| Title:
|
Derivation of non-classical variational principles in the theory of elasticity (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
12 |
| Issue:
|
1 |
| Year:
|
1967 |
| Pages:
|
15-29 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
mechanics of solids |
| MSC:
|
73-49 |
| idZBL:
|
Zbl 0163.19201 |
| idMR:
|
MR0214324 |
| DOI:
|
10.21136/AM.1967.103063 |
| . |
| Date available:
|
2008-05-20T17:37:29Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103063 |
| . |
| Reference:
|
[1] Courant-Hilbert: Methoden der Mathematischen Physik I. |
| Reference:
|
[2] P. Funk: Variationsrechnung und ihre Anwendung in Physik und Technik.Springer 1962, pp. 515-520. Zbl 0119.09101, MR 0152914 |
| Reference:
|
[3] С. Г. Михлин: Вариационные методы в математической физике.Москва 1957. Zbl 0995.90594 |
| Reference:
|
[4] I. Hlaváček: Sur quelques theorémes variationelles dans la théorie du fluage linéaire.Aplikace matematiky 11 (1966), 4, 283-295. |
| Reference:
|
[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, 10.1090/qam/25902 |
| Reference:
|
[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 |
| Reference:
|
[7] K. Washizu: On the variational principles of elasticity and plasticity.ASRL TR 25-18. Massachusetts Inst. of Techn. 1955. |
| Reference:
|
[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 |
| Reference:
|
[9] И. H. Слезингер: Принцип Кастильяно в нелинейной теории упругости.Прикладна механіка5(1959), 1,38-44. Zbl 1047.90504, MR 0102945 |
| Reference:
|
[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 |
| Reference:
|
[11] С. Г. Михлин: Проблема минимума квадратного функционала.Гостехиздат 1952. Zbl 1145.11324 |
| . |
