TITLE:
Geometrically Exact Theory of Contact Interactions–Further Developments and Achievements
AUTHORS:
Alexander Konyukhov, Karl Schweizerhof
KEYWORDS:
Contact Finite Element; Surface-to-Surface Contact; Beam-to-Beam Contact; Curve-to-Surface Contact; Covariant Approach; Geometrically Exact Contact Description
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.3 No.1B1,
July
11,
2013
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.