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Geometrically exact theory of contact interactions – a general approach with a special focus on curve‐tosurface contact
Author(s) -
Konyukhov Alexander,
Schweizerhof Karl
Publication year - 2014
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201410002
Subject(s) - tangent , surface (topology) , discretization , finite element method , focus (optics) , point (geometry) , geometry , curvilinear coordinates , contact angle , mathematics , mathematical analysis , physics , engineering , optics , structural engineering , thermodynamics
Geometrically exact theory of contact interactions is aiming on the development of the unified geometrical formulation of computational contact algorithms for various geometrical situations of contacting bodies leading to contact pairs: surface‐to‐surface, curve‐to‐surface, point‐to‐surface, curve‐to‐curve, point‐to‐curve, point‐to‐point. The construction of the corresponding computational contact algorithms is considered in accordance with the geometry of contacting bodies in covariant and closed forms. These forms can be easily discretized within finite element methods independently of the order of approximation and, therefore, the result is straightforwardly applied within any further method: high order finite element methods, iso‐geometric finite element methods etc. Application for contact between bodies with iso‐ and anisotropic surface, for contact between cables and curvilinear beams is straightforward. Recent developments include the various approaches to describe the ”Curve‐to‐Surface” contact pair; and the “Solid Beam‐to‐Solid Beam” contact algorithm, fully resolving the problem of “parallel tangents” of “Curve‐to‐Curve” contact algorithm. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)