An elastic contact problem for a half-space indented by a flat annular rigid stamp

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Abstract

We consider an elastic contact problem for a half-space indented by a flat annular rigid stamp, which is a three-part mixed boundary value problem. If the distribution of pressure on the contact region is assumed, the contact problem will be reduced to the solution of an infinite set of simultaneous equations. Numerical results are also illustrated for the distributions of the displacements and stresses in the half-space.

Résumé

Nous considérons un problème de contact élastique pour un demi plan entaillé par un poinçon rigide annulaire plat, ce qui représente un problème mixte de valeurs aux limites à trois parties. Si la distribution de la pression sur la région de contact est supposée connue, le problème de contact sera ramené à la résolution d'un système infini d'équations simultanées. Des résultats numériques sont également donnés en illustration des distributions des déplacements et des contraintes dans le demi espace.

Zusammenfassung

Wir untersuchen ein elastisches Kontaktproblem für einen Halbraum, der durch einen flachen ringförmigen starren Stempel eingedrückt ist, was ein dreiteiliges gemischtes Grenzwertproblem darstellt. Falls die Druckverteilung auf die Kontaktzone angenommen ist, wird das Kontaktproblem auf die Lösung eines unendlichen Satzes simultaner Gleichungen reduziert. Es werden auch numerische Resultate für die Verteilungen der Verdrängungen und Spannungen im Halbraum illustriert.

Sumàrio

Si considera il problema del contatto elastico per un semispazio depresso da uno stampo rigido anulare piatto, che è un problema a tre parti con valori limite misti. Assumendo la distribuzione uniforme delle pressioni sulla regione di contatto, il problema viene ridotto alla soluzione di un gruppo infinito di equazioni simultanee. Vengono inoltre illustrati i risultati numerici per la distribuzione degli spostamenti e delle sollecitazioni nel semispazio.

Реферат

Paccмoтpeнa oднaя пpoблeмa yпpyгoгo кoнтaктa для пo лyпpocтpaнcтвa пpи вдaвлeнии плocкoгo кoльцeвoгo жecткoгo штaмпa, чтo пpeдcтaвляe т coбoй тpoйнaя cмeшaннaя кpaeвaя зaдaчa. Ecли пpинятo pacпpeдeлeниe дaвлeния нa зoнe кoнтaктa, тo кoнтaктнaя пpoблeмa cвoдитcя к peщeнию бecкoнeчнoй cиcтeмы coвмecтныч ypaвнeний. Иллюcтpиpo вaны и чиcлeнныe peзyльтaты для pacпpeдeлeний cмeщeний и нaпpяжeний в пoлyпpocтpaнcтвe.

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There are more references available in the full text version of this article.

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