| Title:
|
The number of buckled states of circular plates (English) |
| Author:
|
Marko, Ľubomír |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
113-132 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the exact number of solutions of von Kármán equations for a rotationally symmetric buckling of a thin elastic plate. The plate of constant thickness is in static equilibrium under a uniform compressive thrust applied along its edge in the plane of the plate. The theory of M. G. Crandall, P. H. Rabinowitz [4], is used and the theory of M. S. Berger [1], [3] and M. S. Berger and P. C. Fife [2] is adapted. This work is a part of [6]. () |
| Keyword:
|
Fredholm operator |
| Keyword:
|
static equilibrium |
| Keyword:
|
plate of constant thickness |
| Keyword:
|
Fredholm map of index zero |
| Keyword:
|
singular point |
| Keyword:
|
rotationally symmetric buckled states |
| Keyword:
|
von Kármán plate equations |
| Keyword:
|
operator equation |
| Keyword:
|
proper Sobolev space |
| Keyword:
|
local bifurcation behavior |
| Keyword:
|
nodal properties |
| MSC:
|
34B15 |
| MSC:
|
35B32 |
| MSC:
|
35J65 |
| MSC:
|
37G99 |
| MSC:
|
58E07 |
| MSC:
|
58F14 |
| MSC:
|
73C50 |
| MSC:
|
73H05 |
| MSC:
|
73K10 |
| MSC:
|
74G60 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0682.73036 |
| idMR:
|
MR0990299 |
| DOI:
|
10.21136/AM.1989.104340 |
| . |
| Date available:
|
2008-05-20T18:36:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104340 |
| . |
| Reference:
|
[1] M. S. Berger: On von Kármán's Equations and the Buckling of a Thin Elastic Plate, I The Clamped Plate.Comm. on Pure and Appl. Math. vol. XX, 1967, 687-719. Zbl 0162.56405, MR 0221808, 10.1002/cpa.3160200405 |
| Reference:
|
[2] M. S. Berger P. C. Fife: Von Kármán's Equations and the Buckling of a Thin Elastic Plate, II Plate with General Edge Conditions.Comm. on Pure and Appl. Math., vol. XXI, 1968, 227-241. MR 0229978 |
| Reference:
|
[3] M. S. Berger: Nonlinear Problems with Exactly Three Solutions.Indiana University Math. Journal, vol. 28, No 4 (1979), 689-698. Zbl 0431.47037, MR 0542952, 10.1512/iumj.1979.28.28047 |
| Reference:
|
[4] M. G. Crandall P. H. Rabinowitz: Bifurcation from Simple Eigenvalue.J. Funct. Anal. 8 (1971), 321-340. MR 0288640, 10.1016/0022-1236(71)90015-2 |
| Reference:
|
[5] A. Kufner: Weighted Sobolev Spaces.Teubner, Leipzig, 1980. Zbl 0455.46034, MR 0664599 |
| Reference:
|
[6] Ľ. Marko: Buckled States of Circular Plates.thesis, 1985 (Slovak). |
| Reference:
|
[7] L. Nirenberg: Topics in Nonlinear Functional Analysis.Russian translation, Mir, Moscow 1977. Zbl 0426.47034, MR 0488104 |
| Reference:
|
[8] A. S. Voľmir: Elastic Plates and Shells.(Russian). GITTL, Moscow 1956. |
| Reference:
|
[9] J. H. Wolkowisky: Existence of Buckled States of Circular Plates.Comm. on Pure and Appl. Math. vol. XX, 1967, 549-560. Zbl 0168.45206, MR 0213087 |
| . |
