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The extension of the method of dimensionality reduction to non‐compact and non‐axisymmetric contacts
Author(s) -
Argatov I.,
Heß M.,
Pohrt R.,
Popov V.L.
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600057
Subject(s) - rotational symmetry , hertz , curse of dimensionality , dimensionality reduction , formalism (music) , extension (predicate logic) , contact area , mathematical analysis , mathematics , geometry , physics , classical mechanics , computer science , quantum mechanics , statistics , artificial intelligence , visual arts , programming language , art , musical
The Hertz‐type three‐dimensional frictionless contact problem with a single controlling parameter is considered through a prism of the method of dimensionality reduction (MDR). The corresponding MDR formalism has been developed with respect to the main contact parameters (contact force and contact approach). It is shown that the half‐length of the 1D contact interval can be uniquely interpreted as the harmonic radius of the original contact area. Also, the case of self‐similar contact is studied in detail, and the obtained relations are applied to this case.