Abstract:
In the design of shell structures, challenges such as experience-dependent thickness determination and post-hoc structural rationalization are prevalent. To address these issues, this study proposes a shell thickness design method that integrates structural mechanical performance with parametric design, establishing a closed-loop workflow encompassing "parametric form definition, performance data extraction, thickness decision algorithm, and geometric model reconstruction." By correlating the control points of the surface with the mesh nodes of the surface, equivalent nodal stresses are extracted via finite element analysis, and stress values are converted into variable cross-sectional thicknesses through a mapping function, ultimately generating a variable-thickness double-layer shell. Comparative experiments were conducted on two typical shell types—free-form shells and hyperbolic paraboloid shells—under self-weight loading and simply supported boundary conditions. For free-form shells, the variable-thickness design reduced the peak equivalent stress by 33.9% and the deformation displacement by 21.1% compared to the thin-shell design, while the material consumption was only 65.6% of that of the homogeneous thick shell. For hyperbolic paraboloid shells, the variable-thickness design reduced the peak equivalent stress by 65.2% and the deformation displacement by 44.5%, with the material usage being merely 50.9% of that of the homogeneous thick shell. The results indicate that variable-thickness shells achieve mechanical performance comparable to that of thick shells while using a material quantity close to that of thin shells, verifying the feasibility of "thickness assignment based on force" and providing a computable digital approach for shell thickness design.