Free Access
Issue
ESAIM: M2AN
Volume 20, Number 3, 1986
Page(s) 371 - 402
DOI https://doi.org/10.1051/m2an/1986200303711
Published online 31 January 2017
  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 [Zbl: 0472.76028] [Google Scholar]
  2. 2 T ALTUZARRA,C KNOPF-LENOIR, C SAYETAT and G TOUZOT Interactive opti mum design System Preprints, Tucson Symposium, October 1981 [Google Scholar]
  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 [MR: 408443] [Zbl: 0258.76069] [Google Scholar]
  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 [Google Scholar]
  5. 5 N V BANICHUK, Optimization of Elastic Bars in Torsion Int J Solids and Structures, Vol 12, 1976, pp 275-286 [MR: 411326] [Zbl: 0319.73029] [Google Scholar]
  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 [Google Scholar]
  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 [MR: 519746] [Zbl: 0401.73030] [Google Scholar]
  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 [MR: 443372] [Zbl: 0323.90063] [Google Scholar]
  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 [MR: 1551275] [Zbl: 0149.44508] [Google Scholar]
  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 [Google Scholar]
  11. 11 J CEA, Une méthode Numérique pour la Recherche d un Domaine Optimal Publication IMAN-P2, Nice, 1975 [MR: 464583] [Zbl: 0343.49008] [Google Scholar]
  12. 12 J CEA, Identification de Domaines Springer-Verlag, Lecture Notes in Computer Science, Vol 3, 1973 [Zbl: 0303.93022] [Google Scholar]
  13. 13 J CEA,A GIOAN and J MICHEL, Quelques Résultats sur l'Identification de Domaines Calcolo, III-IV, 1973 [MR: 359319] [Zbl: 0303.93023] [Google Scholar]
  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 [MR: 467469] [Zbl: 0304.93011] [Google Scholar]
  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 [MR: 564948] [Google Scholar]
  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 [Zbl: 0517.73095] [Google Scholar]
  17. 17 J CEA, Lectures on Optimization Theory and Algorithms Springer-Verlag, 1978 [MR: 545791] [Zbl: 0409.90050] [Google Scholar]
  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 [MR: 274915] [Zbl: 0204.46603] [Google Scholar]
  19. 19 G CHAVENT, Analyse Fonctionnelle et Identification de Coefficients Repartis dans les Équations aux Dérivées Partielles These de Doctorat, Paris [Zbl: 0226.35006] [Google Scholar]
  20. 20 D CHENAIS, On theExistence of a Solution in a Domain Identification Problem J Math Anal Appl, Vol 52, N° 2, 1975 [MR: 385666] [Zbl: 0317.49005] [Google Scholar]
  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 [MR: 511593] [Zbl: 0393.73064] [Google Scholar]
  22. 22 M C Cox, The Numerical Evaluation of B-Splines National Physical Laboratory DNAC 4, August 1971 [Zbl: 0252.65007] [Google Scholar]
  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 [MR: 649626] [Zbl: 0237.31002] [Google Scholar]
  24. 24 C DE BOOR, On Calculating with B-Splines J Approx Theory, Vol 6, pp 50-62, 1972 [MR: 338617] [Zbl: 0239.41006] [Google Scholar]
  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 [MR: 386269] [Zbl: 0303.35065] [Google Scholar]
  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 [Zbl: 0452.49011] [Google Scholar]
  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 [Zbl: 0335.49014] [Google Scholar]
  28. 28 A DERVIEUX,B PALMERIO and B ROUSSELET, Dessin Optimal d'un Reacteur Nucleaire par une Methode de Gradient To appear [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  32. 32 C FLEURY and M GERADIN General Nonlinear Programming Methods NATO Advanced Study Institute on Modern Structural Optimization 4-15 August 1980, University of Liège, Belgium [Google Scholar]
