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mechanics of solids
Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of errors are suggested.
[1] E. Reissner: Some variational principles in elasticity. О некоторых вариационных теоремах теории упругости. Проблемы механики сплошной среды, Издат. АН СССР, 1961, 328-337. MR 0096419
[2] К. Ф. Черных: Линейная теория оболочек. ч. II., гл. IX. Издат. Ленингр. унив., 1964. Zbl 1117.65300
[3] С. Г. Михлин: Проблема минимума квадратичного функционала. Москва 1952, гл. IV. Zbl 1145.11324
[4] С. Г. Михлин: Вариационные методы в математической физике. Москва 1957. Zbl 0995.90594
[5] W. S. Dorn A. Schild: A converse to the virtual work theorem for deformable solids. Quart. Appl. Math., 14 (1956), 209-213. DOI 10.1090/qam/79418 | MR 0079418
[6] M. E. Gurtin: Variational principles in the linear theory of viscoelasticity. Arch. Ratl. Mech. Anal., 13 (1963), 3, 179-191. DOI 10.1007/BF01262691 | MR 0214321 | Zbl 0123.40803
[7] O. D. Kellog: Foundations of Potential Theory. Springer, Berlin 1929. MR 0222317
[8] Hu Hai-Chang: On some variational principles in the theory of elasticity and the theory of plasticity. Sci. Sinica 4 (1955) 1, 33. Zbl 0066.17903
[9] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[10] J. Nečas: Sur les normes équivalentes dans $W_p^{(k)} (\Omega)$ et sur la coercitivité des formes formellement positives. Les presses de l'Université de Montreal, Janvier 1966, 102-128.
[11] I. Hlaváček: Derivation of nonclassical variational principles in the theory of elasticity. Aplikace matematiky 12 (1967), 1, 15 - 29. MR 0214324
[12] J. Nečas I. Hlaváček: On inequalities of Korn's type. I. General theory. II. Applications in elasticity. To appear in Arch. Ratl. Mech. Anal.
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