Development and design of new methods of measurement of state of strain of structures

The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect.     

Method of calculation of interaction of wall flows

A flow of viscous compressible fluid in the neighborhood of the line of interaction of wall flows is considered. A method of calculating the line of interaction and the direction of the self-induced secondary flow is developed. Papers [1–3] are devoted to the simulation of a separation flow with singularities in the neighborhood of singular lines and points, where boundary-layer equations are invalid. However, the theories of local separation used at present have mainly been developed only for two-dimensional problems, while the models of viscous-inviscid interaction have restrictions in application for turbulent flows with developed separation. The interaction of three-dimensional wall turbulent flows is considered below. It is assumed that the thickness of the boundary layers and the scales of the interaction zones are small in comparison with the characteristic dimension of the system, while the line of discontinuity of the solutions of the three-dimensional boundary layer equations is the same as the line of interaction of the wall flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1987.The author is grateful to G. Yu. Stepanov and V. N. Ershov for their interest in my work and their valuable remarks.     

Equations of oscillations of rods of variable composition

We obtain differential equations for the general case of longitudinal, torsional, and transverse oscillations of rods to some parts of which masses are being added or detached. We solve certain special problems concerning the oscillations of such rods of variable composition. In deriving generalized equations of oscillations of rods of variable composition we employ the assumption of planar sections, the assumption of small deformations, and other customary simplifications. We also employ the simplifying assumption of close action; i.e., we assume that the masses being detached and added interact with the rod only at the instant of direct contact. Forces of internal nonelastic resistance are not taken into account. We assume also that in the undeformed state the elastic axis is rectilinear and that the centers of gravity of cross sections are not displaced from their initial positions relative to the cross sections. There may be a change of mass per unit length of the rod both on account of a change in density as well as on account of a change in area of a cross section, the latter being understood to be the union of the initial area of the cross section and the areas of the parts being added and detached. In addition, with the rod there may be associated particles of variable mass distributed continuously or discretely along the length of the rod. We assume that these particles do not interact among themselves but only with the rod.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 103–108, January–February, 1972.     

两自由度振动系统的斜碰撞分析

研究斜碰撞振动系统动力学的一个关键问题是对系统在碰撞前后的状态进行合理描述和正确计算．针对两弹性体斜碰撞问题，基于瞬间碰撞假设，提出了采用步进冲量来分析和求解斜碰撞前后的状态关系；并以弹簧摆和振子组成的两自由度斜碰撞振动系统为例，具体介绍了该算法如何实现．用解析方法讨论了该系统在斜碰撞过程中可能出现的各种力学现象，将冲量步进算法得到的数值解与解析结果进行对比，取得了完全一致的结果．该数值方法能适应多种斜碰撞问题的计算．     

沙漠地貌演化过程的湍流大涡模拟研究

采用大涡模拟和混合粒径群体沙粒运动算法结合内置边界方法来模拟沙波纹与沙丘的演化和发展,在平坦沙区形成沙波纹的同时,在沙丘上同样也出现了沙波纹的结构,即沙波纹的发展出现了多尺度现象.此外,还分析了粒径对沙波纹与沙丘自身形态演化和发展的影响,以及沙丘对平坦沙区沙波纹形成发展的作用.     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

Theory of the combustion of small drops of metal

The article discusses the combustion of small drops of metal. It is postulated that the formation of an oxide in the liquid phase starts with the origin of a condensed phase and continues as the result of a reaction between the vapors of the drop and the oxidizer at the surface of the forming particles of the condensed phase. It is shown that the process of the formation of particles of condensed oxide in the gas, for very small drops, has an essentially unsteady-state character. Under these circumstances, a considerable fraction of the vaporization products of a drop does not succeed in condensing after the complete gasification of the drop and remains in the gaseous state.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 47–53, March–April, 1976.     

综合管廊早龄期混凝土温度应力仿真模拟

以汉中市综合管廊为工程背景,通过有限元软件,首先模拟分析综合管廊早龄期温度场,随后将温度场结果附加到管廊结构中求解温度应力,从而分析综合管廊早龄期混凝土温度应力与浇筑长度的关系。模拟分析发现:综合管廊在混凝土浇筑早期,温度场沿长度方向变化不显著,且随着浇筑长度的增加,温度场不变;在墙体温度上升阶段,墙体内部沿长度方向的应力主要为压应力,当墙体混凝土内部温度达到最高,混凝土开始降温,结构内变形由膨胀逐渐变为收缩,内力由压应力逐渐变为拉应力,随着时间的变化,墙体内外温差趋于稳定,墙体温度应力也逐渐平稳,此时温度应力主要受外界环境变化影响;当综合管廊浇筑长度在60m范围内,浇筑长度越大,温度应力越大,但当浇筑长度超过60m,温度应力不再增加。     

Laws of ascent of two volumes of hot gas

The three-dimensional interaction of a pair of thermals spaced a certain distance apart in the horizontal direction is numerically investigated. It is found that the distance between the thermals has a determining effect on the interaction pattern, the height of ascent of the pair, and the structure of the airstreams in the troposphere and atmosphere which they initiate.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 48–51, May–June, 1996.     

