Experimental observation have shown that the heat induced deformation produced by crossed heating lines is significantly affected by the crossing especially at the cross area. Aiming to clarify this effect, through the inherent deformation theory, we numerically clarify and quantify the influence of crossed heating lines on heat induced deformation. First, it is demonstrated that the heat induced deformation of single heating lines may not be super-imposed upon one another to approximate the inherent deformation of the resultant curved surface. Then, a method to accurately predict the heat induced deformation produced by crossed heating lines is proposed.
Line heating is an effective method to form curved shell plates with complex three-dimensional geometry. However, line heating process is mostly dependent on the skill of hard-to-find experienced workers. Therefore, automation is highly required. At present, no automatic system that can accurately form a plate without significant human help has been developed. The main reason of this is that the mechanism of plate forming using the line heating method is highly complicated for analysis with simple analytical models. The difficulty comes from the material and the geometrical nonlinearities as well as the variation of temperature in the spatial and time domains. The study of thermal-elastic-plastic behavior of the line heating process has received attention of many researchers for about the past 40 years.
The first attempt to use an analytical approach to simulate the line heating process was by Suhara (1958) and Iwasaki, Hirabe, Taure, Hujikura and Shiota (1975). They modeled the problem using the beam theory and the solution was obtained analytically. Due to these restrictions, their model can deal only with ideal situations. Iwamura and Rybicki (1973) also analyzed the process using a beam model normal to the heating line, employing the finite-difference approach to solve the problem.
