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Abstract
A simple mathematical method for the estimation of the optimum heat inputs to make the temperature field coincide with a requirement during arc welding has been developed. The optimisation problem in the present work means the objective function which is defined as the difference between the calculated and required temperatures. An analytical solution of the heat flow equation is applied for the calculation of the temperature field in welding, and non-linear programming methods, i.e. the convex programming method and the steepest descent method, have been used to solve the objective function in the problem mathematically. It is concluded that both optimising methods are sufficient to determine the optimum heat input pattern in the case of gas tungsten arc (GTA) welding on thin plate and small sized pipe specimens. Furthermore, the applicability of the estimated optimum heat inputs is evaluated experimentally by bead on plate welding tests.