Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût

Jean Cea

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1986)

  • Volume: 20, Issue: 3, page 371-402
  • ISSN: 0764-583X

How to cite

top

Cea, Jean. "Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 20.3 (1986): 371-402. <http://eudml.org/doc/193482>.

@article{Cea1986,
author = {Cea, Jean},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {directional derivation of the cost function; optimum design problems; distributed systems; bibliography},
language = {fre},
number = {3},
pages = {371-402},
publisher = {Dunod},
title = {Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût},
url = {http://eudml.org/doc/193482},
volume = {20},
year = {1986},
}

TY - JOUR
AU - Cea, Jean
TI - Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1986
PB - Dunod
VL - 20
IS - 3
SP - 371
EP - 402
LA - fre
KW - directional derivation of the cost function; optimum design problems; distributed systems; bibliography
UR - http://eudml.org/doc/193482
ER -

References

top
  1. 1 F ANGRAND, R GLOWINSKI, J PERIAUX, P PERRIER, G POIRIER, O PIRONNEAU, Optimum Design For Potential Flows Communication to Calgary Conference, June, 1980 Zbl0472.76028
  2. 2 T ALTUZARRA, C KNOPF-LENOIR, C SAYETAT and G TOUZOTInteractive opti mum design System Preprints, Tucson Symposium, October 1981 
  3. 3 C BAIOCCHI, Su unProblema a Frontiera Connesso a Questioni di Idraulica, Vol 92, N° 4, 1972 Ann Mat Pura Appl, pp 107-127 Zbl0258.76069MR408443
  4. 4 A BAMBERGER, G CHAVENT and P LAILLY, Étude Mathématique et Numérique d'un Problème Inverse pour l'Équation des Ondes a une Dimension Rapport Interne, N° 14, École Polytechnique, January 1977 
  5. 5 N V BANICHUK, Optimization of Elastic Bars in Torsion Int J Solids and Structures, Vol 12, 1976, pp 275-286 Zbl0319.73029MR411326
  6. 6 N V BANICHUK, On a Two-Dimenstional Optimization Problem in Elastic Bar Torsion Theory MTT, Vol 11, N° 5, 1976, pp 45-52 
  7. 7 N V BANICHUK, Optimality Condition in the Problem of Seeking the Hole Shapes in Elastic Bodies PMM, Vol 41, N° 5, 1977, pp 920-925 Zbl0401.73030MR519746
  8. 8 D BEGIS and R GLOWINSKI, Application de la Methode des Éléments Finisa l'Appro ximation d'un Problème de Domaine Optimal Applied Math and Optimization, Vol 2, No2, 1975, pp 130-169 Zbl0323.90063MR443372
  9. 9 D C BENSON, An Elementary Solution of a Vanational Problem of Aerodynamics J of Opt Theory and Appl, Vol 1, N°2, 1967 Zbl0149.44508MR1551275
  10. 10 S S BHAIVIKATTI and C V RAMAKRISHNAN, Optimum Design of Fillets in flat and Round Tension Bars ASME paper, N° 77-DET-45, 1977 
  11. 11 J CEA, Une méthode Numérique pour la Recherche d un Domaine Optimal Publication IMAN-P2, Nice, 1975 Zbl0343.49008MR464583
  12. 12 J CEA, Identification de Domaines Springer-Verlag, Lecture Notes in Computer Science, Vol 3, 1973 Zbl0303.93022
  13. 13 J CEA, A GIOAN and J MICHEL, Quelques Résultats sur l'Identification de Domaines Calcolo, III-IV, 1973 Zbl0303.93023MR359319
  14. 14 J CEA, A GIOAN and J MICHEL, Adaptation de la Methode du Gradient a un Problème d'Identification de Domaine Springer-Verlag, Lecture Notes in Computer Science, Vol 11, 1974 Zbl0304.93011MR467469
