Simply Curved Shear Panel Theory in Three-Dimensional Space

The increasing complexity of large-scale thin-walled structures can be effectively addressed using hierarchical modelling approaches. However, in structural engineering, true preliminary design phases are often skipped due to the unavailability or insufficient accuracy of reduced models capable of handling the required complexity. Historically, the shear panel theory provided a computationally efficient method for analysing thin-walled structures before the adoption of the finite element method (FEM). While the shear panel theory includes a formulation for curved panels, it remains limited to one-dimensional representations, making it unsuitable for three-dimensional curved shell structures such as fuselages and wing boxes. Consequently, these structures are typically approximated using plane panels, introducing inaccuracies. This paper presents a novel formulation for rectangular simply curved panels in three-dimensional space that extends shear panel theory to simply curved structures by explicitly incorporating the shear centre into the derivation, enabling its use in preliminary design. The new formulation is validated through comparisons with numerical solutions of a wing box featuring a curved leading edge and analytical solutions of stiffened cylindrical shells. The results demonstrate that the curved panel formulation reproduces the analytical solution and significantly improves accuracy over state-of-the-art planar panel models, providing a more robust tool for the preliminary design of simply curved thin-walled structures.