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Slides about shape optimization by the levelset method.



  • G. Allaire, F. Jouve, G. Michailidis, Thickness control in structural optimization via a level set method, to appear in SMO. HAL preprint: hal-00985000 (April 2014).

  • G. Allaire, G. Delgado, Stacking sequence and shape optimization of laminated composite plates via a level-set method, submitted. HAL preprint: hal-01164929 (June 2015).

  • G. Allaire, Ch. Dapogny, A deterministic approximation method in shape optimization under random uncertainties, HAL preprint: hal-01160256v1 (June 2015).

  • Th. Abballe, M. Albertelli, G. Allaire, A. Caron, Ph. Conraux, L. Dall'Olio, Ch. Dapogny, C. Dobrzynski, B. Jeannin, F. Jouve, D. Lachouette, Th. Le Sommer, K.Maquin, G. Michailidis, M. Siavelis, V. Srithammavanh, RODIN project, topology optimization 2.0 ?, Actes du congrès "Simulation" de la Société des Ingénieurs de l'Automobile (SIA), Montigny le Bretonneux, 18-19 mars 2015. Preprint here.

  • G. Allaire, A review of adjoint methods for sensitivity analysis, uncertainty quantification and optimization in numerical codes, Actes du congrès "Simulation" de la Société des Ingénieurs de l'Automobile (SIA), Montigny le Bretonneux, 18-19 mars 2015. Preprint here. Reprinted in the journal "Ingénieurs de l'automobile", no. 836, pp.33-36, July 2015.

  • G. Allaire, Ch. Dapogny, P. Frey, Shape optimization with a level set based mesh evolution method, CMAME 282, 22-53 (2014). HAL preprint: hal-00801704, version 1 (January 2014).

  • N. Vermaak, G. Michailidis, G. Parry, R. Estevez, G. Allaire, Y. Bréchet, Material Interface Effects on the Topology Optimization of Multi-Phase Structures Using A Level Set Method, SMO Vol. 50, no. 4, 623-644 (2014). HAL preprint: hal-01072223, version 1 (October 2014).

  • G. Allaire, Ch. Dapogny, A linearized approach to worst-case design in parametric and geometric shape optimization, M3AS Vol. 24, No. 11 (2014) 2199-2257. HAL preprint: hal-00918896, version 1 (December 2013).

  • G. Allaire, Ch. Dapogny, G. Delgado, G. Michailidis, Multi-phase structural optimization via a level set method, COCV 20, pp.576-611 (2014). HAL preprint: hal-00839464, version 1 (June 2013).

  • D. Schmitt, G. Allaire, O. Pantz, N. Pozin, Shape Optimization of a sodium cooled fast reactor, SNA + MC 2013, 02206 (2014). Electronic version.

  • G. Allaire, F. Jouve, G. Michailidis, Casting constraints in structural optimization via a level set method, proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization, paper 4873 (May 2013).

  • G. Allaire, Ch. Dapogny, P. Frey, A mesh evolution algorithm based on the level set method for geometry and topology optimization, SMO 48 (2013), no. 4, 711-715. HAL preprint: hal-00801704, version 1 (March 2013).

  • E. Dombre, G. Allaire, O. Pantz, D. Schmitt, Shape Optimization of a sodium fast reactor core, ESAIM Proceedings, 38, 319-334 (2012). Internal report, n. 750, CMAP, Ecole Polytechnique (January 2012). 750.pdf.

  • G. Allaire, Ch. Dapogny, P. Frey, Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh, C. R. Acad. Sci. Paris, Série I, 349, pp.999-1003 (2011). Internal report, n. 723, CMAP, Ecole Polytechnique (August 2011). 723.pdf.

  • G. Allaire, A. Kelly, Optimal Design of Low-Contrast Two Phase Structures for the Wave Equation, M3AS, 21, No. 7, pp.1499-1538 (2011). Internal report, n. 692, CMAP, Ecole Polytechnique (August 2010). 692.pdf.

  • G. Allaire, A. Münch, F. Periago, Long time behavior of a two-phase optimal design for the heat equation, SIAM Journal on Control and Optimization, 48(8), pp.5333-5356 (2010). Internal report, n. 690, CMAP, Ecole Polytechnique (August 2010). 690.pdf.

