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Simulation analysis of line heating for marine double curvature plates based on Gaussian mixture heat source model
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Bao-zhu ZHANG1, Kai LIU2, Jin-rui YE2, Zhi-hao QI2, An-shi YAN2, Xing-hua WANG3
Journal of Ship Mechanics | 2026, 30(7) : 1173 - 1184
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Journal of Ship Mechanics | 2026, 30(7): 1173-1184
• Structural Mechanics •
Simulation analysis of line heating for marine double curvature plates based on Gaussian mixture heat source model
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Bao-zhu ZHANG1, Kai LIU2, Jin-rui YE2, Zhi-hao QI2, An-shi YAN2, Xing-hua WANG3
Affiliations
  • 1School of Materials Science and Engineering, China University of Petroleum (East China), Qingdao 266000, China
  • 2School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100190, China
  • 3Jiangsu Automation Research Institute, Lianyungang 222006, China
Published: 2026-07-15 doi: 10.3969/j.issn.1007-7294.2026.07.011
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Line-heating with water cooling is the primary forming process used in shipbuilding to manufacture steel plates with complex double curvature. Owing to its high computational efficiency and reduced trial-and-error cost, finite element simulation has become an essential tool for process optimization and forming-quality control in the fabrication of complex curved plates. However, the Gaussian surface heat source model commonly adopted in existing finite element analysis neglects the transient heat-transfer effect induced by water cooling, leading to large errors in predicted plate deformation and insufficient forming accuracy for engineering applications. To address the thermomechanical modelling challenges in the simulation of line-heating with water cooling, the full-field temperature distribution during the forming process was first measured using an infrared camera. Based on the expectation-maximization algorithm for solving Gaussian mixture models, a Gaussian mixture heat source model incorporating both the heat input and the heat extraction was established. In addition, the material hardening behavior caused by accumulated plastic deformation under repeated thermal loading was considered, accounting for the gradual increase in yield strength and tensile strength. On this basis, a simulation method capable of accurately predicting both the temperature field and deformation of plates formed by line-heating with water cooling was developed, thereby improving the accuracy of existing process simulations. Comparisons between numerical and experimental results show that, relative to the conventional Gaussian heat source model, the proposed Gaussian mixture heat source model effectively captures the rapid heat-transfer process associated with water cooling and reduces the temperature prediction error in the water-cooled region from 200 ℃ to 20 ℃. When combined with the material hardening model, the maximum prediction deviations of transverse and longitudinal deformation are reduced to 2.0% and 1.6%, respectively. The proposed method provides a reliable technical basis for high-precision ship manufacturing.

line heating  /  numerical simulation  /  Gaussian mixture heat source model  /  strain hardening model
张保柱, 刘凯, 叶金蕊, 齐智昊, 闫安石, 王兴华. 基于高斯混合热源模型的船用双曲板水火工艺仿真方法. 船舶力学, 2026 , 30 (7) : 1173 -1184 . DOI: 10.3969/j.issn.1007-7294.2026.07.011
Bao-zhu ZHANG, Kai LIU, Jin-rui YE, Zhi-hao QI, An-shi YAN, Xing-hua WANG. Simulation analysis of line heating for marine double curvature plates based on Gaussian mixture heat source model[J]. Journal of Ship Mechanics, 2026 , 30 (7) : 1173 -1184 . DOI: 10.3969/j.issn.1007-7294.2026.07.011
Year 2026 volume 30 Issue 7
4
2
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doi: 10.3969/j.issn.1007-7294.2026.07.011
  • Receive Date:2025-11-10
  • Online Date:2026-11-03
  • Published:2026-07-15
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  • Received:2025-11-10
Affiliations
    1School of Materials Science and Engineering, China University of Petroleum (East China), Qingdao 266000, China
    2School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100190, China
    3Jiangsu Automation Research Institute, Lianyungang 222006, China
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表12种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)
属
Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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