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An improved mathematical model of soft heart tissue has been developed here. Nonlinear material equations were derived from the fundamental principles of nonequilibrium thermodynamics. The passive ...

Starting from the variational principle of virtual power for the three-dimensional equations of the micropolar theory of elasticity and using generalized series in terms of the plate thickness coor...

This article analyzes the state of foreign investment in the economy of the Russian Federation in conditions of economic, political and infectious instability. Countries investing in the Russian economy are analyzed, and the impact of the COVID-19 pandemic on foreign investment in the Russian economy is assessed. The author identifies the problems that restrain the growth of foreign investment in the Russian economy, and considers the prospects for the development of foreign investment. A number of measures have been proposed to solve the identified problems.

A study was carried out on the photovoltaic and photoconductive properties of fi lm composites of a styrene copolymer with nonyl methacrylate and polyNepoxypropylcarbazole doped with lanthanide complexes Ln2L6·PS (Ln = Nd, Eu, Gd, Yb), HL is the carbacylamidophosphate ligand, CCl3C(O)N(H)P(O)(NEt2)2, N-[bis(diethylamino) phosphoryl]2,2,2-trichloroacetamide; PS is 3,6-dipyridin-2-yl-1,2,4,5-tetrazine, C5H4N–C2N4–C5H4N). In the visible spectral range, these composites were found to have holetype photoconductivity. The internal photoelectric effect is a function of the photogeneration of charge carriers from the metal complex molecules and the sensitizer. EPR was used to study the kinetics of the formation and relaxation of the photogenerated charge carriers. We conclude that the metal complex molecules in the polymer composite enhance the efficiency of photogeneration of nonequilibrium charge carriers and thereby affect the photovoltaic properties of the composites.

There is an increase in the number of patients worldwide who require special home feeding after discharge from the hospital Home clinical nutrition (HCN). The yearly prevalence of home clinical nutrition in 2017 was at 463 cases per million in the United States of America whereby in the 90s it was around 163360 per million in the United States of America and Europe. There isnt an established practice of HCN in the Russian Federation and thereby no data on the amount of patients who require HCN and the new risks associated with it because there isnt prior experience in conducting it. To study the routine practice and identify patients who need HCN, we planned a multicenter observational monitoring programme. The goal of the study is patient monitoring who are unable to completely cover their energy needs with the help of conventional nutrition.

Navier’s closed-form solution for the higher order theory of micropolar plates based on the CUF approach has been developed here. Obtained using a principle of virtual displacements the 2D system of the differential equations for the higher order theory of micropolar elastic plates is solved here for the case of simply supported plates using Navier’s method of the variables separation. For the higher order theory of micropolar plates developed here, which is based on CUF, some numerical examples have been done and the influence the rotation field on the stress–strain fields has been analyzed. Methods of determination of the classical and micropolar elastic moduli of different materials have been analyzed, and available experimental data have been presented in Nowacki’s notations. The obtained equations can be used for calculating the stress–strain and for modeling thin walled structures in macro-, micro- and nanoscale when taking into account micropolar couple stress and rotation effects.

Starting from the variational principle of virtual power for the 3-D equations of the micropolar theory of elasticity in orthogonal curvilinear coordinates and using generalized series in terms of ...

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in...

Photovoltaic and photoconductive properties of styrene–nonyl-methacrylate copolymer and poly(N-epoxypropylcarbazole) film composites doped with the tetranuclear metal complex Cu4L4(OCH3)4 (L– = N,N′-dibenzyl-N″-trichloroacetyltriamidophosphate) and a sensitizer, i.e., an organic compound with intramolecular charge transfer, were investigated. It was found that these composites had hole-type photoconductivity in the visible spectral range. The internal photoelectric effect was determined by the photogeneration of charge carriers from the metal complex and sensitizer. The kinetics of formation and relaxation of photogenerated charge carriers were studied using ESR. It was concluded that metal-complex molecules in the polymer composite increased the efficiency of photogeneration of nonequilibrium charge carriers and affected the composite photovoltaic properties.

First-order models are used in the analysis of the tension–compression and transverse bending modes of beam vibration. The equation of motion for each mode and the expressions for boundary conditions are obtained using the generalized variational principle. Systems of partial differential equations for the longitudinal and bending modes of vibrating beams are reduced to a single fourth-order equation, and frequency equations are obtained. The problem of free and forced vibrations of beams that are simply supported at both ends is presented. An analysis and comparison with well-known theories is performed using computer algebra system Mathematica.

New higher-order models are developed for plane rods and beams based on the linear theory of nonlocal elasticity. The one-dimensional higher-order theory is based on two-dimensional equatio...

New higher order models of micropolar beams, which is based on Carrera unified formulation have been developed here. The higher order theory is based on a variational principle of virtual power and...

