Contact interaction of plastic bodies in bending of thin-walled parts

N.M.Bodunov, G.V.Druzhinin

Kazan State Technical University of A.N.Tupolev's name

K.Marx Str., 10, Kazan, 420111, Russia

We propose here some numeric analytical techniques for calculating the technological parameters of rolling as applied to the thin-walled parts from sheet and profile material bent with stretching on the machines of PRR and SPO type. These techniques are based on the invariant solutions of partial differential equations derived from the group of transformations of stretching (compression) and transfer with respect to the dependent and independent variables.

The boundary-value problems of pressure metal shaping (PMS) possess a number of specific features all resulting in the fact that at solving practical problems one has to resort to some simplifications. The model for the perfect plastico-rigid body is used, for instance, during studies of many a number of technological processes such as bending, rolling, pressing, shamping, and others. Selection and development of methods for solving the nonlinear problems form the basis of many theoretical approaches. The preliminary analytical studies of different local properties of the problem provide a very useful quide to development of problem definition on PCS, and sometimes, when realizing the numerical algorithms they become even decisive. The basic functions predetermine very often the success of a particular algorithm at possibly small machine-time expenditures. For this reason, the selection of independent variables, different notation of the initial system of equations, use of exact integrals of the system, structure of the calculational nets - all this taken together is of large significance for numeric algorithms development. The herein-presented paper deals with the improvement of methods for solving the contact problems of plasticity based on the global approximation of sought solutions and boundary conditions by the functions with use of invariant solutions expansion in series of the basic functions. This technique was used successively in solving the boundary-value problems of statics and dynamics of elasticity theory, hydrodynamics, structure stability, and others.