Fatigue accumulation in an oscillating plate

Michela Eleuteri; Jana Kopfov; Pavel Krej?

doi:10.3934/dcdss.2013.6.909

Article Contents

2013, Volume 6, Issue 4: 909-923. Doi: 10.3934/dcdss.2013.6.909

This issue Previous Article Intertwining semiclassical solutions to a Schrödinger-Newton system Next Article Dynamics of the the dihedral four-body problem

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: August 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 74R20; Secondary: 74H35, 74N30.

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References

[1]	Math. Methods Appl. Sci., 27 (2004), 1697-1710.doi: 10.1002/mma.524.
[2]	Euro. J. Mech. A/Solids, 15 (1996), 705-735.
[3]	Adv. Math. Sci Appl., 10 (2000), 399-415.
[4]	J. of Convex Analysis, 11 (2004), 111-130.
[5]	Research Notes in Mathematics, 404, Chapman & Hall/CRC, Boca Raton, FL, 1999.
[6]	Physica B: Condensed Matter, 407, no. 9 (2012), 1415-1416.
[7]	Submitted.
[8]	Arch. Ration. Mech. Anal., 180 (2006), 183-236.doi: 10.1007/s00205-005-0400-7.
[9]	Z. Angew. Math. Mech., 88 (2008), 199-217.doi: 10.1002/zamm.200700111.
[10]	J. Engng. Mater. Technol., 99 (1977), 2-15.
[11]	(Russian) Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, 9 (1944), 583-590.
[12]	Springer-Verlag, Berlin - Heidelberg, 1989.doi: 10.1007/978-3-642-61302-9.
[13]	Foundations of Civil and Environmental Engineering, 5 (2004), 31-48.
[14]	WIAS Preprint No. 1583, (2010).
[15]	WIAS Preprint No. 1636, (2011).
[16]	Cambridge University Press, 1990.
[17]	NoDEA, Nonlinear Differ. Equ. Appl., 11(2004), 151-189.doi: 10.1007/s00030-003-1052-7.
[18]	Eur. J. Mech. A Solids, 22 (2003), 369-384.doi: 10.1016/S0997-7538(03)00044-5.
[19]	J. Reine Angew. Math., 411 (1990), 39-50.doi: 10.1515/crll.1990.411.39.
[20]	Z. Ang. Math. Mech., 8 (1928), 85-106.