| Title:
|
On Reissner's variational theorem for boundary values in linear elasticity (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
2 |
| Year:
|
1971 |
| Pages:
|
109-124 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
E. Reissner suggested a variational theorem for the theory of elasticity, related closely to the well-known Trefftz method. In the present paper, the Reissner's theorem is discussed within the range of linear anisotropic and non-homogeneous elasticity. For the traction boundary-value problem, the minimal property of the functional and the convergence of any minimizing sequence are proved. For the displacement boundary-value problem and sime mixed problems, it is shown that a modification is necessary. Then, in case of the displacement problem, the maximal property of the functional on the modified class of admissible functions and the convergence of maximizing sequence are proved. () |
| MSC:
|
74B05 |
| MSC:
|
74B99 |
| MSC:
|
74H99 |
| MSC:
|
74P10 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0228.73028 |
| idMR:
|
MR0281402 |
| DOI:
|
10.21136/AM.1971.103335 |
| . |
| Date available:
|
2008-05-20T17:50:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103335 |
| . |
| Reference:
|
[1] 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:
|
[2] D. Rüdiger: Zur Trefftzschen Methode in der Elastizitätstheorie.Appl. Mech., Proc. XIth internát. Congr. appl. Mech., Munich 1964, 350-354, 1966. |
| Reference:
|
[3] К. Ф. Черных: Линейная теория оболочек.ч. II, гл. IX., Издат. Ленинград, унив., 1964. Zbl 1117.65300 |
| Reference:
|
[4] I. Hlaváček: Derivation of non-classical variational principles in the theory of elasticity.Aplikace matematiky 12, 1967, 1, 15-29. MR 0214324 |
| Reference:
|
[5] I. Hlaváček: Variational principles in the linear theory of elasticity for general boundary conditions.Aplikace matematiky 12, 1967, 6, 425 - 448. MR 0231575 |
| Reference:
|
[6] I. Hlaváček J. Nečas: On inequalities of Korn's type. II. Applications to linear elasticity.Archive for Ratl. Mech. Anal. 36, 1970, 312-334. MR 0252845, 10.1007/BF00249519 |
| Reference:
|
[7] С. Г. Михлин: Проблема минимума квадратичного функционала.Гостехиздат, 1952. Zbl 1145.11324 |
| Reference:
|
[8] С. Г. Михлин: Вариационные методы в математической физике.Москва 1957. Zbl 0995.90594 |
| . |
