Full Article - Open Access.

Idioma principal

A DIFFUSE-MORPHING ALGORITHM FOR SHAPE OPTIMIZATION

Raghavan, Balaji; Breitkopf, Piotr; Villon, Pierre;

Full Article:

Shape optimization typically involves geometries characterized by several dozen design variables and a possibly high number of explicit/implicit constraints restricting the design space to admissible shapes. In this work, instead of working with parametrized CAD models, the idea is to interpolate between admissible instances of finite element/CFD meshes. We show that a properly chosen surrogate model can replace the numerous geometry-based design variables with a more compact set permitting a global understanding of the admissible shapes spanning the design domain, thus reducing the size of the optimization problem. To this end, we present a two-level mesh parametrization approach for the design domain geometry based on Diffuse Approximation in a properly chosen locally linearized space, and replace the geometry-based variables with the smallest set of variables needed to represent a manifold of admissible shapes for a chosen precision. We demonstrate this approach in the problem of designing the section of an A/C duct to maximize the permeability evaluated using CFD.

Full Article:

Palavras-chave: Model reduction, CFD, Diffuse Approximation, rasterization,

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18293

Referências bibliográficas
  • [1] Berkooz, G., Holmes, P., Lumley, J.L., “The proper orthogonal decomposition in the analysis of turbulent flows”. Annu Rev Fluid Mech 25(1), 539-575, 1993.
  • [2] Bregler, C., Omohundro, S.M., “Nonlinear image interpolation using manifold learning” Neural Information Processing Systems 973-980, 1995.
  • [3] Breitkopf, P.,“An algorithm for construction of iso-valued surfaces for finite elements. Engineering with Computers 14(2), 146-149, 1998.
  • [4] Breitkopf, P., Naceur, H., Rassineux, A., Villon, P., “Moving least squares response surface approximation: Formulation and metal forming applications” emphComputers and Structures 83(17-18), 1411-1428, 2005.
  • [5] Bui-Thanh, T., Willcox, K., Ghattas, O., van Bloemen Waanders, B., “Goal-oriented, model-constrained optimization for reduction of large-scale systems” Journal of Computational Physics 224(2), 880 -896, 2007.
  • [6] Canny, J., “A computational approach to edge detection” IEEE Transactions on Pattern Analysis and Machine Intelligence 8(6), 679-698, 198
  • [7] Carlberg, K., Farhat, C., “A compact proper orthogonal decomposition basis for optimization-oriented reduced-order models” Proceedings of the12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference Victoria, Canada, 2008.
  • [8] Carlberg, K., Farhat, C., “A low-cost, goal-oriented compact proper orthogonal decomposition basis for model reduction of static systems” emphInternational Journal for Numerical Methods in Engineering 86(3), 381-402, 2010.
  • [9] Chappuis, C., Rassineux, A., Breitkopf, P., Villon, P., “Improving surface remeshing by feature recognition” Engineering with Computers 20(3), 202209, 2004.
  • [10] Chatterjee, A., “An introduction to the proper orthogonal decomposition” Current Science, Special Section: Computational Science 78(7), 808-817, 2005.
  • [11] Coelho, R.F., Breitkopf, P., Knopf-Lenoir, C., “Bi-levelmodel reduction for coupled problems” Int J Struc Multidisc Optim 39(4), 401-418, 2009.
  • [12] Cordier, L., El Majd, B.A., Favier, J., “Calibration of pod reduced order models using tikhonov regularization” International Journal for Numerical Methods in Fluids 63(2), 269-296, 2010.
  • [13] Couplet, M., Basdevant, C., Sagaut, P., “Calibrated reduced-order pod-galerkin system for fluid flow modeling” Journal of Computational Physics 207(1), 192-220, 2005.
  • [14] Dulong, J.L., Druesne, F., Villon, P., “A model reduction approach for real-time part deformation with nonlinear mechanical behavior” International Journal on Interactive Design and Manufacturing 1(4), 229-238, 2007.
  • [15] Kaufman, A., Cohen, D., Yagel, R., “Volume graphics” IEEE Computer 26(7), 51-64, 1993.
  • [16] Larsson, F., Diez, P., Huerta, A., “A flux-free a posteriori error estimator for the incompressible stokes problem using a mixed fe formulation” AIAA Journal 199(37-40), 2383- 2402, 2010.
  • [17] Launder, B.E., Spalding, D.B., “The numerical computation of turbulent flows” Computer Methods in Applied Mechanics and Engineering 3(2), 269-289, 1974.
  • [18] LeGresley, P., Alonso, J., “Airfoil design optimization using reduced order models based on proper orthogonal decomposition” Proceedings of the Fluids 2000 Conference and Exhibit Denver, CO, 2000.
  • [19] Mahdavi, A., Balaji, R., Frecker, M., Mockensturm, E., “Topology optimization of 2d continua for minimum compliance using parallel computing” Int J Struc Multidisc Optim 32(2), 121-132, 2005.
  • [20] Nayroles, B., Touzot, G., Villon, P., “Generalizing the finite element method: diffuse approximation and diffuse elements” Computational Mechanics 10(5), 307-318, 1992.
  • [21] Raghavan, B., Breitkopf, P., “Asynchronous evolutionary shape optimization using highquality surrogates: application to an air-conditioning duct.” Engineering with Computers doi: 10.1007/s00366-012-0263-0
  • [22] Rodriguez, H.C., “Shape optimal design of elastic bodies using a mixed variational formulation” Computer Methods in Applied Mechanics and Engineering 69(1), 29-44, 1988.
  • [23] Sahan, R.A., Gunes, H., Liakopoulos, A., “A modeling approach to transitional channel flow” Computers and Fluids 27(1), 121-136, 1998.
  • [24] Sigmund, O., “A 99 line topology optimization code in MATLAB” Int J Struc Multidisc Optim 21(2), 120-127, 2001.
  • [25] Sofia, A.Y.N., Meguid, S.A., Tan, K.T., “Shape morphing of aircraft wing: Status and challenges” Materials Andamp; Design 31(3), 1284-1292, 2010.
  • [26] Willcox, K., Peraire, J., “Balanced model reduction via the proper orthogonal decomposition” AIAA Journal 40(11), 2323-2330, 2002.
  • [27] Xiao, M., Breitkopf, P., Coelho, R.F., Knopf-Lenoir, C., Villon, P., “Enhanced POD projection basis with application to shape optimization of car engine intake port” Int J Struc Multidisc Optim doi: 10.1007/s00158-011-0757-1
Como citar:

Raghavan, Balaji; Breitkopf, Piotr; Villon, Pierre; "A DIFFUSE-MORPHING ALGORITHM FOR SHAPE OPTIMIZATION", p. 1181-1200 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18293

últimos 30 dias | último ano | desde a publicação


downloads


visualizações


indexações