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Shape design sensitivity of a membrane. (English) Zbl 0497.73097

MSC:
74P99 Optimization problems in solid mechanics
74K15 Membranes
74H45 Vibrations in dynamical problems in solid mechanics
93B35 Sensitivity (robustness)
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[1] Haug, E. J., andRousselet, B.,Design Sensitivity Analysis in Structural Mechanics, I: Static Response Variations, Journal of Structural Mechanics, Vol. 8, pp. 17-41, 1980.
[2] Haug, E. J., andRousselet, B.,Design Sensitivity Analysis in Structural Mechanics, II: Eigenvalue Variations, Journal of Structural Mechanics, Vol. 8, pp. 161-186, 1980.
[3] Rousselet, B., andHaug, E. J.,Design Sensitivity Analysis of Shape Variation, Optimization of Distributed Parameter Structures, Vol. 2, Edited by E. J. Haug and J. Céa, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1981. · Zbl 0516.73105
[4] Rousselet, B.,Shape Design Sensitivity Methods for Structural Mechanics, Optimization of Distributed Parameter Structural Systems, Edited by E. J. Haug and J. Céa, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1981. · Zbl 0516.73107
[5] Rousselet, B., andHaug, E. J.,Design Sensitivity Analysis in Structural Mechanics, III: Effects of Shape Variations for Plate and Plane Elasticity, Journal of Structural Mechanics (to appear).
[6] Rousselet, B.,Static and Dynamic Loads, Pointwise Constraints in Structural Optimization, Proceedings of the Colloquium on Optimization: Theory and Algorithms, Confolant, France, 1981 (to appear). · Zbl 0475.93037
[7] Rousselet, B.,Dynamic Response in Shape Optimization, Communication at 3rd IFAC Symposium on the Control of Distributed Parameter System, Toulouse, France, 1982. · Zbl 0561.49019
[8] Céa, J.,Problems of Shape Optimal Design, Optimization of Distributed Parameter Structures, Vol. 2, Edited by E. J. Haug and J. Céa, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1981.
[9] Chenais, D.,Sur une Famille de Variétés à Bord Lipschitziennes: Application à un Problème d’Identification de Domaines, Annales de l’Institut Fourier, Vol. 27, pp. 201-231, 1977. · Zbl 0333.46020
[10] Necas, J.,Les Méthodes Directes dans la Théorie des Equations Elliptiques, Académie Tchécoslovaque des Sciences, Prague, Czechoslovakia, 1967.
[11] Rousselet, B.,Optimal Design and Eigenvalue Problems, Proceedings of the 8th IFIP Conference, Würzburg, Germany, 1977; Springer-Verlag, Berlin, Germany, 1978. · Zbl 0385.49004
[12] Courant, R. S., andHilbert, D.,Methods of Mathematical Physics, Wiley-Interscience, New York, New York, 1953. · Zbl 0051.28802
[13] Micheletti, A. M.,Perturbazione dello Spettro di un Operatore Ellitico di Tipo Variazionale in Relazione ad una Variazione del Campo, Annali di Mathematica Pura e Applicata, Vol. 47, pp. 267-282, 1973. · Zbl 0283.35036 · doi:10.1007/BF02414915
[14] Rousselet, B.,Identification de Domaines et Problèmes de Valeurs, Thèse de Spécialité, Université de Nice, Nice, France, 1977.
[15] Murat, F., andSimon, J.,Sur le Contrôle par un Domaine Géométrique, Publication du Laboratoire d’Analyse Numérique, Université de Paris 6, Paris, France, 1976.
[16] Bendali, A.,Existence et Régularisation dans un Problème d’Identification de Domaine: Application à l’Analyse Numérique d’un Cas Modèle, Thèse de Spécialité, Université d’Alger, Alger, Algérie, 1975.
[17] Céa, J.,Une Méthode Numérique pour la Recherche d’un Domaine Optimal, IMAN Publication, Université de Nice, Nice, France, 1977.
