Summary
This paper is concerned with finite deformations of elastic bodies in the presence of unilateral constraints. The penalty formulation is applied to introduce the contact constraints. We develop special isoparametric contact elements. Starting from their Gaussian points the distance between the body and the obstacle is determined, where the obstacle is given as aC 2 continuous function. Variation and subsequent consistent linearization yield the tangent matrix of the contact elements in its general form, which can be incorporated into standard finite element schemes.
Übersicht
Es wird das Kontaktverhalten eines deformierbaren Körpers beschrieben, der endliche Deformationen erfährt, wenn er auf ein starres Hindernis gedrückt wird. Dabei findet die Penalty-Formulierung Anwendung. Zur Kontakterkennung werden isoparametrische Kontaktelemente verwendet. Ausgehend von deren Gausspunkten wird der Abstand des Körpers zum Hindernis bestimmt, das alsC 2-stetige Funktion beschrieben wird. Variation und anschließende konsistente Linearisierung liefern die Tangentenmatrix für die Kontaktelemente in allgemeiner Form, die dann in ein standardmäßiges Finit-Element-Programm eingebaut werden kann.
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Wriggers, P., Imhof, M. On the treatment of nonlinear unilateral contact problems. Arch. Appl. Mech. 63, 116–129 (1993). https://doi.org/10.1007/BF00788917
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DOI: https://doi.org/10.1007/BF00788917