  • J. Chetboun, G. Allaire, Flow Control of Curved Air Ducts using Topological Derivatives, Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, H.C. Rodrigues et al. eds., ISSMO (2009). ISBN:978-989-20-1554-5. 1104.pdf

  • G. Allaire, F. de Gournay, F. Jouve, Stress minimization and robust compliance optimization of structures by the level set method, Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, H.C. Rodrigues et al. eds., ISSMO (2009). ISBN:978-989-20-1554-5. 1064.pdf

  • G. Allaire, F. Jouve, Minimum stress optimal design with the level set method, Engineering Analysis with Boundary Elements 32, pp.909-918 (2008). Internal report, n. 618, CMAP, Ecole Polytechnique (June 2007). PDF
  • G. Allaire, F. Jouve, N. Van Goethem A level set method for the numerical simulation of damage evolution, Internal report, n. 629, CMAP, Ecole Polytechnique (December 2007). PDF.
  • F. de Gournay, G. Allaire, F. Jouve, Shape and topology optimization of the robust compliance via the level set method, COCV, 14, pp.43-70 (2008). Internal report, n. 593, CMAP, Ecole Polytechnique (2006). PDF
  • G. Allaire, F. Jouve, Minimum stress optimal design with the level set method, to appear in International Journal of Boundary Elements and Applications. Internal report, n. 618, CMAP, Ecole Polytechnique (June 2007). PDF
  • G. Allaire, Conception optimale de structures, Collection: Mathématiques et Applications, Vol. 58, Springer (2007).
  • G. Allaire, F. Jouve, Coupling the level set method and the topological gradient in structural optimization, in IUTAM symposium on topological design optimization of structures, machines and materials, M. Bendsoe et al. eds., pp3-12, Springer (2006).
  • G. Allaire, S. Gutierrez, Optimal Design with Small Contrast, in IUTAM symposium on topological design optimization of structures, machines and materials, M. Bendsoe et al. eds., pp137-146, Springer (2006).
  • F. de Gournay, Velocity extension for the level-set method and multiple eigenvalues in shape optimization, to appear in SIAM J. Optim. PDF
  • F. de Gournay, Optimisation de formes par la méthode des lignes de niveaux, Thèse de l'Ecole Polytechnique, juillet 2005. PDF
  • G. Allaire, O. Pantz, Structural Optimization with FreeFem++, SMO, 32, pp.173-181 (2006). PDF
  • G. Allaire, S. Gutierrez, Optimal Design in Small Amplitude Homogenization, M2AN, 41, pp.543-574 (2007). Internal report, n. 576, CMAP, Ecole Polytechnique (June 2005). PDF
  • G. Allaire, F. De Gournay, F. Jouve, A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method, Control and Cybernetics, 34, pp.59-80 (2005). (Internal report 555, CMAP, Ecole Polytechnique 2004). PDF
  • G. Allaire, F. Jouve, H. Maillot, Topology optimization for minimum stress design with the homogenization method, , Structural and Multidisciplinary Optimization, 28, pp.87-98 (2004). PDF
  • G. Allaire, F. Jouve, A level-set method for vibration and multiple loads structural optimization, Comput. Methods Appl. Mech. Engrg. 194, pp.3269-3290 (2005). Internal report, n. 542, CMAP, Ecole Polytechnique (June 2004). PDF
  • G. Allaire, Topology optimization with the homogenization and the level-set method, in Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, P. Ponte Castaneda et al. eds., pp.1-13, Kluwer (2004). PDF
  • G. Allaire, F. Jouve, A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method, J. Comp. Phys., 194/1, pp.363-393 (2004). (Internal report 508, CMAP, Ecole Polytechnique 2003) PDF
  • G. Allaire, F. Jouve, A.M. Toader, Structural optimization by the level-set method, in International Series of Numerical Mathematics, vol. 147, pp.1-15, Birkhauser, Basel (2003).
  • G. Allaire, F. Jouve, A.-M. Toader, A level-set method for shape optimization, C. R. Acad. Sci. Paris, Série I, 334, pp.1-6 (2002). PDF
  • G. Allaire, S. Castro, Optimization of nuclear fuel reloading by the homogenization method, Structural and Multidisciplinary Optimization, 24, pp.1-22 (2002)..

  • G. Allaire, Shape optimization by the homogenization method, Springer Verlag, New York (2002).

  • G. Allaire, F. Jouve, Optimal design of micro-mechanisms by the homogenization method, European Journal of Finite Elements, 11, pp.405-416 (2002). PDF
  • H. Hamda, F. Jouve, E. Lutton, M. Schoenauer, M. Sebag, Compact unstructured representations for Evolutionary Design, Applied Intelligence, 16, pp.139-155 (2002). PDF
  • G. Allaire, S. Aubry, F. Jouve, Eigenfrequency optimization in optimal design, Comput. Methods Appl. Mech. Engrg. 190, pp.3565-3579 (2001). PDF
  • G. Allaire, F. Jouve, Conception de micromécanismes par optimisation topologique, Congrès français de mécanique, Nancy, Septembre 2001. PDF
  • G. Allaire, F. Jouve, Optimisation de structures par homogénéisation pour des fonctions-cout générales. Application à l'optimisation de mécanismes, Actes du 5ème colloque national en calcul des structures, pp.853-860, CSMA ed., Teknea (Toulouse) (2001). PDF
  • G. Allaire, A. Henrot, On some recent advances in shape optimization, C. R. Acad. Sci. Paris, Série IIb, t. 329, pp.383-396 (2001).