  15. 15 J CEA, Quelques méthodes sur la recherche d'un domaine optimal Springer-Verlag, Lecture notes m Physics, Vol 85, 1978, pp 135-146 MR564948
  16. 16 J CEA, Numerical Methods of Shape Optimal Design Optimization of Distributed Parameter Structures (Eds E J Haug andJ Cea) Sythoff & Noordhoff, Alphen aan den Rijn, Netherlands, 1981 Zbl0517.73095
  17. 17 J CEA, Lectures on Optimization Theory and Algorithms Springer-Verlag, 1978 Zbl0409.90050MR545791
  18. 18 J CEA and K MALANOWSKI, An example of a Max-Min Problem in Partial Differential Equations SIAM J Control, Vol 8,N° 3, 1970, pp 305-316 Zbl0204.46603MR274915
  19. 19 G CHAVENT, Analyse Fonctionnelle et Identification de Coefficients Repartis dans les Équations aux Dérivées Partielles These de Doctorat, Paris Zbl0226.35006
  20. 20 D CHENAIS, On theExistence of a Solution in a Domain Identification Problem J Math Anal Appl, Vol 52, N° 2, 1975 Zbl0317.49005MR385666
  21. 21 Y W CHUN and E J HAUG, Two Dimensional Shape Optimal Design Int J Num Methods m Engrg , Vol 13, 1978, pp 311-336 Zbl0393.73064MR511593
  22. 22 M C Cox, The Numerical Evaluation of B-Splines National Physical Laboratory DNAC 4, August 1971 Zbl0252.65007
  23. 23 I I DANILJUK, Sur une Classe de Fonctionnelles Intégrales a Domaine Variable d Intégration Actes, Congres Internat Math , 1970, Vol 2, pp 703-715 Zbl0237.31002MR649626
  24. 24 C DE BOOR, On Calculating with B-Splines J Approx Theory, Vol 6, pp 50-62, 1972 Zbl0239.41006MR338617
  25. 25 A DERVIEUX and B PALMERIO, Une Formule d'Identification dans des Problèmes d'Identification deDomaines C R Acad Sci Pans, Serie A,Vol 280, 1975, pp 1697-1700 and 1761-1764 Zbl0303.35065MR386269
  26. 26 A DERVIEUX and B PALMERIO, Hadamard's Variational Formula for a Mixed Problem and an Application to a Problem Related to a Signonni Like Variational Inequality Rapport Labona, IRIA, Rocquencourt, 1979 Zbl0452.49011
  27. 27 A DERVIEUX, B PALMERIO, Une Formule de Hadamard dans les Problèmes d Optimal Design Springer-Verlag, Lecture Notes in Computer Science, Vol 40, 1976 Zbl0335.49014
  28. 28 A DERVIEUX, B PALMERIO and B ROUSSELET, Dessin Optimal d'un Reacteur Nucleaire par une Methode de Gradient To appear 
  29. 29 H J DEULING and W HELFRICH, The Curvature Elasticity of Fluid Membranes A Catalogue of Vesicle Shapes J de Phys , Vol 37, nov 1976, pp 1335-1345 
  30. 30 A FRANCAVILLA, C V RAMAKRISHNAN and O C ZIENKIEVICZ, Optimization of Shape to Minimize Stress Concentration Strain Anal, Vol 10, 1975, pp 63-70 
  31. 31 C FLEURY and V BRAIBANT, Optimization Methods in Structural Design Edited by H Eshenauer and N Olhoff Euromech-Colloquim 164, University of Siegen 
  32. 32 C FLEURY and M GERADINGeneral Nonlinear Programming Methods NATO Advanced Study Institute on Modern Structural Optimization 4-15 August 1980, University of Liège, Belgium 
  33. 33 A FRIEDMAN, Free Boundary Problems for Parabolic Equations, (II) Evaporation or Condensation of a Liquid Drop J Math Mech Vol 9, 1960, pp 19-66 Zbl0091.09302MR144079
