%0 Journal Article %A Henri Champliaud and Zhengkun Feng and Ngan Van LĂȘ and Javad Gholipour %D 2015 %J International Journal of Mechanical and Mechatronics Engineering %B World Academy of Science, Engineering and Technology %I Open Science Index 105, 2015 %T Line Heating Forming: Methodology and Application Using Kriging and Fifth Order Spline Formulations %U https://publications.waset.org/pdf/10002296 %V 105 %X In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades. %P 1623 - 1628