Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates

Jiří Jarušek

Applications of Mathematics (2020)

  • Volume: 65, Issue: 1, page 43-65
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Jarušek, Jiří. "Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates." Applications of Mathematics 65.1 (2020): 43-65. <http://eudml.org/doc/295032>.

@article{Jarušek2020,
abstract = {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.},
author = {Jarušek, Jiří},
journal = {Applications of Mathematics},
keywords = {dynamic contact problem; limited interpenetration; viscoelastic plate; existence of solution},
language = {eng},
number = {1},
pages = {43-65},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates},
url = {http://eudml.org/doc/295032},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Jarušek, Jiří
TI - Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 43
EP - 65
AB - 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.
LA - eng
KW - dynamic contact problem; limited interpenetration; viscoelastic plate; existence of solution
UR - http://eudml.org/doc/295032
ER -

References

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  6. Eck, C., Jarušek, J., Krbec, M., 10.1201/9781420027365, Pure and Applied Mathematics (Boca Raton) 270, Chapman & Hall/CRC, Boca Raton (2005). (2005) Zbl1079.74003MR2128865DOI10.1201/9781420027365
  7. Eck, C., Jarušek, J., Stará, J., 10.1007/s00205-012-0602-8, Arch. Ration. Mech. Anal. 208 (2013), 25-57. (2013) Zbl1320.74083MR3021543DOI10.1007/s00205-012-0602-8
  8. Jarušek, J., 10.1007/s00033-015-0539-5, Z. Angew. Math. Phys. 66 (2015), 2161-2172. (2015) Zbl1327.35364MR3412294DOI10.1007/s00033-015-0539-5
  9. Jarušek, J., Stará, J., 10.1177/1081286517703262, Math. Mech. Solids 23 (2018), 1040-1048. (2018) Zbl1401.74218MR3825900DOI10.1177/1081286517703262
  10. Koch, H., Stachel, A., 10.1002/mma.1670160806, Math. Methods Appl. Sci. 16 (1993), 581-586. (1993) Zbl0778.73029MR1233041DOI10.1002/mma.1670160806
  11. Lagnese, J. E., 10.1137/1.9781611970821, SIAM Studies in Applied Mathematics 10, Society for Industrial and Applied Mathematics, Philadelphia (1989). (1989) Zbl0696.73034MR1061153DOI10.1137/1.9781611970821
  12. Signorini, A., Sopra alcune questioni di statica dei sistemi continui, Ann. Sc. Norm. Super. Pisa, II. Ser. 2 (1933), 231-251 Italian 9999JFM99999 59.0738.01. (1933) MR1556704
  13. Signorini, A., Questioni di elasticità non linearizzata e semilinearizzata, Rend. Mat. Appl., V. Ser. 18 (1959), 95-139 Italian. (1959) Zbl0091.38006MR0118021

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