  34. 34 A FRIEDMAN, Free Boundary Problems for Parabolic Equations (III) Dissolution of a Gas Bubble in Liquid J Math Mech , Vol 9, 1960, pp 327-345 Zbl0090.07801MR144080
  35. 35 A FRIEDMAN, The Stefan Problem in Several Space Variables Trans Amer Math Soc, Vol 133, 1968, pp 51-87 Zbl0162.41903MR227625
  36. 36 P R GARABEDIAN and D C SPENCER, Extremal Methods-in Cavitational Flows J Rat Mech Anal, Vol 1, 1952, pp 359-409 Zbl0046.18504MR48983
  37. 37 P R GARABEDIAN and M SCHIFFER, Convexity of Domain Functionals J d'Analyse Math , Vol 3, 1953, 246-344 Zbl0052.33203MR60117
  38. 38 P GERMAIN, Cours de mécanique des milieux continus Paris, Masson 1973 Zbl0121.41303MR368541
  39. 39 R GLOWINSKI and A MARROCCO, Analyse Numérique du Champ Magnétique d'un Alternateur par Éléments Finis et Sur-relaxation Ponctuelle non Lineaire Comp Math m Appl Mech and Eng, Vol 3,N° 1, Janv 1974 Zbl0288.65068MR413547
  40. 40 R GLOWINSKI and A MARROCCO, Finite Element Approximation and Iterative Methods of Solution for 2-D Nonlinear Magnetostatic Problems Proceedings of COMPUMAG Conf, Oxford, 1976, pp 112-125 
  41. 41. R. GLOWINSKI and A. MARROCCO, Numerical Solutionof Two-Dimensional Magnetostatic Problems by Augmented Lagrangian Methods. Comp. Meth. in Appl. Mech. and Eng., to appear. Zbl0364.65104
  42. 42. E. L. GURVITCH, On Isoparametric Problems for Domains with Partly known boundaries J.O.T.A., Vol. 20, N° 1, 1976, pp. 65-79. Zbl0309.49003MR425723
  43. 43. J. HADAMARDMémoires sur le Problème d'Analyse Relatif à l'Équilibre des Plaques Élastiques Encastrées ( 908). Oeuvre de J. Hadamard, CN.R.S., Paris 1968. JFM39.1022.01
  44. 44. E. J. HAUG, A review of distributed parameter structural optimization literature in E.J. Haug and J. Cea (eds.). Optimization of Distributed Parameter structures, Vol. I, Sijthoff-Noordhoff, Alphen aan den Rijn, Netherlands, 1981, pp. 3-74. MR690959
  45. 45. J. HAUG and B. ROUSSELET, Design sensivity analysis in structural mechanic l, static responses variations. J. of Struct Mech., 1980, 8(1), pp. 17-41 MR607800
  46. 46. E. J. HAUG and J. S. ARORA, Applied Optimal Design. Wiley-Interscience, New-York, 1979. 
  47. 47. E. J. HAUG and J. CEA, Optimization of Distributed Paramefer Structures. Sijthoff & Noordhoff, E-49, 1981. Zbl0511.00034
  48. 48. D. D. JOSEPH, Parameter and Domain Dependence of Eigenvalues of Elliptic Part Differential Equations. Arch. Rat. Mech. Anal., Vol. 24, 1967. Zbl0152.11302MR208194
  49. 49. M. KAC, Can One Hear the Shape of a Drum ? Amm. Math. Mthly., Vol. 73, 1966, pp. 1-23. Zbl0139.05603MR201237
  50. 50. H. H. KAGIWADA and R. E. KALABA, A Practical Method for Determining Green's Functions Using Hadamard's Variational Formula. J. of Opt. Theory and Appl., Vol. 1, N° 1, 1967. Zbl0148.33703
  51. 51. M. KOENIG and J. P. ZOLESIO, Localisation d'un Objet de Forme Convexe Donnée. C.R. Acad. ScL, Paris, 1972, pp. 276, 880-852. Zbl0255.49029
  52. 52. E. S. KRISTENSEN and N. M. MADSEN, On the Optimal Shape of Fillets in Plates Subjected to Multiple in Plane Loading Cases. Int. J. for Num. Meth. in Engr., Vol. 10, 1976, pp. 1007-1011. Zbl0332.73061
