Integration of PGD-virtual charts into an engineering design process

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• 作者：Amaury Courard ; David Néron ; Pierre Ladevèze ; Ludovic Ballere
• 关键词：Model reduction ; PGD ; Geometric parameters ; Virtual chart ; Shape optimisation
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：57
• 期：4
• 页码：637-651
• 全文大小：1,309 KB
• 参考文献：1.Aguado JV, Huerta A, Chinesta F, Cueto E (2015) Real-time monitoring of thermal processes by reduced-order modeling. Int J Numer Methods Eng 102(5):991–1017MathSciNet CrossRef
  2.Alfaro I, González D, Bordeu F, Leygue A, Ammar A, Cueto E, Chinesta F (2014) Real-time in silico experiments on gene regulatory networks and surgery simulation on handheld devices. J Comput Surg 1(1):1CrossRef
  3.Ammar A, Huerta A, Chinesta F, Cueto E, Leygue A (2014) Parametric solutions involving geometry: a step towards efficient shape optimization. Comput Methods Appl Mech Eng 268:178–193MathSciNet CrossRef MATH
  4.Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids: Part II: Transient simulation using space-time separated representations. J Non-Newton Fluid Mech 144(2–3):98–121CrossRef MATH
  5.Ammar A, Zghal A, Morel F, Chinesta F (2015) On the space-time separated representation of integral linear viscoelastic models. Comptes Rendus de Mécanique 343(4):247–263CrossRef
  6.Barrault MYM, Nguyen N, Patera A (2004) An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de l’Académie des Sciences Paris 339:667–672MathSciNet MATH
  7.Bernoulli C (1836) Vademecum des Mechanikers. J. G. Cotta, Stuttgart und TübingenMATH
  8.Bognet B, Leygue A, Chinesta F, Bordeu F (2012) Parametric shape and material simulations for optimized parts design. In: ASME 2012 11th biennial conference on engineering systems design and analysis, American Society of Mechanical Engineers, pp 217–218
  9.Chinesta F, Keunings R, Leygue A (2014) The Proper generalized decomposition for advanced numerical simulations: a Primer., SpringerBriefs in Applied Sciences and TechnologySpringer, ChamCrossRef MATH
  10.Chinesta F, Ladevèze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18(4):395–404CrossRef
  11.Chinesta F, Leygue A, Bordeu F, Aguado J, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20(1):31–59MathSciNet CrossRef
  12.Cremonesi M, Néron D, Guidault PA, Ladevèze P (2013) A PGD-based homogenization technique for the resolution of nonlinear multiscale problems. Comput Methods Appl Mech Eng 267:275–292MathSciNet CrossRef MATH
  13.De Lathauwer L, De Moor B, Vandewalle J (2000) A multilinear singular value decomposition. SIAM J Matrix Anal Appl 21(4):1253–1278MathSciNet CrossRef MATH
  14.González D, Alfaro I, Quesada C, Cueto E, Chinesta F (2015) Computational vademecums for the real-time simulation of haptic collision between nonlinear solids. Comput Methods Appl Mech Eng 283(1):210–223CrossRef
  15.Gunzburger M, Peterson J, Shadid J (2007) Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. Comput Methods Appl Mech Eng 196:1030–1047MathSciNet CrossRef MATH
  16.Ladevèze P (1999) Nonlinear computationnal structural mechanics—new approaches and non-incremental methods of calculation. Springer, New YorkMATH
  17.Ladevèze P (2013) The Virtual chart concept in computational structural mechanics (plenary lecture). In: COMPLAS XII, 3–5 Sept 2013, Barcelona (Spain)
  18.Ladevèze P (2014) PGD in linear and nonlinear Computational Solid Mechanics. In: Separated Representations and PGD-Based Model Reduction, Springer, pp 91–152
  19.Lieu T, Farhat C, Lesoinne A (2006) Reduced-order fluid/structure modeling of a complete aircraft configuration. Comput Methods Appl Mech Eng 195(41–43):5730–5742CrossRef MATH
  20.Maday Y, Ronquist E (2004) The reduced-basis element method: application to a thermal fin problem. J Sci Comput 26(1):240–258MathSciNet MATH
  21.Manzoni A, Quarteroni A, Rozza G (2012) Model reduction techniques for fast blood flow simulation in parametrized geometries. Int J Numer Methods Biomed Eng 28(6–7):604–625MathSciNet CrossRef
  22.Néron D, Ben Dhia H, Cottereau R (2015) A decoupled strategy to solve reduced-order multimodel problems in the PGD and Arlequin frameworks. Comput Mech. doi:10.​1007/​s00466-015-1236-0
  23.Néron D, Boucard PA, Relun N (2015) Time-space PGD for the rapid solution of 3D nonlinear parametrized problems in the many-query context. Int J Numer Methods Eng 103(4):275–292
  24.Néron D, Dureisseix D (2008) A computational strategy for poroelastic problems with a time interface between coupled physics. Int J Numer Methods Eng 73(6):783–804
  25.Néron D, Ladevèze P (2010) Proper generalized decomposition for multiscale and multiphysics problems. Arch Comput Methods Eng 17(4):351–372MathSciNet CrossRef MATH
  26.Nouy A (2010) A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Comput Methods Appl Mech Eng 199(23):1603–1626MathSciNet CrossRef MATH
  27.Patera AT, Rozza G (2006) Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. Version 1.0. Copyright MIT 2006, to appear in (tentative rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering. http://​augustine.​mit.​edu
  28.Raghavan B, Breitkopf P, Tourbier Y, Villon P (2013) Towards a space reduction approach for efficient structural shape optimization. Struct Multidiscip Optim 48(5):987–1000CrossRef
  29.Relun N, Néron D, Boucard PA (2013) A model reduction technique based on the PGD for elastic-viscoplastic computational analysis. Comput Mech 51(1):83–92MathSciNet CrossRef MATH
  30.Rozza G, Veroy K (2007) On the stability of the reduced basis method for Stokes equations in parametrized domains. Comput Methods Appl Mech Eng 196(7):1244–1260MathSciNet CrossRef MATH
  31.Ryckelynck DFC, Cueto E, Ammar A (2006) On the a priori model reduction: overview and recent developments. Arch Comput Methods Eng 13(1):91–128MathSciNet CrossRef MATH
  32.Zlotnik S, Díez P, Modesto D, Huerta A (2015) Proper generalized decomposition of a geometrically parametrized heat problem with geophysical applications. Int J Numer Methods Eng 103(10):737–758MathSciNet CrossRef
  
• 作者单位：Amaury Courard (1)
  David Néron (2)
  Pierre Ladevèze (2)
  Ludovic Ballere (1)
  
  1. AIRBUS Defence & Space, B.P. 20011 33165, Saint-Médard-en-Jalles Cedex, France
  2. LMT, ENS Cachan, CNRS, Université Paris-Saclay, 61 avenue du Président Wilson, 94235, Cachan Cedex, France
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

This article deals with the efficient construction of approximations of fields and quantities of interest used in geometric optimisation of complex shapes that can be encountered in engineering structures. The strategy, which is developed herein, is based on the construction of virtual charts that allow, once computed offline, to optimise the structure for a negligible online CPU cost. These virtual charts can be used as a powerful numerical decision support tool during the design of industrial structures. They are built using the proper generalized decomposition (PGD) that offers a very convenient framework to solve parametrised problems. In this paper, particular attention has been paid to the integration of the procedure into a genuine engineering design process. In particular, a dedicated methodology is proposed to interface the PGD approach with commercial software.