Error controlled adaptive \(h\)- and \(hp\)-finite elements methods for contact problems with applications in production engineering. (Fehlerkontrollierte adaptive \(h\)- und \(hp\)-Finite-Elemente-Methoden für Kontaktprobleme mit Anwendungen in der Fertigungstechnik.) (German) Zbl 1128.74002
Dortmund: Univ. Dortmund, Fachbereich Mathematik (Diss.). Bayreuther Math. Schr. 78, xviii, 216 p. (2006).
The thesis is mainly focused on three topics: modeling of contact problems, \(h\)- and \(hp\)-finite element discretisation and a posteriori error control for contact problems and adaptivity. The author considers some model problems of Signorini type, idealized friction problems, and – as a problem of production engineering – contact problems for an industrial robot supported belt grinding. Furthermore, applications to other modeling problems are discussed. An important aspect, which has to be investigated, is the verification of the obtained results by numerical experiments.
Reviewer: Igor Andrianov (Köln)
MSC:
74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |
74S05 | Finite element methods applied to problems in solid mechanics |
74M15 | Contact in solid mechanics |