Article
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
Summary:
The paper concerns the v. Kármán equations governing the bending of a thin elastic plate under the condition of free boundary. Starting from the definition of a variational solution, the boundary value problem considered is replaced by an equivalent abstract operator equation to which the known theorems of the nonlinear operator theory apply. The main result consists in an existence theorem of a variational solution for the problem under consideration.
References:
[1] Berger M. S., Fife P.: On von Karman's equations and the buckling of a thin elastic plate. 11. Plate with general edge conditions. - Comm. Pure Appl. Math.,21 (1968), 227- 241. DOI 10.1002/cpa.3160210303 | MR 0229978
[2] Fife P.: Non-linear deflection of thin elastic plates under tension. - Comm. Pure Appl. Math., 14 (1961), 81 - 112. DOI 10.1002/cpa.3160140202 | MR 0128697 | Zbl 0099.40802
[3] Knightly G. H.: An existence theorem for the von Kármán equations. - Arch. Rat. Mech. Anal., 27 (1967), 233 - 242. DOI 10.1007/BF00290614 | MR 0220472 | Zbl 0162.56303
[4] Knightly G. H., Sather D.: On nonuniqueness of solutions of the von Kármán equations. - Arch. Rat. Mech. Anal., 36 (1970), 65-78. DOI 10.1007/BF00255747 | MR 0261835 | Zbl 0188.57603
[5] Morozov N. F.: Nonlinear problems in the theory of thin plates. (Russian). - Vestnik Leningr. Univ., 19 (1958), 100-124. MR 0102224
[6] Nečas J.: Les méthodes directes en théorie des équations elliptiques. - Academia, Prague 1967. MR 0227584
[7] Sharij Ju. I., Jurchenko A. S.: Dirichleťs problem for equations of Karman's type. - Diff. urav., 4(1968), 1713-1719. MR 0235279
Search
Partner of
