Mathematical modelling of elastic deflection of a tubular cross-section

Cutting a tubular element into thin rings is an operation often used in engineering processes. Total work of the cutting consists of that necessary for initial deflection of cut material and the cutting work itself. This paper presents mathematical models which describe deflection of cross-section of a single tubular element as well as a single layer of tubes under action of external forces ( acting and reacting ones). The deflection concerns end part of tube hence the cutting object model has been reduced to a thin ring. Results of calculation by using the developed models are presented for selected materials of tubular elements, which are commonly used for structures of the kind; moreover , they are prepared in a form of dimensionless diagrams, that makes it possible to use them for an arbitrary material.