  • G. Allaire, S. Castro, A new approach for the optimal distribution of assemblies in a nuclear reactor, Nümerische Mathematik, 89, pp.1-29 (2001).

  • G. Allaire, S. Aubry, F. Jouve, Shape optimization with general objective functions using partial relaxation, in Topology optimization of structures and composite continua, G.I.N. Rozvany and N. Olhoff eds., pp.239-249, Kluwer Academic Publishers (2000). PDF
  • H. Hamda, F. Jouve, E. Lutton, M. Schoenauer, M. Sebag, Représentations non structurées en optimisation topologique de formes par algorithmes évolutionnaires, 32eme Congrès national d'Analyse Numérique (CANum 2000), Port d'Albret, ESAIM Proceedings, Vol. 11, 153-179 (2002). PDF
  • G. Allaire, F. Jouve, Structural optimization by the homogenization method, in the Proceedings of IUTAM Symposium "Variations of domains and free-boundary problems in solid mechanics", P. Argoul et al. eds., Kluwer Academic Publishers, Dordrecht, pp.293-300 (1999). PDF
  • G. Allaire, S. Aubry, On optimal microstructures for a plane shape optimization problem, Structural Optimization 17, pp.86-94 (1999).

  • G. Allaire, G. Francfort, Existence of minimizers for non-quasiconvex functionals arising in optimal design, Annales de l'Institut Henri Poincaré, Analyse Non-Linéaire, 155, pp.301-339 (1998).

  • G. Allaire, S. Aubry, F. Jouve, Simulation numérique de l'endommagement à l'aide du modèle Francfort-Marigo, Actes du 29ème congrès d'analyse numérique, ESAIM Proceedings, vol. 3, pp.1-9 (1998). PDF
  • G. Allaire, E. Bonnetier, G. Francfort, F. Jouve, Shape optimization by the homogenization method, Nümerische Mathematik 76, pp.27-68 (1997). PDF
  • G. Allaire, The homogenization method for topology and shape optimization, dans "Topology optimization in structural mechanics", G. Rozvany ed., pp.101-134, CISM Courses and Lectures 374, Springer, Wien (1997).

  • G. Allaire, F. Jouve, Optimisation topologique de structures élastiques, Actes du 3ème colloque national en calcul des structures, B. Peseux et al. eds., pp.49-58, Presses Académiques de l'Ouest, Nantes (1997).

  • G. Allaire, E. Bonnetier, G. Francfort, F. Jouve, A topological approach to shape optimization, in Applied Stochastics and Optimization, O. Mahrenholtz et al. eds., ICIAM 95 special issue of ZAMM, Z. angew. Math. Mech. 76, S3, pp.255-258 (1996). PDF
  • G. Allaire, Z. Belhachmi, F. Jouve, The homogenization method for topology and shape optimization. Single and multiple loads case, European Journal of Finite Elements, 5, pp.649-672 (1996). PDF
  • M. Schoenauer, L. Kallel, F. Jouve, Mechanical inclusions identification by evolutionary computation, European Journal of Finite Elements, 5, pp.619-648 (1996). PDF
  • G. Allaire, Relaxation of structural optimization problems by homogenization, "Trends in Applications of Mathematics to Mechanics", M.M.Marques and J.F.Rodrigues Eds., Pitman monographs and surveys in pure and applied mathematics 77, pp.237-251, Longman, Harlow (1995).

  • C. Kane, F. Jouve, M. Schoenauer, Structural topology optimization in linear and nonlinear elasticity using genetic algorithms, 21th ASME Design Automation Conference, Boston, (1995). PDF
  • G. Allaire, Explicit lamination parameters for three-dimensional shape optimization, Control and Cybernetics, vol. 23, pp.309-326 (1994).

  • G. Allaire, R.V. Kohn, Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Europ. J. Mech. A/Solids 12, 6, pp.839-878 (1993).

  • G. Allaire, G. Francfort, A numerical algorithm for topology and shape optimization, "Topology design of structures" Nato ASI Series E, pp.239-248, vol.227, M. Bendsoe et al. eds., Kluwer, Dordrecht (1993).

  • G. Allaire, R.V. Kohn, Topology optimization and optimal shape design using homogenization, "Topology design of structures" Nato ASI Series E, pp.207-218, vol.227, M. Bendsoe et al. eds., Kluwer, Dordrecht (1993).

  • G. Allaire, Structural optimization using optimal microstructures, dans "MECAMAT 93 International Seminar on Micromechanics of Materials", Collection de la Direction des Etudes et Recherches d'Electricité de France, pp.106-114, Eyrolles, Paris (1993).