Change of Accumulation Mechanisms of Irreversible Deformations of Materials in an Example of Viscometric Deformation

Within the framework of the model of large deformations, the deformation of a material exhibiting elastic, viscous, and plastic properties and placed between two rigid cylinders is investigated when turning the internal cylinder. The accumulation of irreversible deformations prior to the onset of plastic flow and upon its termination is associated with creep. Reversible and irreversible deformations according to the model in question are determined by differential transport equations. To calculate the displacement fields, stresses, and reversible, irreversible, and complete deformations, a system of partial differential equations is obtained, for which a finite-difference scheme is constructed.     

Determination of mechanical properties of the bones of the skull

This paper presents the initial results of a research project concerning the mechanism of head injury. In order to begin to define the mechanism, it is necessary to determine mechanical properties of the various skull bones, organize them into constitutive equations, and develop a structural model of the skull. The material presented is concerned primarily with the development of experimental procedures and the results which have been obtained. The specimen-testing program has been split into four parts: (1) The procural of 3/4-in. and 11/2-in.-diam plugs from human skulls at autopsy and the precise determination of specimen location and orientation; (2) the fabrication and strain gaging of small test specimens for basic tension, compression, tension-compression, and shear tests; (3) the conducting of tests; and (4) the correlation of experimental findings with microscopic structure by standard and nonstandard techniques of histology.     

Homogenization of the equations of the Cosserat theory of elasticity of inhomogeneous bodies

The paper deals with the homogenization of a boundary value problem for an inhomogeneous body with Cosserat properties, which is referred to as the original problem. The homogenization process is understood as a method for representing the solution of the original problem in terms of the solution of precisely the same problem for a body with homogeneous properties. The problem for a body with homogeneous properties is called the accompanying problem, and the body itself, the accompanying homogeneous body. As a rule, a constructive homogenization procedure includes the following three stages: at the first stage, the properties of the inhomogeneous body are used to find the properties of the accompanying homogeneous body (efficient properties); at the second stage, the boundary value problem is solved for the accompanying body; at the third stage, the solution of the accompanying problem is used to find the solution of the original problem. This approach was implemented in mechanics of composite materials constructed of numerous representative elements. A significant contribution to the development of mechanics of composites is due to Rabotnov [1–3] and his students. Recently, the homogenization method has been widely used to solve problems for composites of regular structure by expanding the solution of the original problem in a power series in a small geometric parameter equal to the ratio of the characteristic dimension of the periodicity cell to the characteristic dimension of the entire body. The papers by Bakhvalov [4–6] and Pobedrya [7] were the first in the field. At present, there are numerous monographs partially or completely dealing with the method of a small geometric parameter [8–14]. Isolated problems for inhomogeneous bodies with nonperiodic dependence of their properties on the coordinates were considered by many authors. Most of such papers published before 1973 are collected in two vast bibliographic indices [15, 16]. General methods were considered, and many specific problems of the theory of elasticity of continuously inhomogeneous bodies were solved in Lomakin’s papers and his monograph [17]. The theory of torsion of inhomogeneous anisotropic rods was considered in [18]. In 1991, in his Doctoral dissertation, one of the authors of this paper proposed a version of the homogenization method based on an integral formula representing the solution of the original static problem of inhomogeneous elasticity via the solution of the accompanying problem [19, 20]. An integral formula for the dynamic problem of elasticity was published somewhat later [21]. This integral formula was used to develop a constructive method for the homogenization of the dynamic problem of inhomogeneous elasticity, which can be used in the case of both periodic and nonperiodic inhomogeneity of the properties [22]. The integral formula in the case of the Cosserat theory of elasticity was published in [23]. The present paper briefly presents constructive methods for homogenizing the problems of the Cosserat theory of elasticity based on the integral formula.     

Numerical calculation of the problem of cooling of a spherical volume of nonequilibrium-ionized radiating helium

The method is described and the results are presented for numerical calculations of a system of equations of nonsteady gasdynamics, radiation transfer in the continuous spectrum, and the kinetics of collisional ionization and ionization by radiation, which describe the dispersion and cooling of a spherical volume of He. A comparison is made with calculations performed on the assumption of thermodynamic equilibrium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 36–41, March–April, 1976.     

