Numerical mathematical simulation of the strengthening combined local loading of the deformation zone in the process of penetration of indenters of different shapes into the piece body was considered. The simulation results were presented in the form of the pattern corresponding to the Odkvist parameter change depending on the type of the tool and the depth (force) of its penetration into the piece body. Based on the analysis of numerical mathematical simulation data, practical recommendations have been formulated pertinent to the selection of the indenter shape for the processes of gradient strengthening of machine parts in the conditions of combined local loading of the deformation zone. Keywords-numerical mathematical simulation, gradient strengthening of machine parts, combined local loading of the deformation zone, Odkvist parameter, strengthening depth.

The process of complex local loading of the deformation zone is considered using the example of processing a sleeve made of a bronze alloy, the mechanical properties of the cast alloy under study were determined, and the parameters of the microhardness distribution over the cross section of the processed workpiece were investigated. Plots of the distribution of various microhardness parameters over the cross section are plotted depending on the number of processing cycles. A mathematical model of the process under consideration and its comparison with experimental data is shown. The description of the technique in the form of an algorithm of actions for the appointment of technological parameters. An example is presented in the form of a finished nomogram for the assignment of specific processing parameters to obtain a given hardening depth and value.

The mathematical description of nonlocal interactions of particles of the continuum has a number of features. It is of practical importance to take into account those features that make it possible in principle to simultaneously describe in the local (weakly local) approximation two effects observed in elastic materials - the appearance of a boundary layer in the vicinity of the free surface and the nonlinearity of the dispersion law of high- frequency acoustic waves. These effects are explainable from the point of view of solid state physics, which takes into account the discrete atomic structure and interatomic potential interactions occurring at finite distances, but within theframework of one model they are not considered in the mechanics of continuous media. This paper shows the fundamental possibility of implementing such a description within the framework of one model.

A mathematical model of the static bending of a beam interacting with an elastic Winkler base, which perceives only compressive loads, is considered. When constructing the model, the method of initial parameters was used with the involvement of the state vectors of the beam sections and the matrices of the influence of the initial parameters on the state of arbitrary sections. Two options for fastening a beam to some part of the base are considered: a free beam and a cantilever.

The article considers a new method of sliding bearings inner surface hardening by plastic deformation in complex local loading of deformation zone conditions. The main aspects of experimental equipment construction and experimental research preparation are reviewed. The laboratory research results are presented.