We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coefficients depend on the temperature, this leads to a quasi‐linear parabolic partial differential equation. It is our goal to prevent solidification cracking. We address this problem by means of optimal control. It is the intensity profile of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidification interface need to be properly penalized in order to deal with and avoid cracking phenomena. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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