@article{(Open Science Index):https://publications.waset.org/pdf/10002296,
	  title     = {Line Heating Forming: Methodology and Application Using Kriging and Fifth Order Spline Formulations},
	  author    = {Henri Champliaud and  Zhengkun Feng and  Ngan Van LĂȘ and  Javad Gholipour},
	  country	= {},
	  institution	= {},
	  abstract     = {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.},
	    journal   = {International Journal of Mechanical and Mechatronics Engineering},
	  volume    = {9},
	  number    = {9},
	  year      = {2015},
	  pages     = {1623 - 1628},
	  ee        = {https://publications.waset.org/pdf/10002296},
	  url   	= {https://publications.waset.org/vol/105},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 105, 2015},
	}