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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.

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.

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.

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.

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.

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.

This article considers methods of weakly singular and hypersingular integral regularization based on the theory of distributions. For regularization of divergent integrals, the Gauss---Ostrogradskii theorem and the second Green's theorem in the sense of the theory of distribution have been used. Equations that allow easy calculation of weakly singular, singular, and hypersingular integrals in one- and two-dimensional cases for any sufficiently smooth function have been obtained. These equations are compared with classical methods of regularization. The results of numerical calculation using classical approaches and those based of the theory of generalized functions, along with a comparison for different functions, are presented in tables and graphs of the values of divergent integrals versus the position of the colocation point.

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.

We will solve a fracture-mechanics problem for an elastic material with cracks subject to a polyharmonic load created by longitudinal waves with different wavelengths propagating through the material. The frictionless contact between the edges of a finite-length plane crack under the action of two normal harmonic tension/compression waves with different frequencies is studied. The forces of contact interaction and displacement discontinuity are analyzed. The effect of the wave frequency on the stress intensity factor is examined for different normalized wave numbers

The frictional contact interaction of the finite edges of a plane crack under the action of a normally incident harmonic shear wave that produces antiplane deformation is studied. The influence of the forces of contact interaction on the stress intensity factor is analyzed

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied

Dilatometric studies for the end burning of 3Cu—Al pressed samples in air were performed. The results are compared with data on the structural transformations occurring in burning samples of the same composition. A nonequilibrium mechanism of the processes occurring in burning and cooling samples is proposed. Possible reasons of the samples size variations during combustion are analyzed.

A heat-conduction problem is formulated for laminated plates and shells with a heat-conducting layer and debonding between laminas. The approach consists in analyzing how the layer thickness changes in the process of debonding of laminas and deformation of plates and shells. The three-dimensional thermoelastic and heat-conduction equations are expanded into polynomial Legendre series in thickness. The first-order, Timoshenko’s, and Kirchhoff-Love equations are examined. A numerical example of laminated shells with a heat-conducting layer is considered

The combustion of pressed specimens of a stoichiometric Fe2O3-TiO2-Al-C powder mixture burning in the SHS regime is studied. It is found that the final product has the same shape and size as the initial specimen. The composition and structure of the final product, which is highly porous high-melting Al2O3-TiC-Fe(Ti) composite ceramics, are studied. The mechanism of phase and structure formation in the examined system is proposed.

Consideration is given to the contact interaction of the faces of a stationary plane elliptical crack under the action of a harmonic shear wave normally incident on the crack surface. The dependence of the mode II and III stress intensity factors on the wave number is studied for different values of the friction coefficient

The paper deals with the three-dimensional dynamic problem for an elliptic crack interacting with a normally incident harmonic compression–expansion wave, considering the contact interaction of the crack faces. An asymmetric solution is obtained using an iteration algorithm developed earlier. Numerical results are presented

In this paper we consider an algorithm of constrained optimization which arises from boundary variational principles of elastodynamics for bodies with cracks and unilateral constraints on the cracks edges. Variational formulation of unilateral contact problems with friction was considered, boundary variational functionals used with boundary integral equations were obtained and algorithm for solution of the unilateral contact problem with friction was developed. Some numerical results for 3-D elastodynamic unilateral contact problem for bodies with cracks are presented.

The paper reviews published data on structural–phase changes in Cu–Al and Ni–Al metal powders during in situ combustion. The heat‐conservation properties of various structures located around reactive cells in the combustion wave zone are revealed. The mechanism providing for nearly adiabatic combustion conditions is discussed and a microstructural model for this mechanism is justified.

The contact interaction of the faces of a penny-shaped crack in a three-dimensional space is studied for the case of normal incidence of a harmonic tension–compression wave. The problem is solved by the method of boundary integral equations. The dependence of the mode I stress intensity factor on the wave number is studied. The solution is compared with the results obtained for a penny-shaped crack when the contact interaction is neglected.

A plane problem is solved for the contact interaction between the faces of a rectilinear crack under the action of a normally incident harmonic tension–compression wave. Iterative algorithms are presented to solve the problem for both given initial distribution of contact forces and given initial discontinuity in the displacements of the crack faces. The convergence rates of the algorithms, the maximum contact forces, and displacement discontinuities are compared.

A complete and consistent review is made of the results of studies into the contact interaction of crack edges by methods of fracture mechanics. Also some new results are presented.

A three-dimensional problem on the contact interaction between the faces of a rectangular crack under a normally incident harmonic tension–compression wave is considered. The problem is solved by using the method of boundary integral equations and an iterative algorithm. The contact forces and the discontinuity in the displacement of the crack faces are studied. The results obtained are compared with those for a finite plane crack.

