Tangent stiffness for nonlinear heat transfer and its application to additive manufacturing

Abstract

Prediction-correction method is commonly employed in the solution of nonlinear heat transfer equation with temperature dependent thermophysical parameters arising in various engineering problems such as additive manufacturing of metal components. However, the stiffness of such conventional method is secant rather than tangent and thus it only results in suboptimal rate of convergence in Newton's iteration. In this paper, tangent stiffness for nonlinear heat transfer is proposed through the linearization of the weak form and an additional term presents which disappears in the conventional prediction-correction method. Numerical results show that the solution with the proposed tangent stiffness converges much faster than that with secant stiffness and approximately only half of the iteration steps are needed. Especially, in the case that the thermal conductivity varies dramatically with the temperature, the conventional method diverges whereas the tangent stiffness still shows quite good convergence. Application of the proposed method to the modeling of heat transfer in additive manufacturing (AM) process is presented and the obtained temperature results agree quite well with the existing experimental studies. It is worth mentioning that almost half of CPU time is saved due to the application of the proposed tangent stiffness. This saving is of great significance for modeling the AM process of complicated components, which is usually very time-consuming.