Vestnik of Samara University. Natural Science Series

This paper presents a solution to the plane doubly periodic problem of loading an infinite, isotropic, elastic plane with a hexagonal packing of elliptical inclusions. The plane is subjected to one of three types of remote loading: uniaxial tension along one of the inclusion’s axes or pure shear. The regular hexagonal unit cell contains a single elliptical inclusion with its axes perpendicular to the cell boundaries. The size of the inclusion is significantly larger than the plate thickness. The solution is constructed by reducing the problem to finding complex potentials from the boundary conditions, which are derived from the equality of normal forces and displacements in the matrix and the inclusion. This is achieved using conformal mapping techniques and the method of Muskhelishvili. The influence of non-central inclusions is accounted for via a small parameter method. As a result, a system of linear algebraic equations is derived for solving the considered doubly periodic problem, and solutions for several specific cases are obtained. The results were verified against a numerical solution obtained by the finite element method in the Abaqus software package. The solution to this problem serves as a model for the loading of a fibrous composite, which makes it highly relevant. A relatively small number of works in mechanics are devoted to fibrous composites, with most publications focusing on the analysis of experimental studies or numerical solutions. Therefore, this analytical solution possesses significant scientific value. 

This paper presents an experimental methodology for determining deformations of a flexible square plate under distributed loading on its surface using real-time holographic interferometry. A technological sequence for experiment preparation and execution has been developed, ensuring precise compliance with rigid clamping boundary conditions, high-precision stepwise variation of transverse load, and determination of corresponding displacement increments. A systematic experimental study of deformation of a square copper plate (60×60 mm, 300 μm thickness) under hydrostatic pressure with linear distribution along the plate height due to its vertical orientation was conducted. Three base loading levels corresponding to average pressures p_avg ≈ 300, 3330, and 6670 Pa were investigated, with series of incremental increases for each level. Thirty high-quality double-exposure holograms containing from 3 to 71 interference fringes were obtained. The effect of geometrical stiffening of the flexible plate at large deflections was experimentally demonstrated: the tangential stiffness at average pressure 6370 Pa exceeds the initial stiffness of the undeformed plate by more than 4 times. The developed methodology provides displacement field determination with spatial resolution up to 70+ fringes over the 60 × 60 mm area and accuracy in normal displacement of λ/2 ≈ 266 nm. The obtained experimental data create the foundation for subsequent quantitative verification of theoretical models of nonlinear thin plate deformation and identification of real mechanical characteristics of the material and boundary condition parameters.

The article uses the molecular dynamic method (MD) to study the stress-strain state near the tip of the defect, which makes it possible to analyze the crystal structure at the nano- and microscopic levels, which makes it possible to identify and characterize the main patterns of the appearance and growth of defects in bodies under load. Based on the computational experiments carried out, it has been established that with the atomistic and continuum approaches in the mechanics of fracture, their joint use is possible when modeling the deformation processes in the elastic mode of deformation. This article presents the results of a computational experiment in the MD package LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to compare the atomic and continuum approaches. As a solution to continuum mechanics, the asymptotic expansion according to M. Williams is given. A nickel single crystal with a face-centered cubic lattice (FCC) was selected as an experimental sample.

The bending of ultrathin single-layer metal plates in a controlled electric field is modeled. The plate (cantilever) form factor corresponds to elements of high-speed optical shutters in dynamic X-ray lithography. System controllability under the influence of a slowly varying electric field is investigated. The cantilever is a thin rectangular elastic plate, clamped on one side and hinged supported at a certain distance from the opposite free side. Problems of static bending and natural vibrations with a constant electric potential applied to the cantilever are studied. Cantilever motion is simulated with a given feedforward control of this potential over time under transverse bending conditions.

The results of modeling the active medium of an optically pumped metastable argon atom laser are presented. Auxiliary pumping at a wavelength different from the primary pump is used to compensate for losses due to spontaneous emission. The primary pumping occurs at a wavelength of 811.5 nm, and the auxiliary pumping occurs at 810.4 nm. The choice of the auxiliary pumping transition is due to its strong absorption and its wavelength proximity to the primary pumping wavelength, which simplifies the fabrication of a diode pump source. Modeling showed that using auxiliary pumping significantly increases the maximum possible specific laser output power by an order of magnitude.

This paper investigates methods of consumer graphics processor (GPU) virtualization for cloud services applications. A comparative analysis of GPU passthrough, SR-IOV, MIG, and time-sliced vGPU technologies is conducted. A methodology for evaluating virtualized GPU performance based on computational efficiency and latency metrics is presented. An experimental comparison of the consumer NVIDIA RTX 2060 12GB graphics card (Turing architecture, TU106 chip) with professional Quadro RTX solutions on identical silicon is performed. It is shown that virtualization overhead amounts to 5–10 % for graphics workloads and reaches 6–8 % for neural network training. The impact of virtualization on end-to-end latency in cloud gaming, VR/AR rendering, and machine learning inference scenarios is investigated. The economic efficiency of using consumer GPUs with modified software in laboratory and educational environments is substantiated. The research results can be used in designing virtual desktop infrastructure and cloud computing clusters.