Saturation of absorption of the powerful radiation of a system of anharmonic oscillators

Recently, the theory of nonequilibrium systems simulated by a set of anharmonic oscillators has received significant development. The investigation of such kinds of systems is especially important in the study of problems associated with the stimulation of chemical reactions and the development of effective molecular lasers. The systematic analysis of the kinetics of anharmonic oscillators assumes the simultaneous solution of a large number of nonlinear equations describing the population balance of the vibrational levels. Realization of this approach is associated with cumbersome numerical calculations and does not permit obtaining a qualitative picture of the behavior of the system as a function of the different parameters (pressure, temperature, etc.). An approximate analytical theory has been formulated in [1, 2] which permits finding the distribution function over the vibrational states with the effects of anharmonicity taken into account. We will employ the approach developed in these papers to describe a system of anharmonic oscillators under conditions of powerful optical pumping. This problem was discussed in [3], where it was found that such a system changes into a saturation mode in the case of high pumping levels. The existence of this mode is explained by the fact that the maximum rate of energy input into a vibrational degree of freedom is determined by the rate of distribution of this energy over all the vibrational levels, i.e., by the constant of V—V-exchange. For sufficiently large pumpings the approximation of the Boltzmann distribution function adopted in [3] in connection with the calculation of the saturation parameters is too crude. The goal of this paper is to derive in explicit form expressions for the vibrational energy supply, the absorbed power, and so on, under saturation conditions without the use of the approximation indicated above [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 10–15, September–October, 1978.     

Degree of Stability of Equilibrium

ABSTRACT

A theoretical study is made of the hysteretic behavior of a portal frame under constant gravity and variable horizontal loading. Special account is taken of the variation of axial forces in the columns, the model simulating the plastic interaction of the overall shearing and bending in tall rectangular frames and battened columns. The assumed elastic-perfectly plastic behavior of columns makes a mathematical formulation feasible, and a detailed examination is given of the cyclic alternate displacement loading with the P-Δ-A effect taken into consideration. This example clarifies characteristic features of repeated loading such as shakedown, incremental collapse, and alternating plasticity under the combined action of bending moment and axial force existing in a frame member.     

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.     

Minimization of the drag of blunt edges of projecting elements of a hypersonic object

An approximate method is given for calculating the pressure on the critical line of a cylindrical edge of an element projecting above the surface of a hypersonic object. Correlations of the pressure distribution in the interference regions are proposed on the basis of the calculations and analysis of the experimental data. Variational problems of finding the form of a leading edge having minimum drag are set up and solved on the basis of the pressure calculation model obtained. The solutions are sought with the use of Pontryagin's maximum principle. The effect on the minimum drag profile of Mach numbers and blunting of the body is analyzed. The advantage of the optimal form of the edge in comparison with a corresponding rectilinear edge is shown.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1976.     

Experiments of free vibration of shells of revolution

This paper presents experimental techniques used in and results obtained during a series of experiments performed to investigate the free-vibration behavior of 15-in. base-diameter spherical and paraboloidal shell models of various geometric parameters and boundary conditions. The models were manufactured from polyvinyl-chloride (P.V.C.) sheets by a thermo-vacuum process using special molds and templates. To provide the necessary excitation power, a variable control amplitude/frequency audio oscillator was used to drive a loudspeaker which was mounted underneath the models. A recently developed noncontact fiber-optics instrument, referred to as the “Fotonic Sensor”, was employed in determining the motion of the models. Thirty-two models of different configurations and boundary conditions were tested in the series. The natural frequencies were observed for all models, while the mode shapes associated with the first four-to-six resonant frequencies were mapped only for some of the models, using special scanning devices.     

The uniqueness of the solution of boundary-value problems of a thermal model of discharge

The paper is devoted to a nonlinear analysis of superheating [1, 2] instability of an electric discharge stabilized by electrodes [3] in the framework of a thermal model [4] where the stability of the discharge relative to the long-wave and short-wave perturbations is proved in a linear approximation. Similar boundary-value problems arise in the theories of chemically and biologically reacting mixtures [5–7], thermal breakdown of dielectrics [8], thermal explosion [9], in the investigation of nonlinear waves in semiconductors and superconductors [10, 11], and in the investigation of Couette flow with variable viscosity [12]. The uniqueness of the one-dimensional steady solutions of the thermal model of discharge and the stability relative to the small spatial perturbations, respectively, for the exponential and step dependence of the electrical conductivity on the temperature are proved in [3, 13]. The uniqueness of the solutions in the one-dimensional case for the same electrode temperature and arbitrary dependences of the electrical and thermal conductivity on the temperature is established in paper [14]. In the present paper, the existence and uniqueness of steady solutions of the thermal model of discharge in a three-dimensional formulation for arbitrary fairly smooth electrical and thermal conductivity functions of the temperature in the case of isothermal isopotential electrodes are proved analytically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–145, January–February, 1986.The author expresses his gratitude to A. G. Kulikovskii and A. A. Barmin for the formulation of the problem and their discussions.