Application of the averaging method in the calculation of rod structures like plates and beams

A modification of the averaging method that permits one to calculate the averaged characteristics of periodic beam structures such as masts, skeleton spans., etc. by the methods of materials strength is proposed. Siberian State Academy of Telecommunications and Informatics, Novosibirsk 630009. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 169–179, September–October, 1998.     

Experimental studies of the protective properties of flat shock-wave shields in water

An experimental method is presented and an experimental study is made of the protective properties of flat shields for a series of materials of specific thicknesses. The decay factors of the materials are determined, and the characteristics of shock-wave loads which have passed through the shield are examined. S. P. Timoshenko Institute of Mechnics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 99–102, March, 1999.     

Deformation of physically nonlinear stochastic composites

The studies of the deformation of physically nonlinear homogeneous and composite materials are systematized. Algorithms to determine the effective elastic properties and stress–strain state of particulate, laminated, fibrous, and laminated fibrous composite materials with physically nonlinear components are outlined, and their deformation patterns are studied. Composites are considered as two-component materials of random structure. Their effective properties are determined using the conditional averaging method. The nonlinear equations that allow for the physical nonlinearity of the components are solved by an iterative method. The relationship between macrostresses and macrostrains is established. Macrostress–macrostrain curves of homogeneous and composite materials are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 7–38, December 2008.     

Study of the stability of composite shells with allowance for the cracked state of components of the material

An approximate method is described for determining the effective strain characteristics of composite materials with allowance for the presence of plane microcracks in the components. The character of the effect of such defects on the critical loads is illustrated by examining the problem of the stability of a conical shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 46–54, November, 1999.     

Strain analysis of polycrystalline specimens by the method of superimposed holographic interferometry

A new experimental method for analysis of the mechanical properties of crystal materials is proposed. The method combines the advantages of holographic interferometry and the contact method of fixing a recording medium. The proposed approach is shown to be effective in determining the surface displacements and strains. Siberian State Transport University, Novosibirsk 630049. Chelyabinsk State Agroengineering University, Chelyabinsk 454080. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 218–222, January–February, 2000.     

Effective electrostrictive properties of stochastic two-component materials

The paper addresses electrostriction as a nonlinear electromechanical effect in inhomogeneous two-component materials. The method of conditional moments is developed to determine the effective electrostrictive properties of such materials. Exact expressions for the effective characteristics of isotropic composites with oriented inclusions are given. The effect of the shape and volume fraction of inclusions on the effective properties of composite materials is examined. Relevant graphs are plotted Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 3–11, September 2008.     

Analysis of the vibrational behavior of the composite cylinders reinforced with non-uniform distributed carbon nanotubes using micro-mechanical approach

Nanocomposites are a promising new class of structural materials for the aerospace structural components. This paper presents a detailed theoretical investigation of dynamic characteristics of cylinders made of carbon nanotube-reinforced composites. The cylinders are modeled as a cylindrical shell consisting of an isotropic matrix reinforced with transversely isotropic carbon nanotubes. Two different types of carbon nanotube reinforcements are considered: single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs). The effects of carbon nanotube aspect ratio, dispersion, alignment and volume fraction on the elastic modulus are analyzed using the Eshelby–Mori–Tanaka theory. Mass and stiffness matrices are obtained via Ritz method and natural frequencies of the structure are derived through solving the eigenvalue problem. Finally, the effects of the CNT distribution on mode shapes and natural frequencies are discussed.     

Evaluation and prediction of fatigue resistance of metals from the kinetics of variation in surface properties

The paper studies the fatigue resistance of metallic samples subjected to high-cycle loading and microhardness measurement. The fatigue damage of materials during loading is identified as decrease in the thickness of the barrier surface layer, which prevents fatigue failure. It is shown that the thickness of this layer is independent of the plastic characteristics of the material and the level of stress. A method to evaluate accumulated fatigue damage is developed. Kinetic curves of damage accumulation are analyzed. Methods to predict fatigue characteristics are proposed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 86–95, March 2008.     

