous constraints

Abstract

Shell structures are widely used in aerospace, automotive, marine, and civil engineering due to their high stiffness-to-weight ratio and efficient load-carrying capability. Despite extensive research on individual shell geometries, systematic comparative assessments under identical modelling conditions remain limited. To address this gap, this study establishes a unified finite element-benchmarking framework to evaluate the structural performance of five representative geometries: the Annular Plate, Funnel, Parabola Shell, Doubly Curved Panel (DCP), and Helicoid. Finite element simulations were conducted in ANSYS Mechanical by considering five shell thicknesses (2–20 mm) and four boundary conditions (Clamped–Clamped, Clamped–Free, Clamped–Simply Supported, and Simply Supported–Simply Supported), yielding 100 simulation cases. The model was validated against published free-vibration data for a Free–Free annular plate, demonstrating excellent agreement with a maximum natural frequency deviation under 1%. The first six natural frequencies, maximum total deformation, equivalent (von Mises) stress, and maximum principal stress were evaluated. Results indicate that increasing shell thickness consistently increases natural frequencies while reducing deformation and stress across all geometries. Among the configurations, the Annular Plate exhibited the most favourable overall structural performance combining high dynamic stiffness with low deformation and reduced stress concentrations whereas the Helicoid demonstrated the greatest flexibility. This integrated assessment provides practical design guidance for selecting optimal shell geometries during the conceptual design of lightweight structures.