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...
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MDPI AG
2025-04-01
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| Online Access: | https://www.mdpi.com/2075-5309/15/9/1433 |
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| author | Zhuoju Huang Jiemin Ding |
| author_facet | Zhuoju Huang Jiemin Ding |
| author_sort | Zhuoju Huang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1759f288330043d09ffd953d03067e3f |
| institution | DOAJ |
| issn | 2075-5309 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Buildings |
| spelling | doaj-art-1759f288330043d09ffd953d03067e3f2025-08-20T02:59:14ZengMDPI AGBuildings2075-53092025-04-01159143310.3390/buildings15091433Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel ConstructionZhuoju Huang0Jiemin Ding1Department of Structural Engineering, Tongji University, Shanghai 200092, ChinaTongji Architectural Design (Group) Co., Ltd., Shanghai 200092, ChinaIn 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.https://www.mdpi.com/2075-5309/15/9/1433steel structurescurve member fabricationfitting error minimizationLagrange interpolation |
| spellingShingle | Zhuoju Huang Jiemin Ding Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction Buildings steel structures curve member fabrication fitting error minimization Lagrange interpolation |
| title | Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction |
| title_full | Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction |
| title_fullStr | Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction |
| title_full_unstemmed | Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction |
| title_short | Minimum Error Integration Method for Quadrilateral Flat Plate Fitting in Steel Construction |
| title_sort | minimum error integration method for quadrilateral flat plate fitting in steel construction |
| topic | steel structures curve member fabrication fitting error minimization Lagrange interpolation |
| url | https://www.mdpi.com/2075-5309/15/9/1433 |
| work_keys_str_mv | AT zhuojuhuang minimumerrorintegrationmethodforquadrilateralflatplatefittinginsteelconstruction AT jieminding minimumerrorintegrationmethodforquadrilateralflatplatefittinginsteelconstruction |