  53. 53. J. L. LIONS, On the Optimal Control of Distributed Parameter Systems. Techniques of Optimization (Ed. A. Balakrishnan), Academic Press, New-York, 1972. Zbl0275.49001MR405200
  54. 54. J. L. LIONS, Sur quelques Questions d'Analyse, de Mécanique et de Contrôle Optimal. Les Presses de l'Université de Montréal, 1976. Zbl0339.49003MR493633
  55. 55. A. MARROCCO and O. PIRONNEAU, Optimum Design with Lagrangian Finite Elements. Design of an Electro-Magnet. Comp. Meth. in Appl. Mech. and Eng., Vol. 15, 1978, pp. 217-308. 
  56. 56. A. MIELE and D. G. HULL, Sufficiency Proofs for the Problem of the Optimum Transversal Contour. SIAM J. Appl. Math., Vol. 15, N° 2, 1967, pp. 466-477. Zbl0158.44303MR211676
  57. 57. F. MIGNOT, F. MURAT and J. P. PUEL, Variation d'un Point de Retournement par Rapport au Domaine. Comm. on P.D.E., Vol. 4, N° 11, 1979. Zbl0422.35039MR546644
  58. 58. F. MURAT and J. SIMON, Quelques Résultats sur le Contrôle par un Domaine Géomtrique. Publication du L.A. 189, Univ. Paris VI, 1974. 
  59. 59. F. MURAT and J. SIMON, Sur le Contrôle par un DomaineGéométrique. Publication du L.A. 189, Univ. Paris VI, 1976. 
  60. 60. F. MURAT and J. SIMON, Étude de Problèmes d'Optimal Design. Proceedings of the 7th IFIP Conference, Springer-Verlag, Lecture Notes in Computer Sciences, N°41, 1976, pp. 54-62. Zbl0334.49013
  61. 61. P. MOREL, Utilisationen Analyse Numérique de la Formule de Dérivation d'Hadamard. RAIRO, R-2, 1973, pp. 115-119. Zbl0293.65089MR353704
  62. 62 P MORICE, Une Methode d'Optimisation de Forme de Domaine Proc Congress, IFIP-IRIA, Springer-Verlag, 1974 Zbl0376.76072
  63. 63 O PERONNEAU, Optimal Shape Design for Elhptic Systems Springer Series in computational Physics, Springer-Verlag 1984 Zbl0534.49001
  64. 64 O PIRONNEAU, Sur les Problèmes d Optimisation de Structure en Mécanique des Fluides These de Doctorat, Paris VI, 1976 
  65. 65 O PIRONNEAU, On Optimum Design in Fluid Mechanics J Fluid Mech , Vol 64, 1974, pp 97-111 Zbl0281.76020MR347229
  66. 66 O PIRONNEAU, Optimum Design with Lagrangian Finite Elements Design of an Electromagnet Comp Math in Appi Mech and Eng, Vol 15, 1978, pp 207-308 
  67. 67 O PIRONNEAU and C SAGUEZ, Asymptotic Behaviour of Solutions of P D E with Respect to the Domain IRIA Laboria Report N° 218, 1977 
  68. 68 W PRAGER and J E TAYLOR, Problems of Optimal Structural Design J of Appl Mech, 1968, Vol 35, pp 102-106 Zbl0155.52003
  69. 69 V RAMAKRISHNAN and A FRANCAVILLA, Structural Shape Optimization Using Penalty Functions Struct Mech, Vol 3,N°4, 1975, pp 403-432 
  70. 70 J W RAYLEIGH, The Theory of Sound 2nd Ed , Cambridge Umversity Press, 1894-1896 
  71. 71 R F REISENFELD, Berstein-Bezier Methods for the Computer-Aided Design of Free-Form Curves and Surfaces Ph D Thesis, Syracuse University, March 1973 
  72. 72 B ROUSSELET, Sur les Problèmes de Valeurs Propres C R Acad Sci Paris, Serie A, Vol 283, 1976, p 507 Zbl0355.65081
  73. 73 B ROUSSELET, Note on the design Differentiability of the static Response of elastic Structure I struct mech , 10(3), 353-358 (1982-83) MR689822
  74. 74 B ROUSSELET, Shape sensitivity of a membrane Jota Vol 40, N° 4, August 1983 Zbl0497.73097MR717179
