Article
Keywords:
mechanics of solids
Summary:
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.
References:
[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.
DOI 10.1090/qam/25902 |
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