Ciarlet, Philippe G.; Destuynder, Phillipe A justification of a nonlinear model in plate theory. (English) Zbl 0405.73050 Computer Methods Appl. Mech. Engin. 17-18, 227-258 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 97 Documents MSC: 74K20 Plates 74B20 Nonlinear elasticity Keywords:Nonlinear Plate Model; Nonlinear Three-Dimensional Elasticity Model; Asymptotic Expansion Method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Ciarlet, P. G.; Destuynder, P., Une justification d’un modèle non linéaire en théorie des plaques, C.R. Acad. Sci. Paris, 287, 33-36 (1978) · Zbl 0382.73012 [2] Truesdell, C., Comments on rational continuum mechanics, (Three lectures for the International Symposium on Continuum Mechanics and Partial Differential Equations. Three lectures for the International Symposium on Continuum Mechanics and Partial Differential Equations, Univ. Federal do Rio de Janeiro, Aug. 1-5 (1977)) · Zbl 0188.58803 [3] Ciarlet, P. G.; Destuynder, P., Une justification du modèle biharmonique en théorie linéaire des plaques, C.R. Acad. Sci. Paris, 285, 851-854 (1977) · Zbl 0374.73057 [4] P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. To appear in J. Mécanique.; P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional linear plate model. To appear in J. Mécanique. · Zbl 0415.73072 [5] P. Destuynder, Application de la méthode des développements asymptotiques à la théorie des plaques et des coques, Doctoral Dissertation, Univ. Pierre et Marie Curie, Paris.; P. Destuynder, Application de la méthode des développements asymptotiques à la théorie des plaques et des coques, Doctoral Dissertation, Univ. Pierre et Marie Curie, Paris. [6] P. Destuynder, A comparison between the two-dimensional linear plate model and the three-dimensional elasticity model. To appear.; P. Destuynder, A comparison between the two-dimensional linear plate model and the three-dimensional elasticity model. To appear. [7] Lions, J. L., Perturbations singulières dans les problèmes aux limites et en contrǒle optimal, (Lecture Notes in Mathematics, 323 (1973), Springer: Springer Berlin) · Zbl 0268.49001 [8] Rigolot, A., Déplacements finis et petites déformations des poutres droites: Analyse asymptotique de la solution à grande distance des bases, J. Méc. Appl., 1, 175-206 (1977) [9] Stoker, J. J., Nonlinear elasticity (1968), Gordon and Breach: Gordon and Breach New York · Zbl 0187.45801 [10] P.G. Ciarlet, A justification of the von Karmán equations. To appear.; P.G. Ciarlet, A justification of the von Karmán equations. To appear. · Zbl 0443.73034 [11] Adams, R. A., Sobolev spaces (1975), Academic Press: Academic Press New York · Zbl 0186.19101 [12] Truesdell, C.; Noll, W., The non-linear field theories of mechanics, (Flügge, S., Handbuch der Physik, III/3 (1965), Springer: Springer Berlin) · Zbl 0779.73004 [13] Wang, C.-C.; Truesdell, C., Introduction to rational elasticity (1973), Noordhoff: Noordhoff Groningen · Zbl 0308.73001 [14] Valid, R., La mécanique des milieux continus et le calcul des structures (1977), Eyrolles: Eyrolles Paris · Zbl 0454.73003 [15] Nečas, J., Les méthodes directes en théorie des equations elliptiques (1967), Masson: Masson Paris · Zbl 1225.35003 [16] Geymonat, G., Sui problemi ai limiti per i sistemi lineari ellitici, Ann. Mat. Pura Appl., 69, 207-284 (1965) · Zbl 0152.11102 [17] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17, 35-92 (1964) · Zbl 0123.28706 [18] Green, A. E.; Zerna, W., Theoretical elasticity (1968), Univ. Press: Univ. Press Oxford · Zbl 0155.51801 [19] Nečas, J., Theory of locally monotone operators modeled on the finite displacement theory for hyperelasticity, Beiträge zur Analysis, 8, 103-114 (1976) · Zbl 0332.73046 [20] Stoppelli, F., Un teorema di esistenza e di unicità relative allé equazioni dell’elastostatica isoterma per deformazioni finite, Ricerche Mat., 3, 247-267 (1954) · Zbl 0058.39701 [21] Ball, J. M., Convexity condition and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., 63, 337-403 (1977) · Zbl 0368.73040 [22] Meisters, G. H.; Olech, C., Locally one-to-one mappings and a classical theorem on schlicht functions, Duke Math. J., 30, 63-80 (1963) · Zbl 0112.37702 [23] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [24] Céa, J., Optimisation, théorie et algorithmes (1971), Dunod: Dunod Paris · Zbl 0211.17402 [25] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math., 12, 623-727 (1959) · Zbl 0093.10401 [26] Nečas, J.; Naumann, J., On a boundary value problem in nonlinear theory of thin elastic plates, Apl. Mat., 19, 7-16 (1974) · Zbl 0295.73056 [27] Landau, L.; Lifchitz, E., Théorie de l’élasticité (1967), Mir: Mir Moscow · Zbl 0166.43101 [28] Timoshenko, S.; Woinowsky-Krieger, S., Theory of plates and shells (1959), McGraw-Hill: McGraw-Hill New York · Zbl 0114.40801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.