Subject: The economic and social development of the state is largely determined by the current system of innovation and investment development. In this paper, we have studied these systems in Russia and abroad, determined their development in modern conditions, and identified external and internal factors of influence. Goals: Analyze the state of the world and Russian investment potential and prospects for its development. Methodology: The research is based on a dialectical approach, which uses system and institutional approaches, statistical method, comparative analysis, methods of tabular, and graphical data visualization. Results: The processes of development of the world and Russian investment system in modern conditions were studied. The prospects for innovative and investment development are defined. Conclusions: As a result of the study, it was determined that the Russian Federation needs a successfully developing system of innovative investment development that ensures financial independence from international economic influence. However, there are a number of problems that need to be solved at the level of Federal and regional legislative and Executive structures in order to create investment attractiveness and legal security for both Russian and international investors. The prospect of innovative development in Russia is possible in terms of economic structure based on raw material exports, due to the development of the industrial sector of the national economy, high technology, industry, aerospace, energy and information technology, and the development of agricultural production.

A high order theory for functionally graded (FG) beams based on expansion of the two dimensional (2-D) equations of elasticity for functionally graded materials (FGMs) into Legendre's polynomials series has been developed. The 2-D equations of elasticity have been expanded into Legendre's polynomials series in terms of a thickness coordinate. In the same way functions that describe functionally graded relations also has been expanded. Thereby all equations of elasticity including Hook's law have been transformed to corresponding equations for coefficients of Legendre's polynomials expansion. Then system of differential equations in term of displacements and boundary conditions for the coefficients of Legendre's polynomials expansion coefficients has been obtained. Cases of the first and second approximations have been considered in more detail. For the obtained boundary-value problems solution, a finite element method (FEM) has been used and numerical calculations have been done with MATHEMATICA, MATLAB and COMSOL Multiphysics software. Numerical results are presented and discussed.

New theory of higher order for functionally graded (FG) shells, which is based on the expansion of the three-dimensional (3D) equations of elasticity for functionally graded materials (FGMs) into L...

In this paper two approaches, time-domain (TD) and frequency domain (FD) have been applied for the solution of the dynamic unilateral contact problem. We investigate crack in two-dimensional (2-D) plane, homogeneous, isotropic and linear elastic solids under action of the longitudinal P-wave with considering unilateral contact of the crack edges. For the problem solution a special iterative algorithm of the Udzava's type and boundary element methods (BEM) in the time-domain (TD) and frequency domain (FD) are used. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts these integrals to regular ones is applied. Simple regular formulas for their calculation are presented. Numerical results for the crack opening, contact forces and dynamic stress intensity factor (SIF) for the case of a finite I-mode crack in an infinite 2-D domain which is subjected to a harmonic loading with considering crack edges unilateral contact interaction are presented and discussed.

The chaining process of a system of interacting carbon nanotubes (CNTs) under an alternating current electric field is investigated at two regions of different electric field characteristics. For the region of uniform electric field (far from the electrodes), a two-dimensional multiparticle approach based on the dielectrophoretic (DEP) theory and classical mechanics is proposed to investigate the CNT rotational and translation motion. For this scenario, CNT rotation and alignment along the electric field direction occurs first, followed by the translation and chaining processes which were found to be highly dependent on the CNT-to-CNT initial configuration. On the other hand, the presence of high electric field gradients governs the CNT chaining at regions near the electrodes. DEP forces caused by such gradients were computed by finite element analysis and compared to the magnitude of the CNT-to-CNT interacting forces at zones of uniform electric fields. A critical distance of CNT-to-CNT separation was estimated, which determines if a CNT is attracted towards the electrode or if it is attracted by other CNTs away from the electrodes. Experimental evidence of CNTs dynamic motion under electric fields is presented to support the predicted trends.

This paper considers the mathematical formulation of the elastodynamic contact problem for a cracked body. The contact interaction of the crack edges in 2D is studied for the case of normal inciden...

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Since Green’s matrices are widely used for solution of the theoretical and applied problems in science and engineering, it is important to get efficient methods for their calculation. Therefore, a new efficient algorithm for the calculation of Green’s matrices for the boundary value problem (BVP) for the system of ordinary differential equations (ODE) of the first order has been developed here. For any well-defined BVP, a fundamental matrix has to be constructed first; then, using a simple algorithm the corresponding Green’s matrix is calculated. For the fundamental matrix calculation an approach based on the matrix exponential is used. To demonstrate the effectiveness and robustness of the algorithm, Green’s matrices for elastic bar, Euler–Bernoulli, Timoshenko’s and Vekua’s beams have been calculated. All of the presented calculations have been done using the computed algebra software Mathematica. In the cases of the elastic bar, Euler–Bernoulli, Timoshenko’s beams corresponding Green’s functions have been presented in analytical form as the Mathematica output. In the case of the Vekua’s beams analytical expressions for Green’s functions are relatively long; they have been calculated numerically, by using the proposed algorithm. The Green’s matrices for Timoshenko’s and Vekua’s beams have been verified by comparing the solution of the corresponding BVP obtained using Green’s function method with the numerical solution obtained using Mathematica function NDSolve. Proposed algorithm can be applied for solution of the BVP for any linear and some classes of nonlinear systems of the ODE using the Green’s matrices approach.

