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2019 | OriginalPaper | Chapter

Finite Element Methods for Parabolic Problems with Time-Dependent Domains: Application to a Milling Simulation

Authors : Carsten Niebuhr, Alfred Schmidt

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

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Abstract

We consider the finite element discretization of PDEs on time-dependent domains. Approximation of boundary conditions is one of the crucial aspects, as well as an appropriate approach to adaptive mesh refinement. We present some numerical test results and the application to the thermomechanical simulation of a milling process, where the domain changes in time due to material removal.

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previous chapter Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation
next chapter Numerical Investigation of the Conditioning for Plane Wave Discontinuous Galerkin Methods
Literature
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I. Babuška, J. Chleboun, Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions. Math. Comput. 71, 1339–1370 (2001)MathSciNetCrossRef
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E. Bänsch, Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math. 88, 203–235 (2001)MathSciNetCrossRef
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B. Denkena, A. Schmidt, J. Henjes, D. Niederwestberg, C. Niebuhr, Modeling a Thermomechanical NC-Simulation, in Proceedings of 14th CIRP Conference on Modeling of Machining Operations (CIRP CMMO), Procedia CIRP, vol. 8 (2013), pp. 69–74
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B. Denkena, A. Schmidt, P. Maaß, D. Niederwestberg, C. Niebuhr, J. Vehmeyer, Prediction of temperature induced shape deviations in dry milling, in Proceedings of 15th CIRP Conference on Modeling of Machining Operations (CIRP CMMO), Procedia CIRP, vol. 31 (2015), pp. 340–345
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B. Denkena, P. Maaß, A. Schmidt, D. Niederwestberg, J. Vehmeyer, C. Niebuhr, P. Gralla, Thermomechanical deformation of complex workpieces in milling and drilling processes, in Thermal Effects in Complex Machining Processes - Final Report of the DFG Priority Program, ed. by D. Biermann, F. Hollmann. Springer LNPE Series, vol. 1480 (Springer, Berlin, 2017), pp. 219–250
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A. Schmidt, E. Bänsch, M. Jahn, A. Luttmann, C. Niebuhr, J. Vehmeyer, Optimization of engineering processes including heating in time-dependent domains, in System Modeling and Optimization, ed. by L. Bociu, J.A. Desideri, A. Habbal. Springer IFIP AICT Series, vol. 494 (Springer, Berlin, 2017), pp. 452–461
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A. Schmidt, C. Niebuhr, D. Niederwestberg, J. Vehmeyer, Modelling, simulation, and optimization of thermal deformations from milling processes, in Progress in Industrial Mathematics at ECMI 2016, ed. by P. Quintela, P. Barral, D. Gomez, F.J. Pena, J. Rodriguez, P. Salgado, M.E. Vazquez-Mendez. Springer Mathematics in Industry Series, vol. 26 (Springer, Berlin, 2017), pp. 337-343
Metadata
Title
Finite Element Methods for Parabolic Problems with Time-Dependent Domains: Application to a Milling Simulation
Authors
Carsten Niebuhr
Alfred Schmidt
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_43

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