Previous |  Up |  Next


The paper deals with the V. Kármán equations of a thin elastic plate. The edges of the rectangular plate are simply supported or clamped and the membrane effects due to the deflection of the plate do not alter its curvature. It is shown that the boundary condition can be given completely in terms of the deflection function and the stress function. After defining the variational solution of the problem two special cases, namely the buckling problem and the bending problem are treated. A bifurcation theorem is proved in the first case and an existence theorem in the other.
[1] Berger M. S.: On von Kármán's equations and the buckling of a thin elastic plate, I. The clamped plate. - Comm. Pure Appl. Math. 20 (1961), 687-719. DOI 10.1002/cpa.3160200405 | MR 0221808
[2] Berger M. S., Fife P. C.: 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. DOI 10.1002/cpa.3160210303 | MR 0229978 | Zbl 0162.56501
[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] Муштари X. М., Галимов К. 3.: Нелинейная теория упругих оболочек. - Таткнигоиздат, Казань 1957. Zbl 0995.90594
[5] Nečas J.: Les méthodes directes en théorie des équations elliptiques. - Academia, Prague 1967. MR 0227584
[6] Nečas J., Naumann J.: On a boundary value problem in nonlinear theory of thin elastic plates. - Aplikace Matematiky., 19 (1974), 7-16. MR 0338557
[7] Папкович П. Ф.: Строительная механика корабля, II. - Оборонгиз, Ленинград 1941. Zbl 0063.09073
[8] Скрыпиик И. В.: Точки бифуркации вариационных задач. - Математическая физика, В. Р., Наукова Думка, Киев 1971, 117-123. Zbl 1168.35423
[9] Скрыпник И В.: О бифуркации равновесия гибких пластин. - Математическая физика, В. 13., Наукова думка, Киев 1973, 159-161. MR 0327092 | Zbl 1221.53041
Partner of
EuDML logo