Experimental determination of the basic characteristics of heat and mass transfer upon thermoerosion fracture of materials

Using an original technique, heat and mass transfer in the interaction between a high-temperature heterogeneous jet with a high concentration of particles and the surface of structural materials was studied for the first time. The characteristics of heat and mass transfer were obtained under conditions of intense destruction of the materials under the action of a heterogeneous jet whose axis is perpendicular to the heating surface. Based on the results of experimental studies, some signs of high-temperature fracture of steel and cement grout under the action of a heterogeneous jet were revealed. Deceased. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 138–143, March–April, 2000.     

Numerical simulation and optimization of the processes of microwave treatment of dielectrics

The processes of electrodynamics, heat and mass transfer, and thermomechanics in a dielectric under the action of microwave energy are simulated numerically. A method for solving problems of optimization of thermal treatment of materials in microwave apparatus using beam-type chambers is proposed. Saratov State Technical University, Saratov 410054. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 112–119, January–February, 2000.     

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.     

Resonant vibrations of a clamped viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a viscoelastic rectangular plate undergoing resonant vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the Bubnov–Galerkin method. The effect of the mechanical boundary conditions and dissipative-heating temperature on the performance of the sensors is analyzed     

Analysis of the thrust characteristics of jet nozzles designed by various methods

A comparative numerical analysis of the thrust characteristics of axisymmetric jet nozzles designed by various methods is carried out. “Extremal“ nozzles designed by variational methods in the absence/presence of internal shocks (I), so-called “truncated“ nozzles with a uniform characteristic (II), and nozzles designed by the method of conjugate circular arcs (III) are considered. A comparison is carried out for both perfect and real gases (in the latter case the boundary layer gas viscosity is taken into account). It is shown that extremal nozzles are the most efficient, while truncated nozzles are somewhat less so. The thrust characteristics of nozzles designed by the method of conjugate circular arcs for both inviscid and viscous flow are inferior to those of extremal nozzles by 0.7–1%. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-00891).     

Mathematical Modeling of Flows Inside Rotating Bodies Made of Cellular-Porous Materials

A physicomathematical model is developed, which describes gas flows inside rapidly rotating bodies made of cellular-porous materials. Asymptotic and numerical solutions are obtained for some problems of forced centrifugal convection inside cylindrical cellular-porous bodies. The effect of the governing parameters (drag coefficient and dimensionless length of the cylinder) on characteristics and types of flows is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 78–85, November–December, 2005.     

Analysis of the ultimate kinematic characteristics of railgun accelerators of solids

A comparative analysis of the dependences of the ultimate (under heating conditions) velocity on the dimensions and thermal properties of the projectile and on the length of the railgun is performed on the basis of a numerical solution of two-dimensional unsteady equations of magnetic-field diffusion and heat transfer. Homogeneous and multilayer projectiles and homogeneous rails and rails with a resistive coating are considered. It is shown that the ultimate kinematic characteristics of railgun accelerators of solids can be considerably increased by changing the structure and thermal properties of the materials of the projectile and the electrodes. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 156–162, March–April, 1999.     

Describing the elastoplastic deformation of layered shells under axisymmetric loading with allowance for the third invariant of the stress deviator

A method for numerical analysis of the elastoplastic stress–strain state of thin layered shells of revolution under axisymmetric loading is proposed. Constitutive equations describing the elastoplastic deformation of isotropic materials with allowance for the stress mode are used. Numerical results are presented     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed     

Affine transformations of the equations of the linear theory of elasticity

This paper deals with the general formulas of affine transformations that preserve invariance of the static equations of the linear theory of elasticity in the case of arbitrary anisotropic materials. The invariance of the equations with respect to affine transformations allows one to model a given anisotropic material by another material. All anisotropic materials are divided into classes of mutually congruent materials. The congruency conditions are obtained for orthotropic and isotropic materials and for orthotropic and transversely isotropic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 124–134, July–August, 2006.