Piecewise Fifth Order Spline Interpolation for Line Heating Forming Process

A fifth order piecewise spline interpolation model has been developed for computing the evolving geometry of a plate deformed by line heating thermal gradients. 3D formulations are presented and applied to continuously derivable geometries to demonstrate the capability of the methodology. Then the developed formulation is used to form gradually, with a sequence of heating lines, a 3D shape from an initially flat plate. The geometric results obtained from finite element simulations with three heating lines are used to illustrate where heating lines should be applied on a flat plate to achieve the intended geometry of a workpiece. Furthermore, it is shown that applying the developed piecewise fifth order spline interpolation model to the same flat plate produces results very close to the ones obtained from the thermal structural FE simulations.