Visual representation of the kinematics of the continuum

The purpose of this paper is to present some experimentally determined properties of the continuum. The development starts with the illustration of deformed shapes, or metamorphoses, and the introduction of the concept of displacement. From there on, the development follows the classic mechanics-of-continuum presentation, spatial and time derivatives of displacement, strains, stresses and rigid rotations. To unify the presentation, all considerations are applied to the case of a circular ring subjected to diametral compression. Particular advantage is taken of grids, moiré, brittle-coatings and photoelasticity methods to obtain the physical representations of the properties. The following loci are considered: isokinetics, isothetics, isogonics, isoclinics of displacement, displacement trajectories, loci of partial derivative, isogyros, isotenics, isochromatics, isoclinics of strain and stress, isostatics, isopachics, isobars, isostrophics and isoentatics. The understanding of the properties of these fields helps in the visualization of the mechanics of the continuum, in general, and may prove to be particularly useful in the fields of plasticity and finite strain.     

基于阻抗法的矩形截面均压槽气浮支承静态性能分析

针对CFD仿真方法效率低下的状况,提出利用阻抗法来提升气浮支承承载性能的计算速度. 以矩形截面均压槽气浮支承为研究对象,研究了当均压槽高度、角度、数量、半径和供气压力变化对气浮支承承载性能的影响. 结果表明:与CFD仿真方法相比,阻抗法在保证计算结果精度的前提下可提高气浮支承承载力的计算速度. 当均压槽高度、角度、数量、半径和供气压力增大时,阻抗比会增加,气浮支承的承载力和刚度峰值对应的阻抗比也会增加. 当气膜厚度增加时,阻抗比会增加,但承载力会相应地减小. 本文作者通过阻抗法推导了气浮支承承载力简化计算公式,解决了气浮支承在均压槽方向上简化计算的难点,并为阻抗法在均压槽中的研究与应用提供了理论依据.      

Calculation of the explosion of a trotyl bar of infinite length

The dynamics of the explosion of spherical, cylindrical, or flat charges of explosive has been thoroughly studied [1–6]. The form of these charges is such that the energy evolved is distributed under the condition of the instantaneous character of the detonation or of its initiation at the center, along the axis, or at the plane of symmetry of the charge, uniformly over the surface of the charges, which, with an explosion in a homogeneous medium, leads to one-dimensional not fully established motions. It is of interest to investigate the process of the explosion of charges of more general form, where the above distribution of energy ceases to be uniform, and the corresponding motion of the medium ceases to be one-dimensional. An example can be the explosions of charges having the form of a cube, a parallelepiped, an ellipsoid, etc. The study of such cases makes it possible to clarify the resulting redistribution of the energy of the explosion, which can be of importance from the point of view of the search for possibilities of improving the use and the control of this energy. Such investigations have been carried out experimentally (see, for example, [7]); however, up to the present time there has been no rigorous theoretical analysis, which is connected with the great complexity of the corresponding gasdynamic problems. The article discusses the natural generalization of the problem of the explosion of an infinitely long cylindrical charge.     

Flow of an anomalously viscous liquid between two rotating cylinders

One of the most important problems of the theory of processing polymer materials is the investigation of the flow of thermoplasts in the region of deformation of rolling machines. In this paper, an analysis is carried out of this process, based on equations for an anomalously viscous liquid, including the energy equation in the bipolar system of coordinates. An analytical solution is given for this system of equations, and also given are the results of the solution obtained by numerical methods of analysis, taking account of the dependence of the rheological coefficients on the temperature. The dependence of the maximum temperature rise in the region of deformation on the speed of rotation of the rollers, the coordinates of the material feed in the region of deformation, and the rheological coefficients, is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 17–24, March–April, 1976.In conclusion, the authors thank S. A. Regirer for critical comments.     

