PERIODIC CONTACT PROBLEMS FOR A TRANSVERSALLY ISOTROPIC LAYER

This paper describes three-dimensional periodic contact problems of infinite straight chains of punches acting on the face of a transversally isotropic elastic layer, whose other face is subject to sliding support. Isotropy planes are parallel or perpendicular to the layer faces. Contact problems ar...

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Published inJournal of applied mechanics and technical physics Vol. 63; no. 6; pp. 1065 - 1072
Main Authors Pozharskii, D. A., Zolotov, N. B.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2022
Springer Nature B.V
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ISSN0021-8944
1573-8620
DOI10.1134/S0021894422060207

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Abstract This paper describes three-dimensional periodic contact problems of infinite straight chains of punches acting on the face of a transversally isotropic elastic layer, whose other face is subject to sliding support. Isotropy planes are parallel or perpendicular to the layer faces. Contact problems are solved using the method of nonlinear boundary integral equations, which makes it possible to simultaneously determine the contact region and contact pressures. Calculations for known transversally isotropic materials are performed.
AbstractList This paper describes three-dimensional periodic contact problems of infinite straight chains of punches acting on the face of a transversally isotropic elastic layer, whose other face is subject to sliding support. Isotropy planes are parallel or perpendicular to the layer faces. Contact problems are solved using the method of nonlinear boundary integral equations, which makes it possible to simultaneously determine the contact region and contact pressures. Calculations for known transversally isotropic materials are performed.
Author Pozharskii, D. A.
Zolotov, N. B.
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Cites_doi 10.1016/0021-8928(85)90084-x
10.1093/qjmam/hbq029
10.1007/978-94-010-9893-9
10.18522/1026-2237-2021-2-22-33
10.1017/CBO9781139541015
10.1016/s0021-8928(02)00036-9
10.1016/j.wear.2010.02.018
10.1016/s0021-8928(98)00122-1
10.1016/j.ijsolstr.2016.10.016
10.1007/978-3-319-70939-0
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10.1134/s0021894421050035
10.1016/j.jappmathmech.2012.11.010
10.1016/j.jappmathmech.2013.07.017
10.1090/chel/380
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References D. A. Pozharskii, “Periodic Contact and Mixed Problems of the Theory of Elasticity (Review)," Izv. Vuzov. Sev.-Kavk. Region. Estestv. Nauki, No. 2, 22–33 (2021).
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GoryachevaI.G.YakovenkoA.A.Indentation of a Rigid Cylinder with a Rough Flat Base into a Thin Viscoelastic LayerJournal of Applied Mechanics and Technical Physics2021627237352021JAMTP..62..723G436387510.1134/s00218944210500351492.74118
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YastrebovVladislav A.AnciauxGuillaumeMolinariJean-FrançoisThe contact of elastic regular wavy surfaces revisitedTribology Letters20145617118310.1007/s11249-014-0395-z
GoryachevaI.G.The periodic contact problem for an elastic half-spaceJournal of Applied Mathematics and Mechanics1998629599661998JApMM..62..959G168865110.1016/s0021-8928(98)00122-1
Gel’fandI.M.Generalized Functions Vol. 1: Properties and Operations2016USAAmerican Mathematical Society10.1090/chel/3801339.01006
BarberJ.R.Contact Mechanics2018BerlinSpringer10.1007/978-3-319-70939-01400.74001
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GoryachevaI.G.TorskayaE.V.Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indentersWear20102681417142210.1016/j.wear.2010.02.018
FabrikantV.I.Contact and Crack Problems in Linear Elasticity2010SharjahBentham
PanE.ChenW.Static Green’s Functions in Anisotropic Media2015N. Y.Cambridge Univ. Press10.1017/CBO97811395410151332.78001
D. A. Pozharskii, M. V. Bedoidze, and E. D. Pozharskaya, “Periodic Contact Tasks for a Layer," Izv. Vuzov. Sev.-Kavk. Region. Estestv. Nauki, No. 1, 30–32 (2019).
GoryachevaI.G.TorskayaE.V.Periodic Contact Problem for a System of Punches and an Elastic Layer Adhered to an Elastic FoundationTrenie i Iznos199516642652
JinFanWanQiangGuoXuA double-Westergaard model for adhesive contact of a wavy surfaceInternational Journal of Solids and Structures2016102667610.1016/j.ijsolstr.2016.10.016
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PrudnikovA.B.BrychkovYu.A.MarichevO.I.Integrals and Series, Vol. 1: Elementary Functions1986Boca RatonCRC Press0733.00004
