| Title:
|
Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates (English) |
| Author:
|
Jarušek, Jiří |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
43-65 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
dynamic contact problem |
| Keyword:
|
limited interpenetration |
| Keyword:
|
viscoelastic plate |
| Keyword:
|
existence of solution |
| MSC:
|
35Q74 |
| MSC:
|
74D10 |
| MSC:
|
74H20 |
| MSC:
|
74K20 |
| MSC:
|
74M15 |
| idZBL:
|
07177871 |
| idMR:
|
MR4064589 |
| DOI:
|
10.21136/AM.2020.0216-19 |
| . |
| Date available:
|
2020-02-20T09:45:55Z |
| Last updated:
|
2022-03-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147994 |
| . |
| Reference:
|
[1] Bock, I., Jarušek, J.: Unilateral dynamic contact of viscoelastic von Kármán plates.Adv. Math. Sci. Appl. 16 (2006), 175-187. Zbl 1110.35049, MR 2253231 |
| Reference:
|
[2] Bock, I., Jarušek, J.: Unilateral dynamic contact of von Kármán plates with singular memory.Appl. Math., Praha 52 (2007), 515-527. Zbl 1164.35447, MR 2357578, 10.1007/s10492-007-0030-5 |
| Reference:
|
[3] Bock, I., Jarušek, J.: Dynamic contact problem for a bridge modeled by a viscoelastic full von Kármán system.Z. Angew. Math. Phys. 61 (2010), 865-876. Zbl 1273.74352, MR 2726632, 10.1007/s00033-010-0066-3 |
| Reference:
|
[4] Bock, I., Jarušek, J.: Unilateral dynamic contact problem for viscoelastic Reissner-Mindlin plates.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 4192-4202. Zbl 1402.74068, MR 2803022, 10.1016/j.na.2011.03.054 |
| Reference:
|
[5] Borwein, J. M., Zhu, Q. J.: Techniques of Variational Analysis.CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 20, Springer, New York (2005). Zbl 1076.49001, MR 2144010, 10.1007/0-387-28271-8 |
| Reference:
|
[6] Eck, C., Jarušek, J., Krbec, M.: Unilateral Contact Problems. Variational Methods and Existence Theorems.Pure and Applied Mathematics (Boca Raton) 270, Chapman & Hall/CRC, Boca Raton (2005). Zbl 1079.74003, MR 2128865, 10.1201/9781420027365 |
| Reference:
|
[7] Eck, C., Jarušek, J., Stará, J.: Normal compliance contact models with finite interpenetration.Arch. Ration. Mech. Anal. 208 (2013), 25-57. Zbl 1320.74083, MR 3021543, 10.1007/s00205-012-0602-8 |
| Reference:
|
[8] Jarušek, J.: Static semicoercive normal compliance contact problem with limited interpenetration.Z. Angew. Math. Phys. 66 (2015), 2161-2172. Zbl 1327.35364, MR 3412294, 10.1007/s00033-015-0539-5 |
| Reference:
|
[9] Jarušek, J., Stará, J.: Solvability of a rational contact model with limited interpenetration in viscoelastodynamics.Math. Mech. Solids 23 (2018), 1040-1048. Zbl 1401.74218, MR 3825900, 10.1177/1081286517703262 |
| Reference:
|
[10] Koch, H., Stachel, A.: Global existence of classical solutions to the dynamical von Kármán equations.Math. Methods Appl. Sci. 16 (1993), 581-586. Zbl 0778.73029, MR 1233041, 10.1002/mma.1670160806 |
| Reference:
|
[11] Lagnese, J. E.: Boundary Stabilization of Thin Plates.SIAM Studies in Applied Mathematics 10, Society for Industrial and Applied Mathematics, Philadelphia (1989). Zbl 0696.73034, MR 1061153, 10.1137/1.9781611970821 |
| Reference:
|
[12] Signorini, A.: Sopra alcune questioni di statica dei sistemi continui.Ann. Sc. Norm. Super. Pisa, II. Ser. 2 (1933), 231-251 Italian \99999JFM99999 59.0738.01. MR 1556704 |
| Reference:
|
[13] Signorini, A.: Questioni di elasticità non linearizzata e semilinearizzata.Rend. Mat. Appl., V. Ser. 18 (1959), 95-139 Italian. Zbl 0091.38006, MR 0118021 |
| . |