[18] Céa, J., Gioan, A., andMichel, J.,Adaptation de la Méthode du Gradient à un Problème d’Identification de Domaine, Computing Methods in Applied Science and Engineering, Vol. 2, Springer-Verlag, Berlin, Germany, 1974.
[19] Dervieux, A., andPalmerio, B.,Une Formule de Hadamard dans des Problèmes d’Identification de Domaines, Comptes Rendus de l’Académie des Sciences, Vol. 280, pp. 1697-1700, 1975, and Vol. 280, pp. 1761-1764, 1975. · Zbl 0303.35065
[20] Djadane, A.,Régularité d’une Fonctionnelle de Domaines et Application à l’Analyse Numérique d’un Problème Modèle, Thèse de Spécialité, Université d’Alger, Alger, Algérie, 1975.
[21] Joseph, D. D.,Parameter and Domain Dependence of Eigenvalues of Elliptic Partial Differential Equations, Archive of Rational Mechanics and Analysis, Vol. 35, pp. 169-177, 1977.
[22] Licari, J. P., andWarner, W. H.,Domain Dependence of Eigenvalues of Vibrating Plates, SIAM Journal on Applied Mathematics, Vol. 24, pp. 383-395, 1973. · Zbl 0255.73070 · doi:10.1137/0124040
[23] Palmerio, B., andDervieux, A.,Hadamard’s Variational Formula for a Mixed Problem and an Application to a Problem Related to a Signorini-Like Variational Inequality, INRIA, Rocquencourt, Le Chesnay, France, Report No. 339, 1979. · Zbl 0452.49011
[24] Hadamard, J.,Mémoire sur le Problème d’Analyse Relatif à l’Equilibre des Plaques Elastiques Encastrées, Mémoire des Savants Etrangers, Vol. 33, pp. 515-629, 1908.
[25] Kato, T.,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Germany, 1966. · Zbl 0148.12601
[26] Céa, J.,Lectures in Optimization, Theory and Algorithms, Springer-Verlag, Berlin, Germany, 1978.
[27] Aubin, J. F.,Approximation of Elliptic Boundary Problems, Wiley-Interscience, New York, New York, 1972. · Zbl 0248.65063
[28] Dieudonne, J. A.,Eléments d’Analyse, I, Fondements de l’Analyse Moderne, Gauthiers-Villars, Paris, France, 1969.
[29] Lions, J. L., andMagenes, E.,Problèmes aux Limites Nonhomogènes et Applications, Vol. 1, Dunod, Paris, France, 1968.
[30] Zolesio, J. P.,The Material Derivative (or Speed) Method for Shape Optimization, Optimization of Distributed Parameter Structures, Vol. 2, Edited by E. J. Haug and J. Céa, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1981. · Zbl 0517.73097
[31] Germain, P.,Cours de Mécanique des Milieux Continus, Masson, Paris, France, 1973. · Zbl 0254.73001
[32] Simon, J.,Variations par Rapport au Domaine dans des Problèmes aux Limites, Publication du Laboratoire d’Analyse Numérique, Université de Paris, 6, Paris, France, 1980.
[33] Pironneau, O.,Optimum Design with Lagrangian Finite Elements: Design of an Electromagnet, Computer Methods in Applied Mechanics and Engineering, Vol. 15, pp. 207-308, 1978. · Zbl 0403.76001 · doi:10.1016/0045-7825(78)90024-5
[34] Rousselet, B.,Dependence of Eigenvalues with Respect to Shape, Optimization of Distributed Parameter Structural Systems, Vol. 2, Edited by E. J. Haug and J. Céa, Sijthoff and Noordhoff, Alphen aan den Rijn, Holland, 1981. · Zbl 0516.73104
[35] Haug, E. J., andArora, J. S.,Applied Optimal Design, John Wiley and Sons, New York, New York, 1979.
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