Finite-element convergence for contact problems in plane linear elastostatics

Gwinner, Joachim

doi:10.1090/qam/1146620

Author: Joachim Gwinner
Journal: Quart. Appl. Math. 50 (1992), 11-25
MSC: Primary 65N30; Secondary 73C99, 73T05, 73V05
DOI: https://doi.org/10.1090/qam/1146620
MathSciNet review: MR1146620
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Abstract: This paper presents a convergence analysis for the finite-element approximation of unilateral problems in plane linear elastostatics. We consider in particular the deformation of a body unilaterally supported by a frictionless rigid foundation, solely subjected to body forces and surface tractions without being fixed along some part of its boundary, and establish convergence of piecewise polynomial finite-element approximations for mechanically definite problems without imposing any regularity assumption. Moreover we study the discretization of the contact problem with given friction along the rigid foundation.

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