折纸及其折痕设计研究综述

折纸是指不经剪裁和粘接,将二维平面纸张折叠成三维立体的方法,具有设计简单、成形迅速、适用范围广等优点,在可展开式结构、结构组装与自成型等领域有着广阔的应用前景. 本文首先简述了多种典型的新式折纸应用,如屈曲诱导的微尺度三维结构、可折叠太阳能电池板、DNA螺旋组装结构等;根据折纸的曲线折痕数量、相对运动、刚性折叠面、使用纸张数量界定折纸的分类;然后 折痕设计是实现折纸结构的核心问题,着重阐述了折纸的折痕设计方面,包括梳理折痕设计的基本条件,给出若干典型折痕设计如三浦折痕设计、水弹折痕设计、吉村式折痕设计和对角线型折痕设计,介绍典型折痕设计的显著特点及几何条件,将目前折纸折痕设计的创新方法归纳为对经典折痕设计适当改进、形成折痕设计数据库、利用拓扑优化方法、借助成型的汇编算法等;最后,基于当前折纸的研究进展对未来的研究方向进行了展望,其中涉及到可重构折纸结构、四维折纸、多材料折纸和多尺度折纸等.      

高超声速喷管设计理论与方法

在高超声速飞行技术领域,特别是涉及到高焓气体流动的研究,高超声速风洞试验仍然是目前最可靠的研究手段.风洞流场的品质是高超声速风洞研发最重要的一项性能指标,其取决于喷管设计采用的理论与方法,也是风洞设计最关注的一项核心技术.针对二维轴对称型面喷管设计,本文首先综述了传统高超声速喷管设计的主要理论和常用方法,它们在高超声速...     

夯筑遗址加固中楠竹锚杆应力分布变化规律研究

针对西北地区夯筑土遗址楠竹锚固体系,本文在对锚固体中杆体、土体和注浆体的材料性能试验基础上,研究荷载、锚固长度、锚杆直径、孔径、注浆体配比、碳纤维加肋和倾角等因素对楠竹锚杆锚固性能及应力分布规律的影响,同时对荷载、锚固长度和锚杆直径变化状况下的应力分布特征进行数值模拟分析。结果表明:锚杆受力过程中,应力沿杆体分布不均匀;随着锚固长度的增加,应力分布趋于均匀化,而应力峰值沿锚固深度向底端扩展的速度较慢;随着杆体直径和孔径的增加,锚固体应力趋于均匀化,使锚固系统更趋合理化;注浆体强度对应力分布的影响反之;碳纤维加肋可有效提高锚杆的抗劈裂性及锚固力,但会使应力分布更集中化;锚杆布置角度以10°为宜。采用接触单元,模拟杆体与注浆体、注浆体与土体界面间的黏结、咬合效应,不同工况下应力的分布规律、极值大小等参数均与原位试验结果吻合度较好,后期计算分析与研究可予以借鉴。     

聚能射流侵彻页岩储层损伤裂隙形成机制

为研究药型罩对聚能射孔弹侵彻页岩储层的射孔和损伤致裂效果的影响机理,建立了射孔弹-空气-页岩三维模型,设置药型罩的锥角分别为50°、60°、70°和80°,壁厚分别为0.5、1.0和1.5 mm,材料分别为铜、钢、钛和钨。利用ANSYS/LS-DYNA软件进行数值计算,分别从射流速度与形态、页岩射孔效果及页岩孔裂隙形成规律特征等进行系统性分析。研究结果表明：在射孔弹结构中,随着药型罩锥角的减小,射流速度提高、杵体速度降低、侵彻深度增大同时开孔孔径减小。在一定范围内,适当减小药型罩的壁厚,可以提高射流速度、减小杵体质量、增大侵彻深度和开孔倾斜度。药型罩材料对射流速度、杵体结构和页岩射孔效果均有显著影响,其中钨药型罩射孔弹的侵彻深度最大但开孔孔径最小,钛药型罩射孔弹的侵彻深度最小但开孔倾斜度最大,铜比钢药型罩射孔弹的侵彻深度略大但开孔孔径略小。通过研究不同对照组的页岩孔裂隙形成规律特征发现,页岩孔裂隙发育主要发生在杵体对页岩的再扩孔阶段,减小射流初始扩孔孔径、增大杵体直径、提高杵体速度,可以促进页岩孔裂隙发育程度。     