New nonlocal models of plates and shells based on Legendre’s polynomial series expansion have been developed here. The 3-D dynamic equations of the nonlocal elasticity have been presented in an orthogonal system of coordinates. For the development of 2-D models of plates and shells the curvilinear system of coordinates related to the middle surface of the shell has been used along with special hypothesizes based on assumptions that take into account the fact that the plate and shells are thin. Higher order theory is based on the expansion of the 3-D equations of the nonlocal theory of elasticity into Fourier series in terms of Legendre polynomials. The stress and strain tensors, as well as vectors of displacements have been expanded into Fourier series in terms of Legendre polynomials with respect to thickness. Thereby, all equations of the nonlocal theory of elasticity have been transformed to the corresponding equations for the Legendre polynomials coefficients. Then, in the same way as in the classical theory of elasticity, a system of differential equations in terms of displacements with initial and boundary conditions for the Legendre polynomials coefficients has been obtained. All equations for higher order theory of nonlocal plates in Cartesian and polar coordinates as well as for cylindrical and spherical shells in coordinates related to the shells geometry have been developed and presented here in detail. The obtained equations can be used for calculating stress-strain and for modelling thin walled structures in macro, micro and nano scale when taking into account size dependent and nonlocal effects.

Traffic accidents continue to be one of the leading causes of death in all countries of the world. Ukraine has a high motor vehicle accident rate and loss of life has negative social and economic consequences.The article presents the number of road accidents with lethal injury in passenger cars in the Zhytomyr region from 2008-2017. The distribution of accidents has been established depending on the class and availability of safety equipment in the passenger compartment of cars., Дорожно-транспортные происшествия продолжают оставаться одной из основных причин смертности населения во всех странах мира, в том числе для Украины высокая аварийность на автомобильном транспорте и тяжелые потери имеют негативные социальные и экономические последствия.В статье приведено количество дорожно-транспортных происшествий с летальной травмой в салоне легковых автомобилей на территории Житомирской области на протяжении 2008–2017 гг. Установлено распределение проишествий в зависимости от классности и наличия средств безопасности в салоне легковых автомобилей., Дорожньо-транспортні пригоди продовжують залишатися однією з основних причин смертності населення в усіх країнах світу, у тому числі для України висока аварійність на автомобільному транспорті та тяжкі втрати мають негативні соціальні й економічні наслідки.У статті наведена кількість дорожньо-транспортних пригод із летальною травмою в салоні легкових автомобілів на території Житомирської області впродовж 2008–2017 рр. Встановлено розподіл пригод залежно від класності та наявності засобів безпеки в салоні легкових автомобілів.

New higher order models of the electro-magneto-elastic plates and shells have been developed here. The 3-D equations of the linear electro-magneto-elasticity have been presented in an orthogonal system of coordinates. For the creation of 2-D models of plates and shells the curvilinear system of coordinates related to the middle surface of the shell has been used along with special hypothesis based on assumptions that take into account the fact that the considered plates and shells are thin. Higher order theory is based on the expansion of the 3-D equations of the linear theory of the electro-magneto-elasticity into Fourier series in terms of Legendre polynomials. All equations for higher order theory of the electro-magneto-elastic plates in Cartesian and polar coordinates as well as for cylindrical and spherical shells in coordinates related to the shells geometry have been developed and presented here in detail. The obtained equations can be used for calculating the stress-strain and for modelling thin walled structures in macro, micro and nano scale when taking into account coupled electro-magneto-elastic effects.

A high-order theory for beams based on expansion of the two-dimensional (2-D) equations of thermoelasticity and heat conductivity into Legendre polynomials series has been developed. The 2-D equations of thermoelasticity and heat conductivity have been expanded into Legendre polynomials series in terms of a thickness coordinate. Therefore, all equations of thermoelasticity and heat conductivity including Hooke’s and Fourier’s laws have been transformed into corresponding equations for coefficients of Legendre polynomials expansion. Then, the system of differential equations in terms of displacements and temperature and boundary conditions for the coefficients of Legendre polynomials expansion has been obtained. Cases of the first and second approximations have been considered in detail. For obtained boundary-value problems, a finite element method has been used and numerical calculations have been done with COMSOL Multiphysics and MATLAB. Developed theory has been applied for study stress–strain state and temperature distribution in the microelectromechanical and nanoelectromechanical systems and structures.