  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 [MR: 144079] [Zbl: 0091.09302] [Google Scholar]
  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 [MR: 144080] [Zbl: 0090.07801] [Google Scholar]
  35. 35 A FRIEDMAN, The Stefan Problem in Several Space Variables Trans Amer Math Soc, Vol 133, 1968, pp 51-87 [MR: 227625] [Zbl: 0162.41903] [Google Scholar]
  36. 36 P R GARABEDIAN and D C SPENCER, Extremal Methods-in Cavitational Flows J Rat Mech Anal, Vol 1, 1952, pp 359-409 [MR: 48983] [Zbl: 0046.18504] [Google Scholar]
  37. 37 P R GARABEDIAN and M SCHIFFER, Convexity of Domain Functionals J d'Analyse Math , Vol 3, 1953, 246-344 [MR: 60117] [Zbl: 0052.33203] [Google Scholar]
  38. 38 P GERMAIN, Cours de mécanique des milieux continus Paris, Masson 1973 [MR: 368541] [Zbl: 0121.41303] [Google Scholar]
  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 [MR: 413547] [Zbl: 0288.65068] [Google Scholar]
  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 [Google Scholar]
  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. [Zbl: 0364.65104] [Google Scholar]
  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. [MR: 425723] [Zbl: 0309.49003] [Google Scholar]
  43. 43. J. HADAMARD Mémoires sur le Problème d'Analyse Relatif à l'Équilibre des Plaques Élastiques Encastrées ( 908). Oeuvre de J. Hadamard, CN.R.S., Paris 1968. [JFM: 39.1022.01] [Google Scholar]
  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. [MR: 690959] [Google Scholar]
  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 [MR: 607800] [Google Scholar]
  46. 46. E. J. HAUG and J. S. ARORA, Applied Optimal Design. Wiley-Interscience, New-York, 1979. [Google Scholar]
  47. 47. E. J. HAUG and J. CEA, Optimization of Distributed Paramefer Structures. Sijthoff & Noordhoff, E-49, 1981. [Zbl: 0511.00034] [Google Scholar]
  48. 48. D. D. JOSEPH, Parameter and Domain Dependence of Eigenvalues of Elliptic Part Differential Equations. Arch. Rat. Mech. Anal., Vol. 24, 1967. [MR: 208194] [Zbl: 0152.11302] [Google Scholar]
  49. 49. M. KAC, Can One Hear the Shape of a Drum ? Amm. Math. Mthly., Vol. 73, 1966, pp. 1-23. [MR: 201237] [Zbl: 0139.05603] [Google Scholar]
  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. [Zbl: 0148.33703] [Google Scholar]
  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. [Zbl: 0255.49029] [Google Scholar]
  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. [Zbl: 0332.73061] [Google Scholar]
  53. 53. J. L. LIONS, On the Optimal Control of Distributed Parameter Systems. Techniques of Optimization (Ed. A. Balakrishnan), Academic Press, New-York, 1972. [Zbl: 0275.49001] [MR: 405200] [Google Scholar]
  54. 54. J. L. LIONS, Sur quelques Questions d'Analyse, de Mécanique et de Contrôle Optimal. Les Presses de l'Université de Montréal, 1976. [MR: 493633] [Zbl: 0339.49003] [Google Scholar]
  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. [Google Scholar]
  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. [MR: 211676] [Zbl: 0158.44303] [Google Scholar]
  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. [MR: 546644] [Zbl: 0422.35039] [Google Scholar]
  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. [Google Scholar]
  59. 59. F. MURAT and J. SIMON, Sur le Contrôle par un DomaineGéométrique. Publication du L.A. 189, Univ. Paris VI, 1976. [Google Scholar]
  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. [Zbl: 0334.49013] [Google Scholar]
