Free Access
Issue
ESAIM: M2AN
Volume 31, Number 6, 1997
Page(s) 733 - 763
DOI https://doi.org/10.1051/m2an/1997310607331
Published online 31 January 2017
  1. R. ADAMS, 1975, Sobolev spaces, Academic Press, New York. [MR: 450957] [Zbl: 0314.46030] [Google Scholar]
  2. L. J. ALVAREZ VAZQUEZ, P. QUINTELA ESTEVEZ, 1992, The effect of different scalings in the modelling of nonlinearly elastic plates with rapidly varying thickness, Comp. Meth. Appl. Mech. Eng., 96, 1-24. [MR: 1159590] [Zbl: 0759.73032] [Google Scholar]
  3. V. BARBU, T. PRECUPANU, 1978, Convexity and optimization in Banach spaces, Sijthoff and Noordhoff, Bucharest, 1978. [MR: 860772] [Zbl: 0379.49010] [Google Scholar]
  4. D. BLANCHARD, 1981, Justification de modèles de plaques correspondant à différentes conditions aux limites, Thesis, Univ. Pierre et Marie Curie, Paris. [Google Scholar]
  5. D. BLANCHARD, P. G. CIARLET, 1983, A remark on the von Karman Equations, Comp. Meth. Appl. Mech. Eng., 37, 79-92. [MR: 699016] [Zbl: 0486.73051] [Google Scholar]
  6. D. BLANCHARD, G. A. FRANCFORT, 1987, Asymptotic thermoelastic behavior of flat plates, Quart. Appl. Math., 45, 645-667. [MR: 917015] [Zbl: 0629.73007] [Google Scholar]
  7. H. BREZIS, 1973, Opérateurs maximaux monotones et semigroupes de contractions dans les espces de Hilbert, North-Holland. [Zbl: 0252.47055] [Google Scholar]
  8. D. CAILLERE, 1980, The effect of a thin inclusion of high rigidity in an elastic body, Math. Meth. Appl. Sci., 2, 251-270. [MR: 581205] [Zbl: 0446.73014] [Google Scholar]
  9. E. CASAS, 1982, Análisis numerico de algunos problemas de optimización estructural, Thesis, Universidad de Santiago de Compostela. [Google Scholar]
  10. E. CASAS, 1990, Optimality conditions and numerical approximations for some optimal design problems, Control Cibernet, 19, 73-91. [MR: 1118675] [Zbl: 0731.49010] [Google Scholar]
  11. J. CEA, 1971, Optimisation: Théorie et Algorithmes, Dunod, Paris. [MR: 298892] [Zbl: 0211.17402] [Google Scholar]
  12. P. G. ClARLET, 1980, A justification of the von Karman equations, Arch. Rat. Mech. Anal., 73, 349-389. [MR: 569597] [Zbl: 0443.73034] [Google Scholar]
  13. [13]P.G. CIARLET, 1988, Mathematical Elasticity, Vol. 1, North-Holland, Amsterdam. [MR: 936420] [Zbl: 0648.73014] [Google Scholar]
  14. P. G. CIARLET, 1990, Plates and junctions in elastic multi-structures, Masson, Paris. [MR: 1071376] [Zbl: 0706.73046] [Google Scholar]
  15. P. G. CIARLET, P. DESTUYNDER, 1979, A justification of the two dimensional linear plate model, J. Mécanique, 18, 315-344. [MR: 533827] [Zbl: 0415.73072] [Google Scholar]
  16. P. G. CIARLET, P. DESTUYNDER, 1979, A justification of a nonlinear model in plate theory, Comp. Meth. Appl. Mech. Eng., 17/18, 222-258. [MR: 533827] [Zbl: 0405.73050] [Google Scholar]
  17. P. G. ClARLET, S. KESAVAN, 1981, Two-dimensional approximation of three-dimensional eigenvalue problems in plate theory, Comp. Meth. Appl. Mech. Eng., 26, 145-172. [MR: 626720] [Zbl: 0489.73057] [Google Scholar]
  18. P. G. ClARLET, H. LE DRET, 1989, Justification of the boundary conditions of a clamped plate by an asyptotic analysis, Asymptotic Analysis, 2, 257-277. [MR: 1030351] [Zbl: 0699.73011] [Google Scholar]
  19. P.G CIARLET, B. MIARA, 1992, Justification of the two-dimensional equations of a linearly elastic shallow shell, Comm. Pure Appl. Math., 45,327-360. [MR: 1151270] [Zbl: 0769.73050] [Google Scholar]
  20. P. G. CIARLET, P. PAUMIER, 1985, Une justification des équations de Maguerre von Karman pour les coques peu profondes, C. R. Acad. Sc. Paris, 301, 857-860. [MR: 822849] [Zbl: 0594.73066] [Google Scholar]
  21. P. G. CIARLET, P. RABIER, 1980, Les équations de von Karman, Lecture Notes in Mathematics, vol. 826 Springer Verlag, Berlin. [MR: 595326] [Zbl: 0433.73019] [Google Scholar]
  22. A. CIMETIÈRE, G. GEYMONAT, H. LE DRET, A. RAOULT, Z. TUTEK, 1988, Asymptotic theory and analysis for displacements and stress distribution in non linear elstic slender rods, J. Elasticity, 19, 111-161. [MR: 937626] [Zbl: 0653.73010] [Google Scholar]
  23. D. CIORANESCU, J. SAINT JEAN PAULIN, 1988, Reinforced and honey comb structures, J. Math. Pures Appl., 65, 403-422. [MR: 881689] [Zbl: 0656.35031] [Google Scholar]
  24. J. L. DAVET, 1986, Justification de modèles de plaques non lineaires pour des lois de comportement générales, Mod. Math. Anal. Num., 20, 225-249. [EuDML: 193475] [MR: 852680] [Zbl: 0634.73048] [Google Scholar]
