The Determination of Heating Shapes and Locations for Triangle Heating

Thermal forming is a method to form a curved plate by inducing local shrinkage and angular distortion through heating and cooling. In this approach, two different methods are available: line heating and triangle heating. Among them, this paper discusses triangle heating and presents algorithms for determining heating shapes and locations. The heating shape is determined by using the in-plane strain distributions, which are calculated by nonlinear kinematics analysis between the designed and initial shapes, field survey results, and mechanics based on the neutral axis. To predict the angular distortion and shrinkage in various heating conditions, a functional relation of residual deformations is formulated. For the formulation, multivariate analysis and multiple regression techniques are used with data obtained from experiments of unit triangle heating and numerical analysis. Using the determined heating shapes and the functional relation for the residual deformations, a correct triangle heating position is determined by an algorithm, which can predict qualitatively correct angular distortion and shrinkage in the interior and quantitatively correct distortion values on the edge. Finally, analytic verification of the proposed method has been done by applying the method to a convex type plate used in the field. The proposed work can be used for automation of curved plate fabrication in the shipyards.