Determination of optimal shape of a moving punch with friction taken into account

The optimization problem for the contact interaction between a rigid punch and an elasticmediumis considered. It is assumed that that the punch is under the action of some prescribed forces and momenta and moves along a surface bounding a half-space filled with an elastic medium. It is also assumed that themotion is quasistatic and the friction forces arising in the region of contact are taken into account. The punch shape is considered as the desired design variable, and the integral functional characterizing the discrepancy between the pressure distribution in the region of contact that corresponds to the optimized shape of the punch and a given goal distribution of pressure is taken as the minimizing criterion. The optimal shape can be determined efficiently by solving the following two problems: first, to obtain the optimal pressure distribution and then to solve a boundary value problemfor the elastic half-space under the action of the obtained normal pressure and friction forces. By way of example, the optimal shape is analytically determined for a punch of rectangular shape in horizontal projection.     

Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account

We propose a mathematical model of large elastoviscoplastic deformations where intensive deformation results in temperature increasing and heat transfer processes. As an example of applying the model relations, we present a solution of the boundary-value problem on rectilinear motion and heating of a medium located in the gap between coaxial rigid cylindrical surfaces.     

First-order approximation in a steady fluid flow problem with surface forces taken into account

The plane problem of finding the shape of the free surface of an ideal incompressible fluid is considered for a fully developed discharge from an infinite layer through a point sink. The gravitational and surface stress forces are taken into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 166–169, November–December, 1974.The author thanks G. V. Shcherbina for formulation of the problem and valuable advice.     

Mixing of plane laminar relaxing gas jets with radiation taken into account

The influence of a chain pumping reaction mechanism in a diffusion-type continuous-action chemical amplifier on an RF molecule is investigated. The actual flow picture is simulated by boundary-layer equations taking account of coherent radiation. It is shown that the efficiency of a chemical amplifier in a mode with partial fluorine dissociation is sufficiently high under the condition of the presence of a line with 0 v5.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–142, May–June, 1978.The authors are grateful to B. S. Aleksandrov, Yu. V. Lapin, and M. Kh. Strelets for numerous useful discussion.     

Optimal design of reinforced cylindrical shells with corrosive wear taken into account

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 124–128, May–June, 1989.