An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry

dc.contributor.authorPopov, Valentin L.
dc.date.accessioned2022-04-01T08:58:00Z
dc.date.available2022-04-01T08:58:00Z
dc.date.issued2022-02-15
dc.date.updated2022-03-23T01:40:38Z
dc.description.abstractAn approximate solution for a contact problem of profiles which are not axially symmetrical but deviate only slightly from the axial symmetry is found in a closed explicit analytical form. The solution is based on Betti’s reciprocity theorem, first applied to contact problems by R.T. Shield in 1967, in connection with the extremal principle for the contact force found by J.R. Barber in 1974 and Fabrikant’s approximation (1986) for the pressure distribution under a flat punch with arbitrary cross-section. The general solution is validated by comparison with the Hertzian solution for the contact of ellipsoids with small eccentricity and with numerical solutions for conical shapes with polygonal cross-sections. The solution provides the dependencies of the force on the indentation, the size and the shape of the contact area as well as the pressure distribution in the contact area. The approach is illustrated by linear (conical) and quadratic profiles with arbitrary cross-sections as well as for “separable” shapes, which can be represented as a product of a power-law function of the radius with an arbitrary exponent and an arbitrary function of the polar angle. A generalization of the Method of Dimensionality Reduction to non-axisymmetric profiles is formulated.en
dc.description.sponsorshipDFG, 414044773, Open Access Publizieren 2021 - 2022 / Technische Universität Berlinen
dc.identifier.eissn2073-8994
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16652
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15429
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc530 Physikde
dc.subject.othercontact problemen
dc.subject.othernon-axisymmetric indenteren
dc.subject.otherextremal principleen
dc.subject.othergeneralized MDRen
dc.titleAn Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetryen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber390en
dcterms.bibliographicCitation.doi10.3390/sym14020390en
dcterms.bibliographicCitation.issue2en
dcterms.bibliographicCitation.journaltitleSymmetryen
dcterms.bibliographicCitation.originalpublishernameMDPIen
dcterms.bibliographicCitation.originalpublisherplaceBaselen
dcterms.bibliographicCitation.volume14en
tub.accessrights.dnbfreeen
tub.affiliationFak. 5 Verkehrs- und Maschinensysteme::Inst. Mechanik::FG Systemdynamik und Reibungsphysikde
tub.affiliation.facultyFak. 5 Verkehrs- und Maschinensystemede
tub.affiliation.groupFG Systemdynamik und Reibungsphysikde
tub.affiliation.instituteInst. Mechanikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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