  61. 61. P. MOREL, Utilisationen Analyse Numérique de la Formule de Dérivation d'Hadamard. RAIRO, R-2, 1973, pp. 115-119. [EuDML: 193239] [MR: 353704] [Zbl: 0293.65089] [Google Scholar]
  62. 62 P MORICE, Une Methode d'Optimisation de Forme de Domaine Proc Congress, IFIP-IRIA, Springer-Verlag, 1974 [Zbl: 0376.76072] [Google Scholar]
  63. 63 O PERONNEAU, Optimal Shape Design for Elhptic Systems Springer Series in computational Physics, Springer-Verlag 1984 [Zbl: 0534.49001] [Google Scholar]
  64. 64 O PIRONNEAU, Sur les Problèmes d Optimisation de Structure en Mécanique des Fluides These de Doctorat, Paris VI, 1976 [Google Scholar]
  65. 65 O PIRONNEAU, On Optimum Design in Fluid Mechanics J Fluid Mech , Vol 64, 1974, pp 97-111 [MR: 347229] [Zbl: 0281.76020] [Google Scholar]
  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 [Google Scholar]
  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 [Google Scholar]
  68. 68 W PRAGER and J E TAYLOR, Problems of Optimal Structural Design J of Appl Mech, 1968, Vol 35, pp 102-106 [Zbl: 0155.52003] [Google Scholar]
  69. 69 V RAMAKRISHNAN and A FRANCAVILLA, Structural Shape Optimization Using Penalty Functions Struct Mech, Vol 3,N°4, 1975, pp 403-432 [Google Scholar]
  70. 70 J W RAYLEIGH, The Theory of Sound 2nd Ed , Cambridge Umversity Press, 1894-1896 [Google Scholar]
  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 [Google Scholar]
  72. 72 B ROUSSELET, Sur les Problèmes de Valeurs Propres C R Acad Sci Paris, Serie A, Vol 283, 1976, p 507 [Zbl: 0355.65081] [Google Scholar]
  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) [MR: 689822] [Google Scholar]
  74. 74 B ROUSSELET, Shape sensitivity of a membrane Jota Vol 40, N° 4, August 1983 [Zbl: 0497.73097] [MR: 717179] [Google Scholar]
  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 [Zbl: 0516.73104] [Google Scholar]
  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 [Zbl: 0337.49013] [Google Scholar]
  77. 77 B ROUSSELET These sur la conception optimale déformes Université de Nice, 1982 [Google Scholar]
  78. 78 L I RUBINSTEIN, The Stefan Problem A M S , Translations of Mathematical Monographs, Vol 27, Providence, R 1, 1971 [MR: 351348] [Zbl: 0434.35086] [Google Scholar]
  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 [Zbl: 0061.28804] [Google Scholar]
  80. 80 O SERO-GUILLAUME, Problème a Frontière Libre de Type Stefan These, INP Lorraine, Nancy, France, 1978 [MR: 516778] [Zbl: 0418.35080] [Google Scholar]
  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 [MR: 421276] [Zbl: 0271.35017] [Google Scholar]
  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 [Zbl: 0336.73020] [Google Scholar]
  83. 83 G VANDERPLAATS, Approximative Concepts for Numerical Airfoil Optimization NASA Technical Paper N° 1370, 1979 [Google Scholar]
  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 [Google Scholar]
  85. 85 J P ZOLESIO, Identification de Domaine par Déformation These, Université de Nice, 1979 [Google Scholar]
  86. 86 J P ZOLESIO, Un résultat d'Existence de Vitesse Convergente C R Acad Sci Paris, Série A, Vol 283, 1976, p 855 [MR: 428158] [Zbl: 0343.49004] [Google Scholar]
  87. 87 J P ZOLESIO, Localisation du Support d un Contrôle Optimal C R Acad Sci Paris, Serie A, Vol 284, 1977, p 791 [MR: 443352] [Zbl: 0357.49007] [Google Scholar]
  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 [MR: 513446] [Zbl: 0358.49004] [Google Scholar]
  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 [MR: 690991] [Zbl: 0517.73097] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you