Adjoint-based optimization of thermo-fluid phenomena in welding processes

Volkov, Oleg; Protas, Bartosz; Liao, Wenyuan; Glander, Donn W.

doi:10.1007/s10665-009-9292-0

Cited by 21 publications

(22 citation statements)

References 22 publications

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“…The factor is given by the Fresnel absorption function F introduced in (4) which depends on the angle of incidence of the laser beam. Scaling of (32) and (33) proves (19)- (21). The kinematic boundary condition (22) can be deduced analogously as the one for Γ M by…”

Section: Model Derivationmentioning

confidence: 68%

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Analysis and optimal control for free melt flow boundaries in laser cutting with distributed radiation

Vossen

Hermanns

Schüttler³

2013

Z Angew Math Mech

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This work introduces a mathematical model for laser cutting taking account of spatially distributed laser radiation. The model involves two coupled nonlinear partial differential equations describing the interacting dynamical behaviors of the free boundaries of the melt during the process. The model will be investigated by linear stability analysis to study the occurence of ripple formations at the cutting surface. We define a measurement for the roughness of the cutting surface and introduce an optimal control problem for minimizing the roughness with respect to the laser beam intensity along the free melt surface. Necessary optimality conditions will be deduced. Finally, a numerical solution will be presented and discussed by means of the necessary conditions. physical considerations

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Section: Model Derivationmentioning

confidence: 68%

“…Optimization and optimal control of multi-phase problems governed by Navier-Stokes equations with free boundaries or phase transitions have been applied by, e.g., [1,6,15,21]. Since already a single numerical simulation of such a free boundary problem is a difficult issue, optimal control is a very challenging task.…”

Section: Introductionmentioning

confidence: 99%

Analysis and optimal control for free melt flow boundaries in laser cutting with distributed radiation

Vossen

Hermanns

Schüttler³

2013

Z Angew Math Mech

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“…The gradients actually used in minimization algorithm (14), namely the Sobolev gradients ∇ H 1 J and ∇ H 1 J α , can be obtained from (20) and (21) by identifying (16)- (17) with (19), and noting the arbitrariness of the shape perturbations ζ ∈ H 1 (0, L). Then, after integrating by parts and using the boundary conditions, we arrive at…”

Section: Gradient-based Minimization Approachmentioning

confidence: 99%

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

Peng¹,

Niakhai²,

Protas³

2013

SIAM J. Sci. Comput.

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This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a onedimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shapedifferential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.

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“…The temperature satisfies also the following specific boundary conditions on ∂ s (t) (see Refs. [3,8,9])…”

Section: Setting Of the Problemmentioning

confidence: 99%

Approximation and numerical realization of an optimal design welding problem

Chakib

Nachaoui

2013

Numerical Methods Partial

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In this article, we deal with the approximation of an optimal shape design approach for a free boundary problem modeling a welding process. We consider discretization of this problem based on linear finite elements. We prove the existence of discrete optimal solutions. This allows us to show the convergence result of a sequence of discrete solutions to the continuous one. Finally, methods for numerical realization are described and several examples have been carried out to illustrate the efficiency of the proposed approach.

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Adjoint-based optimization of thermo-fluid phenomena in welding processes

Cited by 21 publications

References 22 publications

Analysis and optimal control for free melt flow boundaries in laser cutting with distributed radiation

Analysis and optimal control for free melt flow boundaries in laser cutting with distributed radiation

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

Approximation and numerical realization of an optimal design welding problem

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