April  2013, 6(4): 909-923. doi: 10.3934/dcdss.2013.6.909

Fatigue accumulation in an oscillating plate

1. 

Dipartimento di Matematica, Universit degli Studi di Milano

2. 

via Saldini 50

3. 

20133 Milano.

4. 

Mathematical Institute of the Silesian University

5. 

Na Rybn?ku 1

6. 

746 01 Opava

7. 

Institute of Mathematics, Czech Academy of Sciences

8. 

?itn 25

9. 

11567 Praha 1

Received  October 2011 Revised  February 2012 Published  December 2012

A thermodynamic model for fatigue accumulation in an oscillating elastoplastic Kirchhoffplate based on the hypothesis that the fatigue accumulation rate is proportional tothe dissipation rate, is derived for the case that both the elastic and the plasticmaterial characteristics change with increasing fatigue. We prove the existence ofa unique solution in the whole time interval before a singularity (material failure) occursunder the simplifying hypothesis that the temperature history is a priori given.
Citation: Michela Eleuteri, Jana Kopfov, Pavel Krej?. Fatigue accumulation in an oscillating plate. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 909-923. doi: 10.3934/dcdss.2013.6.909
References:
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show all references

References:
[1]

Math. Methods Appl. Sci., 27 (2004), 1697-1710. doi: 10.1002/mma.524.  Google Scholar

[2]

Euro. J. Mech. A/Solids, 15 (1996), 705-735.  Google Scholar

[3]

Adv. Math. Sci Appl., 10 (2000), 399-415.  Google Scholar

[4]

J. of Convex Analysis, 11 (2004), 111-130.  Google Scholar

[5]

Research Notes in Mathematics, 404, Chapman & Hall/CRC, Boca Raton, FL, 1999.  Google Scholar

[6]

Physica B: Condensed Matter, 407, no. 9 (2012), 1415-1416. Google Scholar

[7]

Submitted. Google Scholar

[8]

Arch. Ration. Mech. Anal., 180 (2006), 183-236. doi: 10.1007/s00205-005-0400-7.  Google Scholar

[9]

Z. Angew. Math. Mech., 88 (2008), 199-217. doi: 10.1002/zamm.200700111.  Google Scholar

[10]

J. Engng. Mater. Technol., 99 (1977), 2-15. Google Scholar

[11]

(Russian) Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, 9 (1944), 583-590. Google Scholar

[12]

Springer-Verlag, Berlin - Heidelberg, 1989. doi: 10.1007/978-3-642-61302-9.  Google Scholar

[13]

Foundations of Civil and Environmental Engineering, 5 (2004), 31-48. Google Scholar

[14]

WIAS Preprint No. 1583, (2010). Google Scholar

[15]

WIAS Preprint No. 1636, (2011). Google Scholar

[16]

Cambridge University Press, 1990. Google Scholar

[17]

NoDEA, Nonlinear Differ. Equ. Appl., 11(2004), 151-189. doi: 10.1007/s00030-003-1052-7.  Google Scholar

[18]

Eur. J. Mech. A Solids, 22 (2003), 369-384. doi: 10.1016/S0997-7538(03)00044-5.  Google Scholar

[19]

J. Reine Angew. Math., 411 (1990), 39-50. doi: 10.1515/crll.1990.411.39.  Google Scholar

[20]

Z. Ang. Math. Mech., 8 (1928), 85-106. Google Scholar

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