混凝土多尺度应力响应方程及其数值模拟

针对混凝土的多相多尺度材料组成特征及其复杂力学响应问题, 首先, 根据混凝土中各组成材料的几何特征, 将C-S-H凝胶、硬化水泥浆体、砂浆及混凝土细观组成分别视为纳观、微观、亚细观和细观尺度上的复合材料, 并利用颗粒空间堆积方法, 重构了混凝土各尺度复合材料的简化几何模型; 其次, 基于重构的几何模型和等效夹杂理论, 通过等效刚度的升阶计算和应力响应的降阶计算, 建立各尺度复合材料应力响应之间的过渡关系, 推导混凝土多尺度应力响应方程, 并编制相应的计算程序; 最后, 以单轴压缩载荷作用为例, 数值计算载荷作用下混凝土各尺度复合材料中的应力响应, 分析骨料空间位置和相互作用以及水化产物刚度、几何形状和空间取向对其应力响应的影响规律. 结果表明, 单轴压缩载荷作用下, 混凝土细观组成中的应力分布并不均匀; 骨料颗粒之间的距离影响到混凝土中的应力分布, 其有效影响范围约为骨料粒径的6倍; 水泥水化产物的刚度、几何形状和空间取向是影响其应力分布的重要因素, 刚度越大, 所受应力越大, 与载荷作用方向的夹角越小, 长椭球形水化产物沿载荷作用方向的应力越大, 扁椭球形水化产物与之相反.      

Mechanics of composite materials with distorted structure (review). continuum theory,fiber composites

Conclusions Investigations of the mechanics of composite materials with structural distortion within the framework of the continuum approach and within the framework of the model of a piecewise-homogeneous body for fibrous composite materials have been reviewed in the present work. On the basis of this review, these investigations must be regarded as in their early stages, In our view, the next stages in this work are to investigate the characteristic static and dynamic problems within the framework of continuum theory [10, 21, 23] and to investigate the stress-strain state in fibrous composite materials with structural distortion taking account of the mutual influence of the fibers.Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, Baku. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No, 5, pp. 3–20, May, 1991.     

基于分子动力学的氧化石墨烯拉伸断裂行为与力学性能研究

与石墨烯相比,氧化石墨烯(graphene oxide, GO)的亲水性、分散性和反应活性更好,更易于作为增强材料而研发生成性能超常的复合材料,但另一方面,由于其电子结构较为复杂,致使目前有关力学方面的研究存在一定差异.本文利用分子动力学方法,建立了羟基、羧基和环氧基等官能团随机分布的GO原子模型;通过单向拉伸模拟,分析了其断裂行为,结果表明,远离羟基和羧基的环氧基对断裂具有"诱导"作用,并从化学成键、体系能量和应力分布三个角度对其机理进行了阐释;此外,进一步研究了拉伸应力$\!$-$\!$-$\!$应变曲线、极限强度、极限应变等力学性能与含氧官能团覆盖度间的关系,结果表明,极限强度、极限应变均随含氧官能团覆盖度的增大而呈减小趋势.分析认为,主要原因是官能团的出现对石墨烯面内的sp$^{2}$杂化形式造成了破坏,进而使得原子间键合能弱化,随着含氧官能团的覆盖度的增大,被弱化的键合能的数量和程度将越大,从而使得GO的极限强度、极限应变等越低. 研究结果可为GO的基础研究和工程应用提供参考.      

垂向冲击下穿戴装备对乘员损伤影响研究

军事人员在战斗中需要穿戴装备,穿戴装备后对车内乘员承受车辆底部爆炸垂向冲击时的损伤有影响。通过垂向冲击试验与仿真模拟的方法,研究了穿戴装备在身上的分布对于乘员损伤的影响。根据AEP55乘员伤害准则,以盆骨z向加速度和腰椎轴向力为乘员损伤的参考目标,首先通过垂向冲击试验的进行,研究了不同穿戴装备质量对于乘员损伤的影响;接着通过有限元模型对试验进行验证和优化,进而研究穿戴装备位置与松紧度对于垂向冲击下乘员损伤的影响。结果表明随着穿戴装备质量的增加,乘员腰椎损伤加重,脊柱损伤概率减小;装备分布在躯干位置越靠近上部,与身体接触松紧度越紧,乘员腰椎与脊柱的负荷越小,越不易受伤。     

Averaging of magnetohydrodynamic streams and applicability of the hydraulic approximation to the calculation of MHD flows in channels

