The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer. Part I. General considerations and thick layer asymptotics

J.B. Alblas, M. Kuipers

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)

Abstract

An approximate solution is obtained for the contact problem of a layer of finite thickness loaded by a rough cylindrical stamp which moves along the boundary. The coefficient of friction is assumed to be constant. The lower side of the layer is attached to a rigid base. In the problem inertial forces are neglected and the solution is approximated by a plane strain solution. This solution is presented in the form of a (convergent) series expansion in powers of the reciprocal thickness parameter, i.e. the ratio of the values of the thickness and the length of the contact region. The coefficients in this expansion satisfy singular integral equations. Numerical results are obtained for large values of the thickness parameter. In part II of this investigation the thin layer asymptotics will be given.
Original languageEnglish
Pages (from-to)99-109
JournalInternational Journal of Solids and Structures
Volume7
Issue number1
DOIs
Publication statusPublished - 1971

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Contact Problem
Rough
sliding
singular integral equations
Integral equations
plane strain
Plane Strain
Singular Integral Equation
Thin Layer
Coefficient
series expansion
Series Expansion
inertia
coefficient of friction
Friction
Approximate Solution
Contact
Numerical Results
expansion
coefficients

Cite this

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title = "The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer. Part I. General considerations and thick layer asymptotics",
abstract = "An approximate solution is obtained for the contact problem of a layer of finite thickness loaded by a rough cylindrical stamp which moves along the boundary. The coefficient of friction is assumed to be constant. The lower side of the layer is attached to a rigid base. In the problem inertial forces are neglected and the solution is approximated by a plane strain solution. This solution is presented in the form of a (convergent) series expansion in powers of the reciprocal thickness parameter, i.e. the ratio of the values of the thickness and the length of the contact region. The coefficients in this expansion satisfy singular integral equations. Numerical results are obtained for large values of the thickness parameter. In part II of this investigation the thin layer asymptotics will be given.",
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The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer. Part I. General considerations and thick layer asymptotics. / Alblas, J.B.; Kuipers, M.

In: International Journal of Solids and Structures, Vol. 7, No. 1, 1971, p. 99-109.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - The two dimensional contact problem of a rough stamp sliding slowly on an elastic layer. Part I. General considerations and thick layer asymptotics

AU - Alblas, J.B.

AU - Kuipers, M.

PY - 1971

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N2 - An approximate solution is obtained for the contact problem of a layer of finite thickness loaded by a rough cylindrical stamp which moves along the boundary. The coefficient of friction is assumed to be constant. The lower side of the layer is attached to a rigid base. In the problem inertial forces are neglected and the solution is approximated by a plane strain solution. This solution is presented in the form of a (convergent) series expansion in powers of the reciprocal thickness parameter, i.e. the ratio of the values of the thickness and the length of the contact region. The coefficients in this expansion satisfy singular integral equations. Numerical results are obtained for large values of the thickness parameter. In part II of this investigation the thin layer asymptotics will be given.

AB - An approximate solution is obtained for the contact problem of a layer of finite thickness loaded by a rough cylindrical stamp which moves along the boundary. The coefficient of friction is assumed to be constant. The lower side of the layer is attached to a rigid base. In the problem inertial forces are neglected and the solution is approximated by a plane strain solution. This solution is presented in the form of a (convergent) series expansion in powers of the reciprocal thickness parameter, i.e. the ratio of the values of the thickness and the length of the contact region. The coefficients in this expansion satisfy singular integral equations. Numerical results are obtained for large values of the thickness parameter. In part II of this investigation the thin layer asymptotics will be given.

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DO - 10.1016/0020-7683(71)90020-5

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