No 4 (2025)

An overview of research methods for improving the physico-mechanical properties of conductive materials grown using additive manufacturing techniques is presented. The review is conducted in order to develop a method for improving the properties of additive steel AISI 316L made by selective laser melting (SLM). This steel is widely used in various industries due to its versatile properties. The main methods of thermal and thermomechanical processing are briefly analyzed. Methods of improving plastic properties by impacting the material to pulses of a strong electromagnetic field, which causes high-density currents in the material considered as well. Based on the review, it is suggested that it is advisable to study the effect of a high-energy electromagnetic field on improving the plastic properties of materials built with selective laser melting.

In this paper, for the first time, a solution is constructed to the dynamic contact problem of the time-harmonic effect of a deformable die on a layer of anisotropic composite material. It is assumed that the stamp occupies the region of the first quadrant and has a complex rheology, in particular, the linear theory of elasticity. The paper uses a universal modeling method developed by the authors, which makes it possible to apply the block element method to both differential and integral equations. The solutions of boundary value problems for deformable dies of complex rheology are constructed in the form of decompositions according to the solutions of boundary value problems for materials of simple rheology described, for example, by Helmholtz equations. This possibility was previously established for materials of a wide range of rheologies using Galerkin transformations. The solution of the two-dimensional Wiener–Hopf integral equation is obtained both in coordinate form and in Fourier transforms. This makes it particularly convenient to further study it using analytical or numerical methods using standard computer programs. They will make it possible to identify certain properties of composites used as structural materials in various engineering technologies dictated by types of anisotropies, as well as in issues of seismology in the study of seismicity in mountainous areas. The constructed integral representation of the solution of the contact problem, which makes it possible to identify terms describing the concentrations of contact stresses under the stamp, makes it possible to select the soles of deformable stamps or the properties of the materials used to get rid of undesirable concentrations of contact stresses or enhance them. Since Vorovich resonances can occur during vibration in contact problems with a deformable die, systems of equations are constructed in the work that allow, when solved, to obtain a dispersion equation for finding resonant frequencies.

A problem on a conditional extremum is formulated, which allows one to determine, based on the second limiting state, the upper limit of the maximum angular velocity of rotation of an axisymmetrically curved, fiber-reinforced disk. The structure is rigidly fixed to the vase or hub; blades can be attached to the outer edge of the disc blade. The materials of the components of the composition are assumed to be rigid-plastic, having asymmetry under tension and compression; the material of the binding matrix may have cylindrical anisotropy. Plastic deformation of the components of the composition is associated with piecewise linear yield criteria. The reinforcement structures of the disc web have meridional symmetry. A two-layer model of a curved disk with a plane-stress state in each of the fictitious composite layers is used. The discretized problem is solved using the simplex method of linear programming theory. The developed numerical algorithm has been verified. Examples of numerical calculation of the maximum angular velocity of rotation of flat, conical and spherical homogeneous and composite disks with different degrees of their curvature are analyzed. The cases of reinforcement of the disk web along geodetic directions and logarithmic spirals, as well as along meridional and circular trajectories, were investigated. The comparison was carried out for disks of the same mass with the same consumption of reinforcement. It has been shown that composite disks with a meridional-circumferential reinforcement structure have the highest load-bearing capacity. It has been demonstrated that even a slight axisymmetric curvature of the disk web leads to a sharp decrease in its load-bearing capacity compared to a similar flat structure.

A quaternion solution to the problem of optimal rotation of a rigid body (spacecraft) from an arbitrary initial to a designated angular position in the presence of constraints on the control variables is presented. To optimize the control process, a combined quality functional was used, which combines in a given proportion the sum of time and control efforts spent on the turn, and the integral of the kinetic energy of rotation during the turn. Based on the maximum principle of L.S. Pontryagin and quaternion models of controlled motion of a rigid body, a solution to the problem was obtained. The properties of optimal motion are disclosed in analytical form. Formalized equations and calculation formulas are written down to construct an optimal rotation program. Analytical equations and relationships for finding optimal control are given. Key relationships are given that determine the optimal values of the parameters of the rotation control algorithm. A constructive scheme for solving the boundary value problem of the maximum principle for arbitrary conditions of rotation (initial and final positions and moments of inertia of a rigid body) is also given. In the case of a dynamically symmetric rigid body, a solution to the reorientation problem in closed form is obtained. A numerical example and the results of mathematical modeling are presented, confirming the practical feasibility of the developed method for controlling the attitude of a spacecraft.

In the work with the purpose of determining the prospects of using the kinetic physical and mathematical theory of creep of metals for performing design calculations when creating new technology products, the results obtained in describing the theory of uniaxial creep processes of 1570R alloy under conditions of steady-state and abrupt changes in thermomechanical loading parameters are presented. It is established that the new physical and mathematical theory of creep of metals being developed, which, unlike the classical phenomenological theory, takes into account the structure of the metal and its change in the creep process, equally well describes the process under steady-state and non-stationary conditions of thermomechanical loading. The important role of the structural state of the metal on the creep process is shown. The main structural parameter determining the characteristics of the process is the scalar density of immobile dislocations.

In this paper, the principle of obtaining conditions for matching input data is formulated. A set of matching conditions is obtained, failure to fulfill which leads to large unavoidable errors in the corners of the rectangle. The problem is solved in analytical form using the method of universal fast expansions. The obtained approximate analytical solution is compared with the test one, the error in determining the plate deflection, torque and bending moments, shear forces and stress tensor components is investigated. It is found that when using a sixth-order boundary function and only one term in the cosines and one term in the sines in the Fourier series in universal fast expansions, the accuracy of the obtained solution significantly exceeds the accuracy of specifying the input parameters of the problem determined by the concept of a continuous medium. In this case, the approximate analytical solution can formally be considered exact.