Kinematic and Dynamic Conditions in Metal Rolling of Porous Materials

Mathematical modeling of plastic deformations in rolling consists in a consequent combination of the general energetic relationship in plasticity and the variation inequality expressed the principle of minimum of entire deformation energy. A real deformation state in a plastic zone beneath rolls and corresponding kinematic and dynamics conditions on the contact surface are considered as a limited one for the consequent approximate deformation states and are found out by the method of approximated approach. Any realization of this method on personal computers requires a rational construction of a kinematic-possible velocity field in the spatial domain on plastic flow. Using the ordinary propositions and a new assumptions the authors have constructed a simple kinematic-possible velocity field in the plastic zone beneath rolls. On the base of the consequent approach in which the general energetic relationship and the variation inequality are interrelated the authors have been able to find out the geometric, kinematic and dynamics characteristics of plastic deformation’s states in metal rolling.

H-solvability of optimal control problem for degenerate parabolic variation inequality

We consider the optimal control problem for degenerate parabolic variation inequality with weight function of potential type that is in differential operator. Using the direct method of calculus of variations we prove the solvability of mentioned above optimal control problem in the class of so-called H-admissible solutions. It is also established that the set of H-admissible pairs is closed in the product of topologies of the state space and the control space.

An Elastodynamic Model of Frictional Contact and Its Influence on the Dynamics of a Workpiece-Fixture System

A model to predict the dynamics of a workpiece-fixture system has been developed based on the equivalency of the dynamic frictional contact problem with a nonlinear friction law to that of a variation inequality problem. Nonlinear finite element method has been employed to solve the problem. A series of experiments under various fixture configurations were conducted on a modular fixture test-bed to determine the dynamic characteristics of the workpiece-fixture system. Model predictions of the dynamic characteristics have been compared to those obtained from the experiments and are found to be in good agreement. It was found that frictional sliding contact at the workpiece-fixture interfaces provides damping to the system and that the nature of this contact and level of damping are highly dependent on contact forces developed through clamping. Clamping sequence was also found to be important in determining dynamic characteristics.

Levels of Sociocultural Development Among Soviet Nationalities: A Partial Test of the Equalization Hypothesis

Recent studies of regional economic development of the Soviet Union have suggested that since 1958, Soviet union republics have become less equal in their levels of industrialization, share of investments, and living standards. This paper assesses the degree to which equality of social and cultural development characterizes Soviet ethnic groups and union republics. Drawing aggregate data chiefly from the 1926, 1959, and 1970 Soviet censuses, the analysis shows that: (1) relative variation (inequality) in the sociocultural development of Soviet nationalities has declined continuously and markedly over time on measures of education and occupational structure, but that large inter-nationality disparities remain in the development of skilled manpower; (2) inter-nationality variation in family role structures has been slower to decline than differences in education and appears to follow a curvilinear pattern: for a time during the Soviet era, inter-nationality differences increased but have been followed recently by significant declines. Furthermore, it is shown that (3) on the average the sociocultural development of union republic populations well exceeds the development of the indigenous nationalities in these republics.