  25. P. DESTUYNDER, 1980, Sur une justification des modèles de plaques et coques par les méthodes asymptotiques, Thesis, Univ. Pierre et Marie Curie. [Google Scholar]
  26. P. DESTUYNDER, 1981, Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité, RAIRO Anal. Num., 15, 331-369. [EuDML: 193386] [MR: 642497] [Zbl: 0479.73042] [Google Scholar]
  27. P. DESTUYNDER, 1985, A classification of thin shell theories, Acta. Appl. Math., 4, 15-63. [MR: 791261] [Zbl: 0531.73044] [Google Scholar]
  28. P. DESTUYNDER, 1986, Une théorie asymptotique des plaques minces en élasticité linéaire, Masson, Paris. [MR: 830660] [Zbl: 0627.73064] [Google Scholar]
  29. G. DUVAUT, J.L. LIONS, 1972, Les inéquations en Mécanique et en Physique, Dunod, Paris. [MR: 464857] [Zbl: 0298.73001] [Google Scholar]
  30. I.M.N. FIGUEIREDO, 1989, Modèles de coques élastiques non linéaires : méthode asymptotique et existence de solution, Thesis, Univ. Pierre et Marie Curie, Paris. [Google Scholar]
  31. K. O. FRIEDRICHS, R. F. DRESSLER, 1961, A boundary-layer theory for elastic plates, Comm. Pure. Appl. Math., 14, 1-33. [MR: 122117] [Zbl: 0096.40001] [Google Scholar]
  32. A. L. GOLDENVEIZER, 1962, Derivation of an approximated theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity, Plikl. Mat. Mech., 26, 668-686. [MR: 170523] [Zbl: 0118.41603] [Google Scholar]
  33. J. HASLINGER, P. NEITTANMAKI, 1988, Finite element approximation for optimal shape design, John Wiley, Chichester. [MR: 982710] [Zbl: 0713.73062] [Google Scholar]
  34. E. J. HAUG, J.S. ARORA, 1979, Applied Optimal Design Mechanical and Strutural Systems, John Wiley, New York. [Google Scholar]
  35. I. HLAVACEK, I. BOCK, J. LOVISEK, 1984, Optimal control of a varitional inequality with applications to structural analysis. Optimal design of a beam with unilateral supports, Appl. Math. Optim., 11, 111-143. [MR: 743922] [Zbl: 0553.73082] [Google Scholar]
  36. I. HLAVACEK, I. BOCK, J. LOVISEK, 1984, Optimal control of a variational unequlity with applications to structural analysis II. Local optimization of the stress in a beam III. Optimal design of an elastic plate, Appl. Math. Optim., 13, 117-136. [MR: 794174] [Zbl: 0582.73081] [Google Scholar]
  37. R.V. KOHN, M. VOGELIUS, 1984, A now model for thin plates with rapidly varying thickness, Int. J. Solids Structures, 20, 333-350. [MR: 739921] [Zbl: 0532.73055] [Google Scholar]
  38. R. V. KOHN, M VOGELIUS, 1985, A new model for thin plates with rapidly varying thickness. II : A convergence proof, Quart. Appl. Math., 43, 1-22. [MR: 782253] [Zbl: 0565.73046] [Google Scholar]
  39. R. V. KOHN, M. VOGELIUS, 1986, A new model for thin plates with rapidly varying thickness. III: Comparison of different scalings, Quart. Appl. Math., 44, 35-48. [MR: 840441] [Zbl: 0605.73048] [Google Scholar]
  40. P. QUINTELA ESTEVEZ, 1989, A new model for nonlinear elastic plates with rapidly varying thickness, Applicable Analysis, 32, 107-127. [MR: 1017526] [Zbl: 0683.73027] [Google Scholar]
  41. P. QUINTELA ESTEVEZ, 1990, A new model for nonlinear elastic plates with rapidly varying thickness II: The effect of the behavior of the forces when the thickness approaches zero, Applicable Analysis, 39, 151-164. [MR: 1095630] [Zbl: 0687.73061] [Google Scholar]
  42. A. RAOULT, 1980, Contribution à l'étude des modèles d'évolution de plaques et à l'approximation d'équations d'évolution linéaires de second ordre par des méthodes multipas, Thesis, Univ. Pierre et Marie Curie, Paris. [Google Scholar]
  43. A. RAOULT, 1985, Construction d'un modèle d'évolution de plaques avec terme d'inertie de rotation, Ann. Mat. Pura Appl., 139, 361-400. [MR: 798182] [Zbl: 0596.73033] [Google Scholar]
  44. A. RAOULT, 1992, Asymptotic modeling of the elastodynamics of a multistructure, Asymptotic Analysis, 6, 73-108. [MR: 1188078] [Zbl: 0777.73033] [Google Scholar]
  45. L. TRABUCHO, J.M. VIANO, 1996, Mathematical modelling of rods, in: (P. G. Ciarlet, J. L. Lions, eds.) Handbook of numerical analysis, Vol. IV, North-Holland, Amsterdam. [MR: 1422507] [Zbl: 0873.73041] [Google Scholar]
  46. J.M. VIAÑO, 1983, Contribution à l'étude des modèles bidimensionnelles en thermoélasticité de plaques d'épaisseur non constante, Thesis, Univ. Pierre et Marie Curie, Paris. [Google Scholar]
  47. K. YOSIDA, 1975, Functional Analysis, Springer Verlag, Berlin. [Google Scholar]

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