We study the contact interaction of the faces of a finite rectilinear crack under harmonic compression–expansion and shear waves incident at an arbitrary angle. An iterative algorithm based on the variational principles of elastic theory is used. The contact interaction and displacement discontinuity of the crack faces are analyzed. The crack-tip stress intensity factors are calculated. The results are compared with those obtained regardless of the contact interaction

The paper reports results of dynamic x‐ray photography of self‐propagating high‐temperature synthesis of a 3Cu–Al powder mixture in the regime of thermal explosion. The stages of formation of the final product are considered, beginning with the heating of the starting mixture and interaction of its components and ending with phase transitions during cooling of the product — intermetallides Cu9Al4 and Cu3Al, which are the main components of Cu based tribotechnical materials. It is shown that upon heating in the temperature range of 550 – 590°C, the intensity of diffraction lines of Al drops to the background level. The exothermicreaction of synthesis of the intermetallide is initiated at a temperature of 610 – 630°C. In the period of sharp increase in temperature to 1040°C, the presence of the starting copper and the newly formed high‐temperature β′ phase with the Cu9Al4 tructure are detected simultaneously in the combustion wave. When cooled to 300$°C, the material contains two cubic phases — Cu9Al4 and an α‐solid solution of Al in Cu. Further cooling is accompanied by formation and increase of peaks of the Cu3Al phase with an orthorhombic lattice. The phase composition of aluminum bronze produced by SHS with combustion in the regime of thermal explosion is not in equilibrium.

The microstructural evolution of Cu–Al powder compacts during self-propagating high-temperature synthesis was studied by metallography and x-ray diffraction analysis. The results indicate that local combustion sites (reaction cells) in the samples are surrounded by intermetallic shells embedded in the copper matrix. The process is accompanied by the development of thermal gradients between different microstructural constituents and heat accumulation in the reaction cells. The microstructure effects on the engineering performance of the materials studied are assessed.

Expressions are derived for the singular kernels of a system of integral equations that describe a three-dimensional dynamic problem for a cracked elastic body under harmonic loading. The order of singularity of the kernels of the integral equations is analyzed. Relations that allow reducing hypersingular surface integrals to ordinary contour ones are obtained. Test calculations are conducted.

Thein situ structural changes in powder metallic mixtures of exothermic compositions compacted by pressing and sintered by the method of self-propagating high-temperature synthesis are studied. It is shown that temperature gradient exist between the structural components of the mixture during the whole of the burning wave. The role of oxidation processes in reaction cells is investigated and the causes of the thermal heterogeneity of powder mixtures during burning are explained.

The effect of contact between the sides of a rectilinear crack in the planeR 2={x: x3=0} on the characteristics of the fallure mechanics is studied for the case in which the crack is affected by harmonic tensile-compression waves and shifts. The surfaces of the crack may assume any orientation relative to the direction of propagation of the waves. The presence of friction in the zone of contact of the sides of the crack is taken into account. The method of solving the problem stated is iterative in nature and is based on the solution of a sequence of boundary integral equations for the Fourier coefficients of the displacement discontinuity vector and the contact force vector. It is also corrected at each step of the solution so as to satisfy one-sided restrictions in the zone of contact.

The laws of heat transfer and eutectic liquid mixtures redistribution between layers of bimetallic powder materials in the process of consolidation while self-propagating high temperature synthesis mode were investigated. It was determined that temperature gradients exist on both sides of the interface between layers of porous nickel and an exothermal mixture of 15% Al–85% Ni. The temperature decreased from the interface to the centers of the layers. Inhomogeneous temperature distribution was the cause of liquid phase transfer from the combustion zone (near the interface) to the cold peripheral zones of the inert powder layers. The observed laws were confirmed by the results of physical metallurgy investigation.

Measurement of temperatures is made at different points in the volumes of exothermic cells and intervening spacings in model powder metallic preform mixtures during their combustion under thermal-explosion conditions. The presence of temperature gradients is found, as are regularities in their change in interrelation with specific features of migration of eutectics and melts formed in a porous metallic skeleton consolidated in a combustion wave.

This article is an analytical review of studies of process combustion in pressings made from mixtures of exothermic metal powders. We establish the macrokinetic features of combustion of mixtures with nonstoichiometric composition as well as the factors accelerating sintering of the pressings with an exothermic reaction. We suggest thermophysical models for consolidation during combustion of a system of metal powders with nonstoichiometric composition.

We formulate a contact problem of the theory of elasticity with unilateral constraints for cracked bodies under random variable loading and consider a special case of harmonic loads very important for practical applications. The problem is solved by the method of boundary integral equations of the elastodynamic theory of cracked bodies. We also analyze typical singularities of the kernels of potentials of these equations and develop an algorithm for the solution of unilateral contact problems of the dynamics of cracked bodies based on the determination of the saddle point of a subdifferential boundary functional. We solve dynamical problems of propagation of plane harmonic compression-dilatation waves in a plane with cracks of finite lengths under the assumption of unilateral contact of the crack lips. We present numerical results and investigate the effect of contact interaction of the crack lips both quantitatively and qualitatively.

This article - the second part of a survey of dynamic problems of fracture mechanics - looks at questions related to the solution of dynamic problems of the theory of elasticity for cracked bodies in which the crack edges can come into contact with one another during deformation.

An analytical survey is presented on the scope for using self-propagating high-temperature synthesis for sintering tribotechnical materials and components, particularly ones based on powder bronzes. The major macrokinetic characteristics of the burning have been established, as have the working properties of the materials.

In this, the first part of the survey we have discussed only certain aspects of dynamic fracture mechanics. The surveyed material has been selected with a preference for the most highly developed parts of the theory, specifically those elements which have direct bearing on the second part of the survey. We have also included information on the dynamic fracture mechanics of initially stressed materials, in the development of which one of the authors has been a major contributor.