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SSRN 2023年

作者： Bremer, Scholte J.L. Aarts, Ronald G.K.M. Römer, Gert-Willem R.B.E. Department of Mechanics of Solids Surfaces & Systems Faculty of Engineering Technology University of Twente Drienerlolaan 5 Enschede7522NB Netherlands Chair of Applied Mechanics and Data Analysis Department of Mechanics of Solids Surfaces & Systems Faculty of Engineering Technology University of Twente Drienerlolaan 5 Enschede7522NB Netherlands

In high power laser material processing technologies, such as laser welding, laser cladding or laser surface treatment, tailoring the spatial intensity profile of the laser beam, popularly known as beam shaping, is used to optimise the processing results in terms of processing quality and/or production rate. To allow for dynamic beam shaping — i.e. tailoring the intensity profile during processing — dynamic optics in the optical setup are required. Current dynamic optical devices suitable to shape a single high power laser beam are Galvanometer Scanners and Deformable Mirrors. However, an objective comparison of the beam shaping capabilities, such as resolution and shaping performance, of these beam shaping devices is lacking. This work proposes a novel mathematical framework to analyse and compare the two beam shaping concepts. This framework is used to quantify beam shaping capabilities as function of relevant laser setup parameters. Next, using the mathematical framework, the performance of the Galvanometer Scanner and Deformable Mirror is simulated when targeting a splitted laser beam, creating a horseshoe shaped intensity profile and creating a square uniform profile. Results show that, in practice, both devices will be able to create these three desired laser intensity profiles in the focal plane, with similar small average errors when compared to the desired beam shape. However, the error distributions show differences which are characteristic for the physical limitations of each individual beam shaping device. © 2023, The Authors. All rights reserved.

关键词： Laser materials processing

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Bayesian stochastic multi-scale analysis via energy considerations

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Advanced Modeling and Simulation in Engineering Sciences 2020年第1期7卷 1-35页

作者： Sarfaraz, Muhammad S. Rosić, Bojana V. Matthies, Hermann G. Ibrahimbegović, Adnan Institute of Scientific Computing Technische Universität Braunschweig Braunschweig 38106 Germany Chair for Applied Mechanics and Data Analysis University of Twente Drienerlolaan 5 Enschede 7522 NB Netherlands Chair for Computational Mechanics Université de Technologie de Compiègne Compiègne 60205 France

Multi-scale processes governed on each scale by separate principles for evolution or equilibrium are coupled by matching the stored energy and dissipation in line with the Hill-Mandel principle. We are interested in cementitious materials, and consider here the macro- and meso-scale behaviour of such a material. The accurate representations of stored energy and dissipation are essential for the depiction of irreversible material behaviour, and here a Bayesian approach is used to match these quantities on different scales. This is a probabilistic upscaling and as such allows to capture, among other things, the loss of resolution due to scale coarsening, possible model errors, localisation effects, and the geometric and material randomness of the meso-scale constituents in the upscaling. On the coarser (macro) scale, optimal material parameters are estimated probabilistically for certain possible behaviours from the class of generalised standard material models by employing a nonlinear approximation of Bayes’s rule. To reduce the overall computational cost, a model reduction of the meso-scale simulation is achieved by combining unsupervised learning techniques based on a Bayesian copula variational inference with functional approximation forms. © 2020, The Author(s).

关键词： Bayesian updating Gauss–Markov–Kalman filter Upscaling

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