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mechanics of solids
Generalized variational principles, suggested by Hu Hai-Chang and Washizu or Hellinger and Reissner respectively, are derived on the base of complementary energy respectively. Besides, a short survey of further variational theorems, which follow from the fundamental principles, and the proof of the convergence for a method based on one of them, are presented.
[1] Courant-Hilbert: Methoden der Mathematischen Physik I.
[2] P. Funk: Variationsrechnung und ihre Anwendung in Physik und Technik. Springer 1962, pp. 515-520. MR 0152914 | Zbl 0119.09101
[3] С. Г. Михлин: Вариационные методы в математической физике. Москва 1957. Zbl 0995.90594
[4] I. Hlaváček: Sur quelques theorémes variationelles dans la théorie du fluage linéaire. Aplikace matematiky 11 (1966), 4, 283-295.
[5] W. Prager J. L. Synge: Approximations in elasticity based on the concept of function space. Quart. Appl. Math. 5, 3 (1947), 241-269. MR 0025902
[6] Hu Hai-Chang: On some variational principles in the theory of elasticity and the theory of plasticity. Scientia Sinica 4 (1955), 1, 33-55. Zbl 0066.17903
[7] K. Washizu: On the variational principles of elasticity and plasticity. ASRL TR 25-18. Massachusetts Inst. of Techn. 1955.
[8] E. Reissner: On some variational theorems in elasticity. Problems of Continuum Mechanics, 370-381. Contributions in honor of 70th birthday of N. I. Muschelišvili, 1961. MR 0122087
[9] И. H. Слезингер: Принцип Кастильяно в нелинейной теории упругости. Прикладна механіка5(1959), 1,38-44. MR 0102945 | Zbl 1047.90504
[10] Л. Айнола: О вариационной задаче Кастильяно динамики нелинейной теории упругости. Изв. АН Эстон. CCP 10 (1961), 1, сер. физ.-мат., 22-27. Zbl 1160.68305
[11] С. Г. Михлин: Проблема минимума квадратного функционала. Гостехиздат 1952. Zbl 1145.11324
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