On the contact of a rigid sphere and a thin plate

We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a deformation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. Ho...

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Bibliographic Details
Published inMathematical and computer modelling Vol. 43; no. 1; pp. 119 - 131
Main Authors Thredgold, J.M., Lucas, S.K., Howlett, P.G.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 2006
Elsevier Science
Subjects
Contact
Deformation
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Physics
Ring load
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Thin plate
Thin plate
Deformation
Ring load
Contact
Plate theory
Deflection
Linear elasticity
Applied mathematics
Contact problems
Classical theory
Flat plate
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Summary:We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a deformation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. However, for both small deflections using classical linear elastic theory and large deflections using von Kármán theory, looking at some typical parameter values we find that the radius of the ring is so small that for practical purposes it should be considered as a point load.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2005.04.015