Finite-element convergence for contact problems in plane linear elastostatics. (English) Zbl 0743.73025
Summary: 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.
MSC:
74S05 | Finite element methods applied to problems in solid mechanics |
74A55 | Theories of friction (tribology) |
74M15 | Contact in solid mechanics |
49L99 | Hamilton-Jacobi theories |
74S30 | Other numerical methods in solid mechanics (MSC2010) |
74P10 | Optimization of other properties in solid mechanics |
49M15 | Newton-type methods |