At the present time the hydraulic approximation equations are used widely for calculating MHD flows in channels. Several years ago these solutions were considered as a method of expanding our ideas of the qualitative effect of various factors on the MHD flow in the channel of a MHD device. Today, however, the hydraulic analysis methods are beginning to be used for calculations on specific systems. In this case the selection of a particular design solution frequently is based on an analysis of the over-all characteristics (efficiency, power delivered to the external load, etc.) obtained from the hydraulic calculation, where a few percent rather than tens of percent are taken into account.On the other hand, it is known [1] that in gas dynamics the results of the hydraulic calculation for the same specific nonuniform stream may differ by an order of magnitude of tens of percent depending on the averaging method used, since the magnitude of this difference depends on the degree of nonuniformity of the actual stream.We may expect that the nonuniformity of the MHD streams will be far greater than for the gas dynamic flows as a result of the nonuniformities of the force and the thermal effect of the currents flowing in the stream. These nonuniformities may be associated, for example, with the nonuniform distribution of the currents in the channel cross section because of the nonuniform electrical conductivity, which may be significant in spite of the weak nonuniformity of the temperature distribution, or with the presence in the cross section of forces associated with the induced longitudinal component of the magnetic field, the presence of anisotropy of the electrical conductivity, etc.Moreover, in contrast with gas dynamics, in the design of various MHD devices several characteristics (power delivered to the external load, various efficiencies, etc.) which may be calculated in terms of the average value of the gas dynamic parameters are of great importance. Thus, it seems probable that the question of the applicability of the hydraulic approximation to the calculation of MHD flows in channels, the rational selection of the means for averaging the actual flows, the comparison of the results of the hydraulic calculations with the experimental data, and so on, may be far more significant than was the case for the study of gas dynamic flows.     

Generalization of the Stefan model to allow for both velocity and temperature jumps

We obtain an expression for the energy dissipation due to an evolving nonmaterial interface across which the mass density, velocity, stress, energy density, heat flux, entropy density, and temperature may be discontinuous. This expression is a sum of three terms: the product of the interfacial mass flux with the interfacial energy release; the scalar product of the interfacial velocity slip with the interfacial friction; and, the product of the interfacial temperature jump, scaled by the interfacial temperature average, with the interfacial heating. When the surface in question is a phase interface, we propose, on the basis of the interfacial dissipation inequality, supplemental relations that determine the interfacial energy release, the interfacial friction, and the interfacial heating constitutively as functions of the interfacial mass flux, the interfacial velocity slip, and the scaled interfacial temperature jump. As a step toward an understanding of the role that such interfacial relations may serve in theories for phase transitions, we investigate a problem involving the solidification of a pure substance in the absence of flow. Received February 17, 1999     

In Memory of Our Honorary Editor-in-Chief Editorial Board of Applied Mathematics and Mechanics

Chien Wei-zang,one of the founders of modern mechanics in China,a world renowned scientist,educator,outstanding social leader,prominent leader of the Chinese Democratic League and a close friend of the Communist Party of China,the Vice Chairman of the 6th,7th,8th,and 9th National Committee of Chinese People's Political Consultative Conference, the Vice Chairman of the 5th, 6th, and 7th Central Committee of Chinese Democratic League, the Honorary Chairman of the 7th, 8th, and 9th Central Committee of Chinese Democratic League, a senior member of Chinese Academy of Science, the President of Shanghai University, the Director of Shanghai Institute of Applied Mathematics and Mechanics, and the Honorary Editor-in Chief of Applied Mathematics and Mechanics, Passed away at the age of 98 in Shanghai at 6:20 AM on July 30,2010.     

Masonry structures made of monolithic blocks with an application to spiral stairs

