| Title:
|
The Reissnerian algorithms in the refined theories of the bending of plates (English) |
| Author:
|
Hanuška, Alexander |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
13 |
| Issue:
|
6 |
| Year:
|
1968 |
| Pages:
|
441-455 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Starting from the refined theories of the bending of plates proposed by I. Babuška and M. Práger and using the variational principle a differential equation of infinite order is derived for the special case of one unknown function $w_0(x,y)$. By the introduction of polymoments and poly-shear forces it is shown that the obtained boundary conditions represent a generalization of Kirchhoff's boundary conditions and, therefore, the solution corresponds to the fundamental stress state only. () |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0261.73038 |
| DOI:
|
10.21136/AM.1968.103194 |
| . |
| Date available:
|
2008-05-20T17:43:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103194 |
| . |
| Reference:
|
[1] I. Babuška M. Práger: Reissnerian Algorithms in the Theory of Elasticity.Bulletin de l'Academie Polonaise des Sciences, Série des sciences techniques, Vol. VIII, No. 8, 411 - 417, 1960, (in Russian) Механика, сб. переводов, Но 6, стр. 123-128, 1961. |
| Reference:
|
[2] I. Babuška, al.: Algorithmi of the Reissnerian Type in the Mathematical Theory of Elasticity.(in Czech), Sborník 24 Fak. inž. stav. ČVUT v Praze, Státní ped. naklad., pp. 15 - 47, Praha 1961. |
| Reference:
|
[3] I. Babuška: Die Stabilität mit Rücksicht auf das Definitionsgebiet und die Frage der Formulierung des Plattenproblems.(Vorbericht), Aplikace Matematiky, 7, No 6, str. 457-461, 1962, (in Russian) Механика, сб. переводов, Но 2, стр. 149-153, 1963. |
| Reference:
|
[4] I. Babuška: Problems of Optimal Reduction of Three-Dimensional Problems of the Theory of Elasticity.Theory of Plates and Shells, pp. 15 - 28, Vydavatelstvo SAV, Bratislava, 1966. |
| Reference:
|
[5] А. И. Лурье: К теории толстых плит.Прикладная математика и механика, T. VI, Вып. 2-3, стр. 151-168, 1942. Zbl 0147.22303 |
| Reference:
|
[6] А. И. Лурье: Пространственные задачи теории упругости.Гос. изд. техн-.теор. лит., Москва, 1955. Zbl 1160.26300 |
| Reference:
|
[7] А. Л. Гольденвейзер: Построение приближенной теории изгиба пластинки методом асимптотического интегрирования уравнений теории упругости.Прикл. мат. и мех. T. XXVI, Но. 4, стр. 668-686, 1962. Zbl 1005.68507 |
| Reference:
|
[8] K. О. Friedrichs R. F. Dressler: A Boundary-Layer Theory for Elastic Plates.Comunications on Pure and Applied Mathematics, Vol. XIV, pp. 1 - 33, 1961. MR 0122117 |
| Reference:
|
[9] И. И. Ворович: Некоторые математические вопросы теории пластин и оболочек. Механика твердого тела.Труды всесоюзного съезда по теоретической и прикладной механике, стр. 116-136, Изд. Наука, Москва 1966. Zbl 1155.78304 |
| Reference:
|
[10] И. И. Ворович: Общие проблемы теории пластин и оболочек.Всесоюзная конф. по теории оболочек и пластинок 1966, стр. 896-903, Изд. Наука, Москва, 1966. Zbl 1155.78304 |
| Reference:
|
[11] A. L. Goldenveizer: The principles of reducing three-dimensional problems of elasticity to two-dimensional problems of the theory of plates and shells.Applied Mechanics, Proc. of the 11th Int. Congr. of Appl. Mech., Munich (Germany) 1964, Ed. H. Görtler, pp. 306-311, Springer Verlag, Berlin - Heidelberg - New York, 1966. |
| Reference:
|
[12] E. Reissner: On the foundation of the theory of elastic shells.Applied Mechanics, Proc. of the 11th Int. Congr. of Appl. Mech., Munich (Germany) 1964, Ed. H. Görtler, pp. 20-30, Springer Verlag, Berlin- Heidelberg- New York, 1966. |
| Reference:
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[13] L. N. G. Filon: On the expansion of polynomials in series of functions.Proc. London Math. Soc., Vol. 4, II series, pp. 396-430, 1906. |
| Reference:
|
[14] L. H. Donnell: A theory for thick plates.Proc. 2nd U.S. Nat. Congr. Appl. Mech., pp. 369-373, 1954. MR 0086504 |
| Reference:
|
[15] В. А. Агарев: Метод начальных функций для двухмерных краевых задач теории упругости.Изд. АН УССР, Киев, 1963. Zbl 1145.93303 |
| Reference:
|
[16] Л. С. Лейбензон: Собрание трудов.T. 1, Изд. АН СССР, Москва 1951. Zbl 1165.94313 |
| Reference:
|
[17] В. К. Прокопов: Применение символического метода к выводу уравнений теории плит.Прикл. мат. и мех., T 29, Вып. 5, стр. 902-919, 1965. Zbl 1099.01519 |
| Reference:
|
[18] A. Hanuška: The second approximation of the Reissnerian algorithmic in the theory of bending of plates.(in Slovak), Stavebnícky časopis SAV, XV, 9, pp. 523-540, 1967. |
| Reference:
|
[19] E. H. Mansfield: The bending and stretching of plates.(Int. Series of Monographs on Aeronautics and Astronautics. Div. I, vol. 6, Pergamon Press, Oxford - London - New York, 1964. Zbl 0125.42002, MR 1111482 |
| Reference:
|
[20] E. Reissner: On the derivation of boundary conditions for plate theory.Proc. Roy. Soc., London (A) 276, pp. 178-186, 1963. Zbl 0133.43501, MR 0158590 |
| . |
