Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (“short memory”) form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.
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I. Bock, J. Jarušek: Unilateral dynamic contact of viscoelastic von Kármán plates. Adv. Math. Sci. Appl. 16 (2006), 175–187.
I. Bock, J. Jarušek: Unilateral dynamic contact of von Kármán plates with singular memory. Appl. Math., Praha 52 (2007), 515–527.
I. Bock, J. Jarušek: Dynamic contact problem for a bridge modeled by a viscoelastic full von Kármán system. Z. Angew. Math. Phys. 61 (2010), 865–876.
I. Bock, J. Jarušek: Unilateral dynamic contact problem for viscoelastic Reissner-Mindlin plates. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 4192–4202.
J. M. Borwein, Q. J. Zhu: Techniques of Variational Analysis. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 20, Springer, New York, 2005.
C. Eck, J. Jarušek, M. Krbec: Unilateral Contact Problems. Variational Methods and Existence Theorems. Pure and Applied Mathematics (Boca Raton) 270, Chapman & Hall/CRC, Boca Raton, 2005.
C. Eck, J. Jarušek, J. Stará: Normal compliance contact models with finite interpenetration. Arch. Ration. Mech. Anal. 208 (2013), 25–57.
J. Jarušek: Static semicoercive normal compliance contact problem with limited interpenetration. Z. Angew. Math. Phys. 66 (2015), 2161–2172.
J. Jarušek, J. Stará: Solvability of a rational contact model with limited interpenetration in viscoelastodynamics. Math. Mech. Solids 23 (2018), 1040–1048.
H. Koch, A. Stachel: Global existence of classical solutions to the dynamical von Kármán equations. Math. Methods Appl. Sci. 16 (1993), 581–586.
J. E. Lagnese: Boundary Stabilization of Thin Plates. SIAM Studies in Applied Mathematics 10, Society for Industrial and Applied Mathematics, Philadelphia, 1989.
A. Signorini: Sopra alcune questioni di statica dei sistemi continui. Ann. Sc. Norm. Super. Pisa, II. Ser. 2 (1933), 231–251. (In Italian.)
A. Signorini: Questioni di elasticità non linearizzata e semilinearizzata. Rend. Mat. Appl., V. Ser. 18 (1959), 95–139. (In Italian.)
This work was supported by the institutional research plan RVO 67985840.
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Jarušek, J. Solvability of a Dynamic Rational Contact with Limited Interpenetration for Viscoelastic Plates. Appl Math 65, 43–65 (2020). https://doi.org/10.21136/AM.2020.0216-19
- dynamic contact problem
- limited interpenetration
- viscoelastic plate
- existence of solution