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%.
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.
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