Line heating is an essential process in the formation of ship hull plates with a complex curvature. Electromagnetic induction heating is widely used in the line heating process. In electromagnetic induction heating, the shape of the coil and the air gap between the inductor and workpiece could influence the heat source distribution. Moreover, in the line heating process, the change of curvature of the plate will cause a change of the air gap of the inductor. Magnetic thermal coupling calculation is an effective method for simulating induction heating. This paper used the finite element method to calculate the distribution of heat sources in different initial plate curvatures and coil widths. The changes in heat source distribution and its laws were investigated. The results show that when the coil width is less than 100 mm, the effect of plate curvature on heat source distribution and strain distribution is not apparent; when the coil width is greater than 100 mm, the plate curvature has a visible effect on the heat generation distribution. In the case of a curvature increasing from 0 to 1 and a coil width equal to 220 mm, the Joule heat generation in the center of the heating area is reduced by up to 21%.

Integrated heating and mechanical rolling forming (IHMRF) has recently been introduced for manufacturing complex curvature hull plates. It fabricates the target curved plate by sequential loading along the multipath. Accurate and efficient prediction of the deformation of the plate is the basis for developing the process planning and ensuring the quality of the forming. The inherent-strain method is ideal for this purpose, but its prediction accuracy needs to be improved. This paper proposes a multipath process-based inherent-strain method (MPISM), which considers the effect of the sequential loading process of the multipath on plate deformation. First, the effect of loading paths near the plate edge was investigated, which in turn clarified the rationale for obtaining the inherent strain only in the plate center. Secondly, a strain correction strategy was established by analyzing the variation pattern of the inherent strain caused by the crossing or proximity of the previous path and the subsequent path. This allowed the effects of the loading process to be taken into account in the elastic analysis. Based on the plate-and-shell theory, the idea of an equivalent inherent strain distribution is also presented. This makes the loading of inherent strains more accurate in the elastic finite-element model. MPISM predictions and experimental results show good agreement. Compared with the thermo-elastic–plastic finite element method, the MPISM substantially improves efficiency while maintaining accuracy. Compared with the original inherent-strain method, the MPISM is more accurate in terms of deformation magnitude prediction.

Integrated heat and roll forming (IHMRF) is a process that uses thermal and mechanical loads to produce localized plastic strains in plates to form complex curvature hull plates. The magnitude of the resulting plastic strain depends mainly on the following forming parameters: the machining parameters (power of the heat source, speed of the heat source, and the forming depth of the rollers), the thickness of the plate, and the thermo-physical and mechanical properties of the plate. Finding the correspondence between the plastic strain and forming parameters is the key to selecting the appropriate machining parameters for forming. A data-driven approach is ideal for this purpose. However, due to the characteristics of the IHMRF process, the forming process involves a large number of variables, and different materials have different temperature-dependent yield strengths. These high-dimensional input characteristics create a conflict between the required number of samples and the model training requirements. This paper presents a physically informed data-driven (PIDD) approach for modeling the relationship between forming parameters and plastic strains in IHMRF. Based on dimensional analysis and domain knowledge, the proposed method derives the basic thermal and mechanical relationships between the forming parameters, obtaining a much smaller number of physical parameters. These physical parameters are expressions of the physical knowledge of forming in low-dimensional space. Using the physical parameters yields higher accuracy on fewer sample data points than directly using the forming parameters as input features. Furthermore, the models trained on a variety of commonly used materials and plate thicknesses achieved comparable accuracy to the numerical simulation with unseen materials and plate thicknesses. Experimental and numerical simulations further verify the effectiveness of the proposed method by machining plates of various materials to the same shape.

Line heating processes play a significant role in the fabrication of structural steel components, particularly in industries such as shipbuilding, aerospace, and automotive manufacturing, where dimensional accuracy and minimal defects are critical. Traditional methods, such as the finite element method (FEM) simulations, offer high-fidelity predictions but are hindered by prohibitive computational latency and the need for case-specific re-meshing. This study presents a physics-aware, data-driven neural network that delivers fast, high-fidelity temperature predictions across a broad operating envelope. Each spatiotemporal point is mapped to a one-dimensional feature vector. This vector encodes thermophysical properties, boundary influence factors, heatsource variables, and timing variables. All geometric features are expressed in a path-aligned local coordinate frame, and the inputs are appropriately normalized and nondimensionalized. A lightweight multilayer perceptron (MLP) is trained on FEM-generated induction heating data for steel plates with varying thickness and randomized paths. On a hold-out test set, the model achieves MAE = 0.60 °C, RMSE = 1.27 °C, and R2 = 0.995, with a narrow bootstrapped 99.7% error interval (−0.203 to −0.063 °C). Two independent experiments on an integrated heating and mechanical rolling forming (IHMRF) platform show strong agreement with thermocouple measurements and demonstrate generalization to a plate size not seen during training. Inference is approximately five orders of magnitude (~10⁵) faster than FEM, enabling near-real-time full-field reconstructions or targeted spatiotemporal queries. The approach supports rapid parameter optimization and advances intelligent line heating operations.

The surface-flattening process has many applications in industries such as shipbuilding. Curved surfaces in the industry are usually formed from flat surfaces, so the target surface needs to be flattened to obtain its corresponding initial shape. In addition, the surface flattening process obtains the inherent strain distribution required in forming. Different forming methods in the plate forming process will produce different membrane deformations, such as shrinkage in the line heating and tensile in the roller forming. Therefore, different surface-flattening methods should be used to obtain the inherent strain distribution suitable for different forming methods. This paper proposes a method to perform the surface flattening using the finite element method and constrain the membrane strain generated in the flattening deformation by modifying the material constitutive relationship. Using a dual modulus material constitutive model in membrane deformation makes the surface more inclined to deform at locations with less stiffness during the flattening process. This method yields predominantly tensile or compressive membrane strain without changing the bending strain. By modifying the material model, this method can control the compressive strain region and the principal strain direction. The results of the proposed method applying to different surface shapes and its application in the surface-forming process are given in this paper.

Curved plate forming is essential in shipbuilding but traditionally relies on manual methods with low efficiency. Achieving automation in curved plate forming requires robust methods to generate processing solutions. This paper introduces a novel method for deriving the processing routes and strain distributions necessary to form complex curve plate using integrated heating and mechanical rolling forming equipment. The key aspects of this method include analyzing the target surface and solving for the required processing strains based on finite element analysis, discretizing the strain paths and refining them into engineering-feasible processing routes, deriving processing schemes from the calculated strains, and predicting and validating the processing schemes using the inherent strain method. The method is validated by applying it to typical surface of ship hull plates. Key outcomes demonstrate the method’s effectiveness and applicability: (1) The proposed method effectively establishes a quantitative relationship between the target surface geometry, processing routes, and the required processing strains. (2) By analyzing various target surface cases, the method demonstrates wide applicability. Standardized procedures can be applied to different surface shapes to derive the necessary processing routes and strains, thereby laying a solid foundation for the automation of curved hull plate forming. (3) Experimental forming tests on typical curved surfaces confirm that the processing schemes based on the proposed strain generation method can reliably achieve the desired geometries, showcasing the method’s capability to guide practical forming processes. The comparison between the formed and target shapes shows that the processing deviation of the schemes generated by this method remains within 5 mm, demonstrating high accuracy.