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H. Ding (1260_CR2) 2006
V.M. Alexandrov (1260_CR18) 2001
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I.G. Goryacheva (1260_CR7) 1995; 16
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V.I. Fabrikant (1260_CR4) 2010
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References_xml – reference: FabrikantV.I.Non-traditional contact problem for transversely isotropic half-spaceThe Quarterly Journal of Mechanics & Applied Mathematics201164151170281384210.1093/qjmam/hbq0291248.74031
– reference: FabrikantV.I.Contact and Crack Problems in Linear Elasticity2010SharjahBentham
– reference: GoryachevaI.G.Mechanics of Frictional Interaction2001MoscowNauka
– reference: AleksandrovV.M.Doubly periodic contact problems for an elastic layerJournal of Applied Mathematics and Mechanics2002662973052002JApMM..66..297A193007510.1016/s0021-8928(02)00036-9
– reference: AlexandrovV.M.PozharskiiD.A.Three-Dimensional Contact Problems2001DordrechtKluwer10.1007/978-94-010-9893-91101.74002
– reference: BarberJ.R.Contact Mechanics2018BerlinSpringer10.1007/978-3-319-70939-01400.74001
– reference: PanE.ChenW.Static Green’s Functions in Anisotropic Media2015N. Y.Cambridge Univ. Press10.1017/CBO97811395410151332.78001
– reference: DavtyanD.B.PozharskiiD.A.The action of a strip punch on a transversely isotropic half-spaceJournal of Applied Mathematics and Mechanics2012765585662012JApMM..76..558D309747310.1016/j.jappmathmech.2012.11.0101270.74147
– reference: PrudnikovA.B.BrychkovYu.A.MarichevO.I.Integrals and Series, Vol. 1: Elementary Functions1986Boca RatonCRC Press0733.00004
– reference: DingH.ChenW.ZhangL.Elasticity of Transversely Isotropic Materials2006DordrechtSpringer1101.74001
– reference: GoryachevaI.G.TorskayaE.V.Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indentersWear20102681417142210.1016/j.wear.2010.02.018
– reference: GoryachevaI.G.The periodic contact problem for an elastic half-spaceJournal of Applied Mathematics and Mechanics1998629599661998JApMM..62..959G168865110.1016/s0021-8928(98)00122-1
– reference: GalanovB.A.The method of boundary equations of the hammerstein-type for contact problems of the theory of elasticity when the regions of contact are not knownJournal of Applied Mathematics and Mechanics20027729730510.1016/0021-8928(85)90084-x
– reference: JinFanWanQiangGuoXuA double-Westergaard model for adhesive contact of a wavy surfaceInternational Journal of Solids and Structures2016102667610.1016/j.ijsolstr.2016.10.016
– reference: YastrebovVladislav A.AnciauxGuillaumeMolinariJean-FrançoisThe contact of elastic regular wavy surfaces revisitedTribology Letters20145617118310.1007/s11249-014-0395-z
– reference: SoldatenkovI.A.The periodic contact problem of the plane theory of elasticity. Taking friction, wear and adhesion into accountJournal of Applied Mathematics and Mechanics200277297305313640610.1016/j.jappmathmech.2013.07.017
– reference: GoryachevaI.G.YakovenkoA.A.Indentation of a Rigid Cylinder with a Rough Flat Base into a Thin Viscoelastic LayerJournal of Applied Mechanics and Technical Physics2021627237352021JAMTP..62..723G436387510.1134/s00218944210500351492.74118
– reference: Gel’fandI.M.Generalized Functions Vol. 1: Properties and Operations2016USAAmerican Mathematical Society10.1090/chel/3801339.01006
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– reference: PrudnikovA.B.BrychkovYu.A.MarichevO.I.Integrals and Series, Vol. 2: Special Functions1986Boca RatonCRC Press0733.00004
– reference: GoryachevaI.G.TorskayaE.V.Periodic Contact Problem for a System of Punches and an Elastic Layer Adhered to an Elastic FoundationTrenie i Iznos199516642652
– reference: D. A. Pozharskii, “Periodic Contact and Mixed Problems of the Theory of Elasticity (Review)," Izv. Vuzov. Sev.-Kavk. Region. Estestv. Nauki, No. 2, 22–33 (2021).
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Snippet This paper describes three-dimensional periodic contact problems of infinite straight chains of punches acting on the face of a transversally isotropic elastic...
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SubjectTerms Applications of Mathematics
Boundary integral method
Classical and Continuum Physics
Classical Mechanics
Contact pressure
Elastic layers
Fluid- and Aerodynamics
Integral equations
Isotropic material
Isotropy
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
Title PERIODIC CONTACT PROBLEMS FOR A TRANSVERSALLY ISOTROPIC LAYER
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