@article{M2AN_1997__31_6_733_0, author = {Alvarez-V\'asquez, L. J. and Via\~no, J. M.}, title = {Modeling and optimization of non-symmetric plates}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {31}, year = {1997}, pages = {733-763}, mrnumber = {1485753}, zbl = {0894.73088}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1997__31_6_733_0} }
Alvarez-Vásquez, L. J.; Viaño, J. M. Modeling and optimization of non-symmetric plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 31 (1997) pp. 733-763. http://gdmltest.u-ga.fr/item/M2AN_1997__31_6_733_0/
[1] Sobolev spaces, Academic Press, New York. | MR 450957 | Zbl 0314.46030
, 1975,[2] 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
, , 1992,[3] Convexity and optimization in Banach spaces, Sijthoff and Noordhoff, Bucharest, 1978. | MR 860772 | Zbl 0379.49010
, , 1978,[4] Justification de modèles de plaques correspondant à différentes conditions aux limites, Thesis, Univ. Pierre et Marie Curie, Paris.
, 1981,[5] A remark on the von Karman Equations, Comp. Meth. Appl. Mech. Eng., 37, 79-92. | MR 699016 | Zbl 0486.73051
, , 1983,[6] Asymptotic thermoelastic behavior of flat plates, Quart. Appl. Math., 45, 645-667. | MR 917015 | Zbl 0629.73007
, , 1987,[7] Opérateurs maximaux monotones et semigroupes de contractions dans les espces de Hilbert, North-Holland. | Zbl 0252.47055
, 1973,[8] 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
, 1980,[9] Análisis numerico de algunos problemas de optimización estructural, Thesis, Universidad de Santiago de Compostela.
, 1982,[10] Optimality conditions and numerical approximations for some optimal design problems, Control Cibernet, 19, 73-91. | MR 1118675 | Zbl 0731.49010
, 1990,[11] Optimisation: Théorie et Algorithmes, Dunod, Paris. | MR 298892 | Zbl 0211.17402
, 1971,[12] A justification of the von Karman equations, Arch. Rat. Mech. Anal., 73, 349-389. | MR 569597 | Zbl 0443.73034
, 1980,[13]Mathematical Elasticity, Vol. 1, North-Holland, Amsterdam. | MR 936420 | Zbl 0648.73014
, 1988,[14] Plates and junctions in elastic multi-structures, Masson, Paris. | MR 1071376 | Zbl 0706.73046
, 1990,[15] A justification of the two dimensional linear plate model, J. Mécanique, 18, 315-344. | MR 533827 | Zbl 0415.73072
, , 1979,[16] A justification of a nonlinear model in plate theory, Comp. Meth. Appl. Mech. Eng., 17/18, 222-258. | MR 533827 | Zbl 0405.73050
, , 1979,[17] Two-dimensional approximation of three-dimensional eigenvalue problems in plate theory, Comp. Meth. Appl. Mech. Eng., 26, 145-172. | MR 626720 | Zbl 0489.73057
, , 1981,[18] Justification of the boundary conditions of a clamped plate by an asyptotic analysis, Asymptotic Analysis, 2, 257-277. | MR 1030351 | Zbl 0699.73011
, , 1989,[19] Justification of the two-dimensional equations of a linearly elastic shallow shell, Comm. Pure Appl. Math., 45,327-360. | MR 1151270 | Zbl 0769.73050
, , 1992,[20] 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
, , 1985,[21] Les équations de von Karman, Lecture Notes in Mathematics, vol. 826 Springer Verlag, Berlin. | MR 595326 | Zbl 0433.73019
, , 1980,[22] 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
, , , , , 1988,[23] Reinforced and honey comb structures, J. Math. Pures Appl., 65, 403-422. | MR 881689 | Zbl 0656.35031
, , 1988,[24] Justification de modèles de plaques non lineaires pour des lois de comportement générales, Mod. Math. Anal. Num., 20, 225-249. | Numdam | MR 852680 | Zbl 0634.73048
, 1986,[25] Sur une justification des modèles de plaques et coques par les méthodes asymptotiques, Thesis, Univ. Pierre et Marie Curie.
, 1980,[26] Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité, RAIRO Anal. Num., 15, 331-369. | Numdam | MR 642497 | Zbl 0479.73042
, 1981,[27] A classification of thin shell theories, Acta. Appl. Math., 4, 15-63. | MR 791261 | Zbl 0531.73044
, 1985,[28] Une théorie asymptotique des plaques minces en élasticité linéaire, Masson, Paris. | MR 830660 | Zbl 0627.73064
, 1986,[29] Les inéquations en Mécanique et en Physique, Dunod, Paris. | MR 464857 | Zbl 0298.73001
, , 1972,[30] Modèles de coques élastiques non linéaires : méthode asymptotique et existence de solution, Thesis, Univ. Pierre et Marie Curie, Paris.
, 1989,[31] A boundary-layer theory for elastic plates, Comm. Pure. Appl. Math., 14, 1-33. | MR 122117 | Zbl 0096.40001
, , 1961,[32] 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
, 1962,[33] Finite element approximation for optimal shape design, John Wiley, Chichester. | MR 982710 | Zbl 0713.73062
, , 1988,[34] Applied Optimal Design Mechanical and Strutural Systems, John Wiley, New York.
, , 1979,[35] 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
, , , 1984,[36] 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
, , , 1984,[37] A now model for thin plates with rapidly varying thickness, Int. J. Solids Structures, 20, 333-350. | MR 739921 | Zbl 0532.73055
, , 1984,[38] 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
, , 1985,[39] 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
, , 1986,[40] A new model for nonlinear elastic plates with rapidly varying thickness, Applicable Analysis, 32, 107-127. | MR 1017526 | Zbl 0683.73027
, 1989,[41] 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
, 1990,[42] 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.
, 1980,[43] 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
, 1985,[44] Asymptotic modeling of the elastodynamics of a multistructure, Asymptotic Analysis, 6, 73-108. | MR 1188078 | Zbl 0777.73033
, 1992,[45] 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
, , 1996,[46] Contribution à l'étude des modèles bidimensionnelles en thermoélasticité de plaques d'épaisseur non constante, Thesis, Univ. Pierre et Marie Curie, Paris.
, 1983,[47] Functional Analysis, Springer Verlag, Berlin.
, 1975,