Isogeometric topology optimization of C1-continuous multi-patch shell structures

This study presents a multi-patch isogeometric topology optimization framework for Kirchhoff–Love (K–L) spatial shells. The main challenge arises from the 𝐶 1 -continuity requirement of the K–L formulation, which is difficult to satisfy across multi-patch interfaces. To address this issue, a strong 𝐶 1 -continuous construction method is developed for multi-patch spatial surfaces. The geometrically 𝐺 1 gluing condition is derived and extended to 3D surfaces by introducing the additional isogeometric basis functions. As a result, reconstructed basis functions with strong 𝐶 1 continuity are obtained across patch interfaces, and directly employed for K–L shell analysis and topology optimization. The surface-gradient results verify the continuity of the reconstructed basis functions. A one-patch and a reconstructed two-patch quarter-cylindrical shell show consistent mechanical and optimization responses, confirming the accuracy of the multi-patch reconstruction. More numerical examples with increasing geometric and patch complexity are then investigated to demonstrate the applicability and robustness of the proposed method. The optimized results exhibit clear and reasonable load-transfer layouts, smooth deformation and stress fields across patch interfaces, and stable convergence histories. The comparison of different shell thicknesses reveals the influence of membrane and bending stiffness on the optimized layout. Thicker K–L shells tend to produce more concentrated structural topologies, whereas thinner shells generate more dispersed and feature-rich material layouts, which are consistent with the concept of full-scale optimized designs. These findings indicate that the proposed framework provides an effective route for topology optimization of complex multi-patch Kirchhoff–Love spatial shells.