The extension of the method of dimensionality reduction to non‐compact and non‐axisymmetric contacts. Issue 10 (21st April 2016)

• Record Type: Journal Article
• Authors: Argatov, I.; Heß, M.; Pohrt, R.; Popov, V.L.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 96:Issue 10(2016)
• Page Start: 1144
• Page End: 1155
• Publication Date: 2016-04-21
• Subjects: Contact problem -- unilateral contact -- self‐similar contact -- method of dimensionality reduction; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600057
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract : 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. Abstract : 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.