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Coupling structural optimization and trajectory optimization methods in additive manufacturing

Abstract : This work investigates path planning optimization for powder bed fusion additive manufacturing processes, and relates them to the design of the built part. The state of the art mainly studies trajectories based on existing patterns and, besides their mechanical evaluation, their relevance has not been related to the object’s shape. We propose in this work a systematic approach to optimize the path without any a priori restriction. The typical optimization problem is to melt the desired structure, without over-heating (to avoid thermally induced residual stresses) and possibly with a minimal path length. The state equation is the heat equation with a source term depending on the scanning path. Two physical 2-d models are proposed, involving temperature constraint: a transient and a steady state one (in which time dependence is removed). Based on shape optimization for the steady state model and control for the transient model, path optimization algorithms are developed. Numerical results are then performed allowing a critical assessment of the choices we made. To increase the path design freedom, we modify the steady state algorithm to introduce path splits. Two methods are compared. In the first one, the source power is added to the optimization variables and an algorithm mixing relaxation-penalization techniques and the control of the total variation is set. In a second method, notion of topological derivative are applied to the path to cleverly remove and add pieces. eventually, in the steady state, we conduct a concurrent optimization of the part’s shape and of the scanning path. This multiphysics optimization problem raises perspectives gathering direct applications and future generalizations.
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https://tel.archives-ouvertes.fr/tel-03106260
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Submitted on : Monday, January 11, 2021 - 4:33:30 PM
Last modification on : Tuesday, January 12, 2021 - 3:32:45 AM

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Mathilde Boissier. Coupling structural optimization and trajectory optimization methods in additive manufacturing. Optimization and Control [math.OC]. Institut Polytechnique de Paris, 2020. English. ⟨NNT : 2020IPPAX084⟩. ⟨tel-03106260⟩

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