The broad topic of the present work is Statics and Kinematics of masonry structures, made of monolithic blocks, modelled a la Heyman, that is rigid bodies loaded by external forces, submitted to unilateral constraints, and undergoing small displacements, under the simplifying assumption that sliding on rough interfaces is prevented. Specifically, in this work, we study the effect, in terms of internal forces, of specified loads, by using given settlements/eigenstrains to trigger special regimes of the internal forces. Although our scope here is the analysis of masonry structures composed by monolithic pieces, and whose blocks are not likely to break at their inside, the method we propose can also be applied to generic masonry structures, such as those made of bricks or small stones. Heyman’s assumptions translate, for unilateral continua, into a normality assumption which allows to employ the two theorems of Limit Analysis. These continuous structures may actually fracture everywhere at their inside, forming rigid blocks in relative displacement among each other. Such piecewise rigid-body displacements in masonry are physiological, and rather than the result of over-loading, are most likely the direct product of small changes of the displacement type boundary conditions. However, when in a part of the structure a specific piecewise rigid-body displacement nucleates, that part of the structure exhibits a one degree of freedom mechanism, and becomes statically determined. Therefore, the internal forces can be computed, despite the original uncracked structure being abundantly overdetermined, and then admitting infinite many statically admissible stress regimes. With these assumptions, in the present paper we study the equilibrium and the effect of settlements in a masonry structure made of monolithic blocks. In particular, the triple helical stair of the convent of San Domingos de Bonaval, located in the Bonaval district of Santiago de Compostela, is considered as case study.     

Conjugated heat and mass transfer between a reactive solid and a gas in the presence of nonequilibrium chemical reactions

An investigation of a multicomponent boundary layer taking account of nonequilibrium chemical reactions has been made in a number of publications [1–3]; here, the temperature of the solid was assumed to be known or was determined from the condition of the conservation of energy at the interface between the gas and the solid, taking account of the solution of the equation of thermal conductivity in the solid phase. At the same time, heating of the material of a coating is an unavoidable step in any mechanism of thermokinetic decomposition and, in view of this, it is necessary to take account of the lag of the heat-transfer process inside the solid. Therefore, it is necessary to solve the equation of the energy balance in the solid phase simultaneously with the system of the equations of the boundary layer, i.e., the conjugate problem. The present article discusses the problem of flow around a solid in the vicinity of a frontal critical point, taking account of the dependence of the processes taking place in the solid body on the time, in the presence of two heterogeneous and one homogeneous reactions. The distributions of the velocity, the temperature, and the concentrations in the boundary layer are obtained, as well as the mass rate of entrainment of the material at different moments of time. The time of the change between kinetic and diffusion conditions of the course of the heterogeneous chemical reactions (the ignition time) is determined. It is established that, in the presence of a homogeneous chemical reaction, the mass rate of entrainment is less than with a frozen flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–128, March–April, 1974.     

Dynamics of the general Lorenz family

The present work is devoted to investigating the dynamical entities of the general Lorenz family, which contains four independent parameters. The classical Lorenz system, the Chen system, and the Lü system are all contained by the system considered in this paper as special cases. First, the properties of the equilibria, in particular, the stability of the non-hyperbolic equilibrium obtained by using the center manifold theorem and the technique of the polar transformation, the pitchfork bifurcation and the degenerate pitchfork bifurcation, Hopf bifurcations, and the local stable and unstable manifold character, are all analyzed when the parameters are varied in the space of parameters. Based on the theoretic analysis and numerical simulations, the dynamics of the system are discussed subtly under all kind of the critical state. Second, the properties of the existence of homoclinic and heteroclinic orbits for the system are rigorously studied. Finally, the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters is investigated.     

Investigation of the one-dimensional motion of a snow avalanche along a flat slope

In view of the developing construction in mountainous regions where there is danger from avalanches, the problem of protection against avalanches has become timely. In the solution of this problem, various methods can be used in practice; in connection with the use of these methods, there arise a great number of engineering and mechanical problems. In particular, in the design of structures for protection against avalanches, information is needed on the parameters of moving avalanches, i.e., on velocities, heights of the front, densities of the snow, etc., that is to say, calculations of the motion of avalanches along a slope, as well as of their interaction with the structure under consideration. From a practical point of view, information on the maximal range of the throw, i.e., on the boundary of the avalanche danger zone, is also important. The present article is devoted to an analytical and numerical investigation of the one-dimensional motion of an avalanche; an asymptotic solution is obtained to the problem of the one-dimensional motion of an avalanche along a homogeneous slope.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 7–14, September–October, 1973.     

弯曲波在含非圆孔洞无限压电薄板中的散射

基于线性压电动力学理论,采用波函数展开法、保角映射以及复变函数,对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析,给出了其动弯矩集中系数(DMCF)的解析表达式.为说明问题,以PZT-4为例,讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响,并分别...