Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction

In modern steel structures such as bridges and buildings, curved members are increasingly adopted. Current industry practices often approximate mildly curved surfaces with flat plates within tolerances, but optimizing this substitution to minimize fitting errors while reducing the quantity of curved plates remains a critical engineering challenge. While traditional approaches that rely on empirical craftsmanship or least-squares fitting lack precision, this study proposes a minimum error integration method that integrates Lagrange interpolation-based error estimation with an adaptive step-size steepest descent algorithm to reduce fitting error. Numerical experiments are performed to compare the proposed method against the least-squares method across two scenarios: (1) surfaces with typical shape and curvature and (2) a practical engineering case. Our results demonstrate at most a 75.5% reduction in fitting errors for analytical curved plates with particularly significant improvements in biconvex curvature scenarios. A practical engineering validation reveals that the method increases the proportion of planarizable plates from 27% to 45% under identical tolerance criteria, effectively reducing curved-plate fabrication demands and thus reducing cost and carbon emissions. The proposed optimization method offers a mathematically grounded alternative to experience-dependent practices. These findings validate the method’s potential to enhance cost-effectiveness and manufacturing sustainability in steel structure projects, suggesting broader applicability in curvature-driven construction scenarios.