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Bifurcation theory for elastic plates subjected to unilateral conditions. (English) Zbl 0364.73030


MSC:

74G60 Bifurcation and buckling
74K20 Plates
35R99 Miscellaneous topics in partial differential equations
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[1] Budiansky, B., Theory of buckling and post-buckling behavior of elastic structures, (Yih, Chia Shun, Advances in Applied Mechanics, Vol. 14 (1974), Academic Press: Academic Press New York) · Zbl 0195.26703
[2] Do, Cl, Problèmes de valeurs propres d’inéquations variationnelles; application aux plaques minces, (International Congress of Mathematicians. International Congress of Mathematicians, Vancouver (1974))
[3] Do, Cl, Problèmes de valeurs propres pour une inéquation variationnelle sur un cône et application au flambement unilatéral d’une plaque mince, C. R. Acad. Sci. A, 280, 45-48 (1975) · Zbl 0298.73077
[4] Do, Cl, The buckling of a thin elastic plate subjected to unilateral conditions, (Germain, P.; Naijroles, B., Applications of methods of functional analysis to problems of mechanics. Applications of methods of functional analysis to problems of mechanics, Lecture Notes in Mathematics, Vol. 503 (1976), Springer: Springer Berlin) · Zbl 0337.73034
[5] H. Beirao da VeigaJ. Functional Anal.; H. Beirao da VeigaJ. Functional Anal. · Zbl 0431.47039
[6] J. P. Dias and J. HernandezJ. Math. Pures Appl.; J. P. Dias and J. HernandezJ. Math. Pures Appl.
[7] Moreau, J. J., La notion de sur-potentiel et les liaisons unilatérales en élastostatique, C. R. Acad. Sci. A, 267, 954-957 (1968) · Zbl 0172.49802
[8] Berger, M. S., On von Karman’s equations and the buckling of thin elastic plate, I, the clamped plate, Comm. Pure Appl. Math., 20, 687-719 (1967) · Zbl 0162.56405
[9] Berger, M. S., A bifurcation theory for nonlinear elliptic partial differential equations and related systems, (Keller, J. B.; Antman, S., Bifurcation Theory and Nonlinear Eigenvalue Problems (1969), Benjamin: Benjamin New York) · Zbl 0181.11603
[10] Berger, M. S.; Fife, P., On von Karman’s equations and the buckling of thin elastic plate, II, plate with general edge conditions, Comm. Pure Appl. Math., 21, 227-241 (1968) · Zbl 0162.56501
[11] Landau, L.; Lifchitz, E., (Théorie de l’élasticité, Physique théorique, Vol. VII (1967), Editions Mir: Editions Mir Moscou) · Zbl 0166.43101
[12] Duvaut, G.; Lions, J. L., Les inéquations en Mécanique et en Physique (1972), Dunod: Dunod Paris · Zbl 0298.73001
[13] Duvaut, G.; Lions, J. L., Problèmes unilatéraux dans la théorie de la flexion forte des plaques, J. Méca, 13, No. 1, 51-74 (1974) · Zbl 0294.73060
[14] Potier-Ferry, M., Charges limites et théorème d’existence en théorie des plaques élastiques, C. R. Acad. Sci. A, 280, 1385-1387 (1975) · Zbl 0311.73028
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