| Title:
|
Inhomogeneous boundary value problems for the von Kármán equations. I (English) |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Naumann, Joachim |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
4 |
| Year:
|
1974 |
| Pages:
|
253-269 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence of a "variational" solution to the system of nonlinear equations, governing the equilibrium of a thin elastic plate is proved. The boundary conditions correspond with a plate, the edge of which is partially clamped, supported and elastically supported or clamped, being loaded by moments, transversal loads and by forces in the plane of the plate. In Part I only "fixed" plates are studied, i.e. such that any deflection of a rigid plate on rigid supports and clampings is eliminated by the kinematic constraints. () |
| MSC:
|
35A15 |
| MSC:
|
35Q99 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0313.35064 |
| idMR:
|
MR0377307 |
| DOI:
|
10.21136/AM.1974.103539 |
| . |
| Date available:
|
2008-05-20T17:59:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103539 |
| . |
| Reference:
|
[1] Berger M. S., Fife P.: On von Kármán's equations and the buckling of a thin elastic plate, II. Plate with general edge conditions.Comm. Pure Appl. Math., 21 (1968), 227-241. MR 0229978, 10.1002/cpa.3160210303 |
| Reference:
|
[2] Brézis H.: Équations et inéquations non-linéaires dans les espaces véctoriels en dualité.Ann. Inst. Fourier, Grenoble, 18 (1968), 115-176. MR 0270222, 10.5802/aif.280 |
| Reference:
|
[3] Fife P.: Non-linear deflection of thin elastic plates under tension.Comm. Pure Appl. Math., 14 (1961), 81-112. Zbl 0099.40802, MR 0128697, 10.1002/cpa.3160140202 |
| Reference:
|
[4] Hlaváček I., Nečas J.: On inequalities of Korn's type, I. Boundary-value problems for elliptic systems of partial differential equations.Arch. Rat. Mech. Anal., 36 (1970) 305-311. Zbl 0193.39001, MR 0252844 |
| Reference:
|
[5] Jakovlev G. N.: Boundary properties of functions of class $W_p^{(1)}$ on the domains with angular points.(Russian). DAN SSSR, 140 (1961), 73-76. MR 0136988 |
| Reference:
|
[6] Knightly G. H.: An existence theorem for the von Kármán equations.Arch. Rat. Mech. Anal., 27 (1967), 233-242. Zbl 0162.56303, MR 0220472, 10.1007/BF00290614 |
| Reference:
|
[7] Knightly G. H., Sather D.: On nonuniqueness of solutions of the von Kármán equations.Arch. Rat. Mech. Anal., 36 (1970), 65-78. Zbl 0188.57603, MR 0261835, 10.1007/BF00255747 |
| Reference:
|
[8] Morozov N. F.: Nonlinear problems in the theory of thin plates.(Russian). Vestnik Leningr. Univ., 19 (1955), 100-124. MR 0102224 |
| Reference:
|
[9] Naumann J.: An existence theorem for the v. Kármán equations under free boundary conditions.Apl. mat. 19 (1974), 17-27. MR 0346294 |
| Reference:
|
[10] Naumann J.: On bifurcation buckling of thin elastic shells.(to appear). Zbl 0303.73031, MR 0373426 |
| Reference:
|
[11] Nečas J.: Les méthodes directes en théorie des equations elliptiques.Academia, Prague 1967. MR 0227584 |
| . |
