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Pré-Publication, Document De Travail Année : 2023

Optimal control of the temperature by the laser path and the thermal treatment time in selective laser melting process

Résumé

Additive manufacturing by laser fusion on metal oxides powder bed such as e.g. alumina (Al2O3) or aluminium titanate (Al2T iO5) has developed considerably in the last few years and allows today the production of a wide range of complex objects. The mathematical problem considered is to control the temperature inside some part Ω of a powder layer. This phenomenon is governed by a parabolic initial boundary value problem with a heat source corresponding to the laser trajectory on some part of the boundary ∂Ω. The main questions concern the optimization of the trajectories scanned by the laser on the boundary ∂Ω according to given criteria: imposing that during the thermal process the temperature reaches a melting value in the structure to be built, a desired temperature distribution at the end of the thermal process, minimizing the thermal gradients, all this in the shortest possible thermal treatment time. To achieve this goal, we start by proving the existence of an optimal control, followed by first order necessary optimality conditions. Finally, we establish a second order sufficient optimality condition. Keywords. Optimal control problems, parabolic equations, heat equations with moving source, trajectories, time of thermal treatment, cost functionals, existence of an optimal control, adjoint problem, first order necessary optimality conditions, second order sufficient optimality conditions.
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Dates et versions

hal-04316237 , version 1 (30-11-2023)

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  • HAL Id : hal-04316237 , version 1

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Hiba Hmede, Serge Nicaise, Luc Paquet, Ali Wehbe. Optimal control of the temperature by the laser path and the thermal treatment time in selective laser melting process. 2023. ⟨hal-04316237⟩
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