Contact formulation via a velocity description allowing efficiency improvements in frictionless contact analysis

A velocity description, based on the consideration of contact from the surface geometry point of view, is used for a consistent formulation of contact conditions and for the derivation of the corresponding tangent matrix. Within this approach differential operations are treated as covariant derivatives in the local surface coordinate system. The main advantage is a more algorithmic and geometrical structure of the tangent matrix, which consists of a “main”, a “rotational” and a pure “curvature” term. Each part of the tangent matrix contains the information either about the internal geometry of the contact surface or about the change of the geometry during incremental loading and can be estimated in a norm during the analysis. Representative examples with contact and bending of shells modelled with linear and quadratic elements over some classical second order geometrical figures serve to show situations where keeping all parts of the tangent matrix is not necessary.