Previous |  Up |  Next


Title: On a contact problem for a viscoelastic von Kármán plate and its semidiscretization (English)
Author: Bock, Igor
Author: Lovíšek, Ján
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 50
Issue: 3
Year: 2005
Pages: 203-217
Summary lang: English
Category: math
Summary: We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of stationary variational inequalities of von Kármán type. We derive conditions for applying the Banach fixed point theorem enabling us to solve the biharmonic variational inequalities for each time step. (English)
Keyword: von Kármán system
Keyword: viscoelastic plate
Keyword: integro-differential variational inequality
Keyword: semidiscretization
Keyword: Banach fixed point theorem
MSC: 49J40
MSC: 65R20
MSC: 74D10
MSC: 74K20
idZBL: Zbl 1099.49003
idMR: MR2133727
DOI: 10.1007/s10492-005-0014-2
Date available: 2009-09-22T18:22:00Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] I. Bock: On large deflections of viscoelastic plates.Math. Comput. Simul. 50 (1999), 135–143. Zbl 1053.74560, MR 1717642, 10.1016/S0378-4754(99)00066-X
Reference: [2] I. Bock, J. Lovíšek: On unilaterally supported viscoelastic von Kármán plates with a long memory.Math. Comput. Simul. 61 (2003), 399–407. MR 1984140, 10.1016/S0378-4754(02)00095-2
Reference: [3] I. Bock, J. Lovíšek: On a contact problem for a viscoelastic plate with geometrical nonlinearities.In: IMET 2004 Proceedings of the conference dedicated to the jubilee of Owe Axelsson, Prague, May 25-28, 2004, J.  Blaheta, J.  Starý (eds.), Institute of Geonics AS CR, Praha, pp. 38–41.
Reference: [4] P. G. Ciarlet, P. Rabier: Les équations de von Kármán.Springer Verlag, Berlin, 1980. MR 0595326
Reference: [5] G. Duvaut, J.-L.  Lions: Les inéquations en mécanique et en physique.Dunod, Paris, 1972. MR 0464857
Reference: [6] O. John: On Signorini problem for von Kármán equations.Apl. Mat. 22 (1977), 52–68. Zbl 0387.35030, MR 0454337
Reference: [7] J. Kačur: Application of Rothe’s method to evolution integrodifferential equations.J.  Reine Angew. Math. 388 (1988), 73–105. MR 0944184
Reference: [8] E. Muñoz Rivera, G. Perla Menzala: Decay rates of solutions to a von Kármán system for viscoelastic plates with memory.Q.  Appl. Math. 57 (1999), 181–200. MR 1672191, 10.1090/qam/1672191
Reference: [9] J. Naumann: On some unilateral boundary value problem for the von Kármán equations.Apl. Mat. 20 (1975), 96–125. MR 0437916


Files Size Format View
AplMat_50-2005-3_4.pdf 341.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo