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.
| 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 |