Geometrically Exact Theory of Contact Interactions–Further Developments and Achievements

Alexander Konyukhov, Karl Schweizerhof

Department of Mechanical Engineering, University of Nottingham-Ningbo China, Ningbo, People’s Republic of China.
Institute of Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany.

DOI: 10.4236/ojapps.2013.31B1004                

Abstract

The focus of the current contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The construction of the corresponding computational contact algorithms are considered in accordance with the geometry of contact bodies in a covariant form. These forms can be easily discredited within finite element methods independently of order of approximation and, therefore, the result is straightforwardly applied within iso-geometric finite element methods. This approach is recently became known as geometrically exact theory of contact interaction [10]. Application for contact between bodies with iso- and anisotropic surface, for contact between cables and curvilinear beams as well as recent development for contact between cables and bodies is straightforward. Recent developments include the improvement of the curve-to-surface (deformable) contact algorithm.

Keywords

Contact Finite Element; Surface-to-Surface Contact; Beam-to-Beam Contact; Curve-to-Surface Contact; Covariant Approach; Geometrically Exact Contact Description

Conflicts of Interest

The authors declare no conflicts of interest.

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