TITLE:
Geometrically Exact Theory of Contact Interactions—Applications with Various Methods FEM and FCM
AUTHORS:
Alexander Konyukhov
KEYWORDS:
Closest Point Projection Procedure, Curvilinear Coordinate System, Covariant Derivative and Linearization, Finite Cell Method
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.8,
August
26,
2015
ABSTRACT: 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
various methods such as the finite element method (FEM), the finite discrete
method (FDM) 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. As particular
new development it is shown also the possibility to easy combine with the
Finite Cell Method.