In this paper a new theory for shells, plates and rods has been developed. The proposed theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including Hooke׳s law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. The case of axially symmetric shell has been considered in more details. As a special case of the general approach the equations of the first and second approximations have been developed for circular plates, curvilinear rods and cylindrical shells. Numerical calculations have been done numerically using the finite element method (FEM) along with the Comsol Multiphysics, Matlab and Mathematica software.

A high-order theory for arched rods and beams based on expansion of the two-dimensional (2D) equations of elasticity into Legendre’s polynomials series has been developed. The 2D equations of elasticity have been expanded into Legendre’s polynomials series in terms of a thickness coordinate. Thereby, all equations of elasticity including Hooke’s law have been transformed to corresponding equations for coefficients of Legendre’s polynomials expansion. Then system of differential equations in term of displacements and boundary conditions for the coefficients of Legendre’s polynomials expansion coefficients has been obtained. Cases of the first and second approximations have been considered in details. For obtained boundary-value problems, a finite element method has been used and numerical calculations have been done with COMSOL Multiphysics and MATLAB. Developed theory has been applied for study pull-in instability and stress–strain state of the electrostatically actuated micro-electro-mechanical Systems.

This article addresses weakly singular, hypersingular integrals, which arise when the boundary integral equation (BIE) methods are used for 3-D potential theory problem solutions. An approach based on the theory of distributions and the application of the second Green theorem has been explored for the calculation of such divergent integrals. The divergent integrals have been transformed to a form that allows easy and uniform calculation of weakly singular and hypersingular integrals. For flat boundary elements (BE), piecewise constants and piecewise linear approximations, only regular integrals over the contour of the BE have to be evaluated. Furthermore, all calculations can be done analytically, so no numerical integration is required. In the case of 3-D, rectangular and triangular BE have been considered. The behavior of divergent integrals has been studied in the context that the collocation point moves to the contour of the BE.

Two different boundary element methods (BEM) for crack analysis in two dimensional (2-D) antiplane, homogeneous, isotropic and linear elastic solids by considering frictional contact of the crack edges are presented. Hypersingular boundary integral equations (BIE) in time-domain (TD) and frequency domain (FD), with corresponding elastodynamic fundamental solutions are applied for this purpose. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts the hypersingular integrals to regular integrals is applied. Simple regular formulas for their calculation are presented. For the problems solution while considering frictional contact of the crack edges a special iterative algorithm of Udzava's type is elaborated and used. Numerical results for crack opening, frictional contact forces and dynamic stress intensity factors (SIFs) are presented and discussed for a finite III-mode crack in an infinite domain subjected to a harmonic crack-face loading and considering crack edges frictional contact interaction using the TD and FD approaches.

Description of satellite navigationals which function simultaneously is resulted, namely: American GPS, Russian GLONASS, European Galileo and Chinese Compass. The general amount of sputniks makes more than one hundred units, every system applies that least 3 frequencies, the range-finder signals of new type appear with more more difficult structure and higher descriptions. In the article the review perspective signals is presented for all four system., Приведен анализ характеристик спутниковых навигационных систем, которые функционируют одновременно: американской GPS, российской ГЛОНАСС, европейской «Галилео» и китайской «Компас». Общее количество спутников составляет больше ста единиц, каждая система применяет всего 3 частоты, появляются дальномерные сигналы нового типа с более более сложной структурой и высшими характеристиками. В статье также представлен обзор перспективных сигналов по всех четырех системах., Приведений аналіз характеристик сигналів супутникових навігаційних систем, які функціонують, одночасно, а саме: американської GPS, російської ГЛОНАСС, європейської «Галілео» і китайської Компас. Загальна кількість супутників складає більше ста одиниць, кожна система застосовує щонайменше 3 частоти, з’являються далекомірні сигнали нового типу з більш складнішою структурою і більш високими характеристиками. У статті також представлений огляд перспективних сигналів по всіх чотирьох системах.

In this paper a high order theory for functionally graded (FG) axisymmetric cylindrical shells based on the expansion of the axisymmetric equations of elasticity for functionally graded materials (FGMs) into Fourier series in terms of Legendre's polynomials is presented. Starting from the axisymmetric equations of elasticity, the stress and strain tensors, the displacement, traction and body force vectors are expanded into Fourier series in terms of Legendre's polynomials in the thickness coordinate. In the same way the material parameters that describe the functionally graded material properties are also expanded into Fourier series. All equations of the linear elasticity including Hooke's law are transformed into the corresponding equations for the Fourier series expansion coefficients. Then a system of differential equations in terms of the displacements and the boundary conditions for the Fourier series expansion coefficients is obtained. In particular the first and second order approximations of the exact shell theory are considered in more details. The obtained boundary-value problems are solved by the finite element method (FEM) with COMSOL Multiphysics and MATLAB software. Numerical results are presented and discussed.