Article
MSC:
35J05,
35J60,
35J65,
73K12,
74B20,
74K20 | MR 0634281 | Zbl 0478.73032 | DOI: 10.21136/AM.1981.103934
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Keywords:
existence of solution; nonlinear relation between intensity of stresses and deformations
existence of solution; nonlinear relation between intensity of stresses and deformations
Summary:
A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.
References:
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[2] Н. Ф. Ершов: Об упруго-пластическом изгибе пластинок при больших прогибах. Строительная механика и расчет сооружений. Н.-З, 1962. Zbl 1005.68507
[3] О. John J. Nečas: On the solvability of von Kármán equations. Aplikace matematiky 20 (1975), 48-62, MR 0380099
[4] I. Hlaváček J. Naumann: Inhomogeneous boundary value problems for the von Kármán equations, I. Aplikace matematiky 19 (1974), 253-269. MR 0377307
[5] J. Franců: On Signorini problem for von Kármán equations (The case of angular domain). Aplikace matematiky 24 (1979), 355 - 371. MR 0547039 | Zbl 0479.73041
[6] G. H. Knightly: An existence theorem for the von Kármán equations. Arch. Rat. Mech. Anal., (1967), 233-242. MR 0220472 | Zbl 0162.56303
[7] И. В. Скрыпник: Нелинейные еллщтгические уравнения высшего порядка. ,Наукова думка", Киев 1973. Zbl 1131.90321
[8] R. Kodnár: Non-linear problems of the orthogonal anisotropic shallow shells. Proceedings of summer school "Theory of nonlinear operators". Abhandlungen der Akademie der Wissenschaften der DDR. N-6, 1977.
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