The study solves the problem of quasi-static deformation and stability of a cylindrical shell discretely reinforced with a cyclically symmetric system of stringers along which moves a uniformly distributed radial load. Due to the cyclic symmetry of the problem, a shallow panel with one stringer is conceptually isolated from the shell and further solutions are performed for that individual panel. The meridional edges of this panel may have boundary conditions of either symmetry or antisymmetry, depending on the expected buckling mode of the entire shell. The reinforcing effect of the stringer (considered as a beam) is incorporated in a contact formulation. The problem is solved in a contact formulation and in a quasi-static version. The problem is reduced to a system of two differential equations with discontinuous coefficients, which is associated with the discreteness of stringer position. In addition, the equations include load movement velocity as a parameter. The equations are solved by the Bubnov method. The resulting system of linear algebraic equations is solved in the regular way. Two special cases of the problem formulation, characterized by different ways of considering shell and stringer stiffness, are considered. In the examples given, the influence of stringer stiffness on the critical velocity of load movement is analyzed in various formulations.

In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.

Приближенно решена задача об осесимметричном деформировании тонкой цилиндрической оболочки под действием локального температурного поля, действующего по кольцевой части ее боковой поверхности. Решение базируется на использовании классической теории оболочек и применении аппарата обобщенных функций. В связи с последним точное решение задачи невозможно и используется решение методом Бубнова в высоких приближениях. Рассмотрен также и вариант исследования обратной задачи, когда по известным перемещениям оболочки можно установить допускаемые температурные режимы ее термообработки. Приведены примеры. Результаты работы могут быть использованы при прогнозировании напряженно-деформированного состояния тонкостенных конструкций в условиях нестационарного аэродинамического нагрева их отдельных участков, вызванного как конвективным теплопереносом, так и теплотой химических реакций (окисление, катализ).

A new variational formulation for the linear hierarchical theory of thick heterogeneous orthotropic shells resulting in the equations resolved for first-order covariant derivatives along one vector field is proposed. The shell theory of Nth order is constructed on the background of the Lagrangian formalism of the analytical mechanics of continua and the dimensional reduction approach combined with the biorthogonal expansion technique. Primo, the three-dimensional model of an elastic shell is referred to a curvilinear frame normally attached to a two-dimensional smooth oriented manifold corresponding to some base surface and represented as Lagrangian system with one field variable, the quasi-translation vector defined on the cotangent fibration of two-dimensional manifold, and the volumetric density of Lagrange’s functional. Secundo, one of the coordinates on the manifold is selected, and the quasi-stress vector on surfaces normal to the base vector corresponding to this coordinate is defined by differentiation of the Lagrangian density on covariant derivative of the quasi-translation. Application of the Legendre transform to the Lagrangian results in the volumeric density of the new mixed functional depending on the quasi-translation, quasi-stress, and time and remaining spatial derivatives of the quasi-translation. Use of the biorthogonal expansions for both quasi-translation and quasi-stress leads hence to the system of field variables of the first kind and generalized forces and consequently to the surface and contour density of the new functional interpreted as generalized Routh functional of a two-dimensional continuum system. Finally, application of the Hamilton principle results in the statement of the initial-boundary value problem for the system of equations resolved for the first-order covariant derivatives of field variables and generalized forces and interpreted as generalized Routh equations for a shell model as continuum-discrete system. The use of the obtained shell theory formulation in problems of normal wave dispersion in heterogeneous elastic waveguides for the analysis of imaginary and complex branches corresponding to evanescent wave modes is shown.

Статья посвящена изучению изменения нательного мужского костюма как важнейшего элемента материальной культуры мордовского народа. Мордва была первым крупным по численности народом, присоединившимся к России в середине XVI в. С этого периода начинается христианизация мордвы, сыгравшая существенную роль в ее сближении с русским народом. В результате тесных межкультурных контактов с соседями, особенно с русскими, в мужской одежде мордвы нашли отражение элементы других культур, верований, обрядов и традиций. Наибольшие изменения традиционного мордовского костюма наблюдались в конце XIX — первой четверти XX века. Они связаны с использованием для изготовления одежды фабричных материалов, а также с заимствованиями отдельных компонентов костюма у соседних народов, проживавших в Волго‑Уралье. Результат анализа источниковой и литературной базы показал, что наиболее подробно в этнографических источниках и произведениях мордовского фольклора описаны особенности изготовления и, в частности, покроя рубахи, выбора цвета, материала и подбора одежды по сезону. The article aims to study the changes in the male underwear clothing as an essential element of the material culture of the Mordovian people. Mordva was the first large ethnic group to join Russia in the middle of the XVI century. The Christianization of the Mordva started from that moment on and played a significant role in its rapprochement with the Russian people. As a result of close intercultural contacts with different ethnic groups, especially with Russians, the Mordovian men’s costume reflected influences of other cultures, beliefs, rites, and traditions. The most notable changes in the traditional Mordovian costume were observed in the late XIX — fi rst quarter of the XX century and are associated with the use of factory‑made fabric and borrowing individual costume elements from neighboring peoples living in Volga‑Urals. The study of the literature on the topic showed that ethnographic sources and Mordovian folklore provide the most detailed descriptions of the manufacture of shirts, color selection, material, and clothing choice according to the season.

Abstract—Three material lifetime models are compared within the framework of the hypothesis of accumulation of residual strains. The models are based on the Ramberg–Osgood law, an alternative empirical law, and a so-called theoretical law constructed from the solutions of various differential equations in linear and nonlinear sections in a stress–strain curve. Postulating a linear section in a stress–strain curve is shown to automatically leads to the fact that the endurance limit is determined by the point of proportionality limit.

As a result of the experiments, epoxy nanocomposites based on titanium dioxide nanoparticles in the form of opaque blue-gray films were obtained. The composition and structure of epoxy nanocomposites were studied by scanning electron microscopy and infrared spectroscopy. The properties of the obtained film nanocomposites were investigated to determine the glass transition temperature, and the mechanical properties of the films were tested in tension, where the tensile strength, elastic modulus, and relative deformation were determined

THE DYNAMICS OF ELASTIC PLANE WAVEGUIDES is studied on the basis of the extended formulation of the plate theory of Nth order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.

In this paper, we develop the consistent mathematical models and appropriate lowconsuming numerical methods for investigating the nonlinear strain and buckling behavior of statically loaded thin-walled structures with cutouts. The numerical simulation allowed us to study the effects of the dimensions of rectangular cutouts on the buckling of cylindrical shells loaded by the external pressure.

The discretization of the boundary value problem for laminated composite shells is based on the finite difference approach using the regular mesh with the constant grid step and the difference operators of the second order of accuracy. The dynamic relaxation method is proposed for the solution of the nonlinear problem. The evolutionary equations of the dynamic relaxation are constructed, and the optimum parameters of the converging linear iterative process are estimated.

To investigate the processes of geometrically nonlinear deformation of plates and shells made of composite materials with differently shaped cutouts, conservative difference schemes are being developed within the framework of Timoshenko's model that allow one, on the basis of the variational-difference approach jointly with the quasi-dynamic form of the time-dependent technique, to construct a single-type algorithm for solving both static and dynamic problems.

We consider the plane problem of diffraction of acoustic waves on thin elastic curvilinear cylindrical shells enclosed in an absolutely rigid screen. The major attention is given to the problem of the determination of the hydrostatic pressure exerted on the shells [1, 2]. Expressions for the transfer function are obtained on the basis of the theory of thin layer.