Geometrically exact theory for contact interactions of 1D manifolds. Algorithmic implementation with various finite element models

摘要

The intuitive understanding of contact between bodies is based on the geometry of adjoining bodies. A more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system. The best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies. This leads to a systematical analysis of geometrical situations leading to contact pairs - surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line. Each contact pair is inherited with a special coordinate system based on its geometrical properties. The current contribution is concentrating on contact between ID manifolds in 3D space - this is the majority of edge-to-edge, beam-to-beam, cable-to-edge etc. contact cases. The geometrically exact curve-to-curve contact approach is then systematically combined together with various finite element approaches - classical finite elements, isogeometric beam finite elements and also with a new developed solid-beam approach. Examples illustrating the diversity of various finite element combinations e.g. within knot mechanics are shown.