An analytical model based on the similarity in temperature distributions in laser forming

Laser forming of a metal plate involves a complex thermoplastic process. To accurately control the deformation of a metal plate, its temperature distribution must be obtained first. In this paper, three-dimensional finite element method simulations of the temperature field that account for the temperature dependence of the thermal properties of the materials were carried out. By defining a dimensionless temperature T* and a special Y-coordinate Y*, we found that temperature distributions in the Y′ direction are similar for different thicknesses. An analytical model of the temperature of the high-temperature zone in the Y′ direction is derived for the first time based on the similarity of temperature distributions and data obtained from regression analysis. The comparison of analytical and numerical results shows good agreement with respect to temperature distributions. This investigation is of significance for the prediction of a deformation field in future works.