  75. 75 B ROUSSELET, Dependence of Eigenvalues with respect to Shape Optimization of Distributed Parameter Structures (Eds E J Haug and J Cea) Sijthoff and Noordhoff Alphen aan den Rijn, Netherlands, 1981, pp 1235-1364 Zbl0516.73104
  76. 76 B ROUSSELET, Problème Inverse de Valeurs Propres Optimization Techniques Springer-Verlag, Lecture Notes in Computer Sciences, Vol 2,N°41, 1976, pp 77-85 Zbl0337.49013
  77. 77 B ROUSSELETThese sur la conception optimale déformes Université de Nice, 1982 
  78. 78 L I RUBINSTEIN, The Stefan Problem A M S , Translations of Mathematical Monographs, Vol 27, Providence, R 1, 1971 Zbl0434.35086MR351348
  79. 79 I J SCHOENBERG, Contributions to the Problem of Approximations of Equidistant Data by Analytic Functions J Appl Math , Vol 4, 1946, pp 45-99, 112-141 Zbl0061.28804
  80. 80 O SERO-GUILLAUME, Problème a Frontière Libre de Type Stefan These, INP Lorraine, Nancy, France, 1978 Zbl0418.35080MR516778
  81. 81 B A TROESCH and H R TROESCH, Eigenfrequencies of an Elliptic Membrane Math of Comp , Vol 27, N° 126, 1973, pp 755-772 Zbl0271.35017MR421276
  82. 82 V TVERGAARD, On the Optimum Shape of a Fillet in a Fiat Bar with Restrictions Proc IUTAM Symposium on Structural Design, Warsaw, Springer-Verlag, New-York, 1973 Zbl0336.73020
  83. 83 G VANDERPLAATS, Approximative Concepts for Numerical Airfoil Optimization NASA Technical Paper N° 1370, 1979 
  84. 84 O C ZIENKIEWICZ and J S CAMPBELL, Shape Optimiztion and Sequential Linear Programming Optimum Structural Design (Ed R H Gallagher and O C Zienkiewicz), Wiley, New-York, 1973 
  85. 85 J P ZOLESIO, Identification de Domaine par Déformation These, Université de Nice, 1979 
  86. 86 J P ZOLESIO, Un résultat d'Existence de Vitesse Convergente C R Acad Sci Paris, Série A, Vol 283, 1976, p 855 Zbl0343.49004MR428158
  87. 87 J P ZOLESIO, Localisation du Support d un Contrôle Optimal C R Acad Sci Paris, Serie A, Vol 284, 1977, p 791 Zbl0357.49007MR443352
  88. 88 J P ZOLESIO, An Optimal Design Procedure for Optimal Control Suppor Lecture Notes in Economical and Mathematical Systems, N° 14, pp 207-233, 1977 Zbl0358.49004MR513446
  89. 89 J P ZOLESIO, The Material Derivative(Or Speed) Methodfor Shape Optimization Optimization of Distnbuted Parameter Structures (Eds E J Haug and J Cea), Sijthoff & Noordhoff, Alphen aan den Rijn, Netherlands, 1981 Zbl0517.73097MR690991

Citations in EuDML Documents

top
  1. Maatoug Hassine, Mohamed Masmoudi, The topological asymptotic expansion for the Quasi-Stokes problem
  2. Pedro Morin, Ricardo H. Nochetto, Miguel S. Pauletti, Marco Verani, Adaptive finite element method for shape optimization
  3. M.-C. Delfour, J.-P. Zolésio, Analyse des problèmes de forme par la dérivation des minimax
  4. Maatoug Hassine, Mohamed Masmoudi, The topological asymptotic expansion for the Quasi-Stokes problem
  5. Maatoug Hassine, Philippe Guillaume, Removing holes in topological shape optimization
  6. Philippe Guillaume, Maatoug Hassine, Removing holes in topological shape optimization
  7. G. Allaire, C. Dapogny, G. Delgado, G. Michailidis, Multi-phase structural optimization via a level set method

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.