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.     

Capture of small drops by large drops in an electric field

In the investigation of the process of the breakdown of emulsions by the coalescence of drops, up to the present time, use has been made of the theory of the coagulation of colloids (for example, [1]). However, there is a considerable difference between colloids and emulsions. Forces of attraction, bringing about the coalescence of two colloidal particles, become predominant at distances much greater than the particle size, so that, in a hydrodynamic sense, it can be assumed that colloidal particles do not interact. On the contrary, the disperse phase in emulsions consists of molecularly smooth spherical drops with a size from a few tenths of a micron or more and, with approach of the drops, forces of hydrodynamic interaction, inhibiting coalescence, become substantial. As a rule, the drops can be regarded as rigid undeformed spheres since their surface is stabilized by surface-active substances. With the approach of such spheres, the layer of liquid between them generates a braking force proportional to the rate of approach of the drops and inversely proportional to the distance between their surfaces. As a result, the approach of drops under the action of a finite force takes place over an infinite time. It follows from this that the process of the coalescence of drops requires the presence of a force of attraction, rising to infinity with approach of the drops, and any theory of coalescence must take simultaneous account of the forces of attraction of the drops and of the hydrodynamic forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–68, September–October, 1973.     

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.     

Lie symmetries,symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems

For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries, symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general infinitesimal transformation of Lie groups. Based on the invariance of the equations of motion for the system under general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations, and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations, constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained, and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of non-Noether exact invariants and adiabatic invariants are given in the special infinitesimal transformations. Finally, one example is given to illustrate the application of the method and results.     

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, 它们在高超声速喷管设计中曾经发挥了重要作用, 包括理论方法, 近似方法和基于两者的修正方法. 然后, 考虑高温气体效应, 分析了高焓喷管设计时面临的困难与问题, 从流动介质物性变化、高温边界层发展和非平衡过程效应三方面, 综述了国内外在高超声速高焓喷管设计方面的研究进展. 最后, 对于高焓喷管的设计理论和方法的发展作了展望, 期望对于推动我国高超声速高焓喷管设计技术的发展提供一些有意义的启示.      

反倾层状岩质边坡失稳的断裂力学分析

反倾层状岩质边坡的高危地质灾害承载体在自然界中普遍存在,为研究其失稳破坏机制,将反倾边坡岩层简化为一个带裂缝的悬臂梁,建立了由一组结构面控制边坡稳定性的断裂力学模型,推导了各岩层结构面等效应力强度因子和岩层及边坡稳定性判据。分析了岩层倾角、层厚、结构面长度、内摩擦角和粘聚力5个因素对边坡的稳定性影响。结果表明,随着岩层倾角和结构面长度的增加,边坡不稳定区域增加,坡脚处的抗滑稳定性减小;随着内摩擦角和粘聚力的增大,边坡不稳定区域减小,坡脚处的抗滑稳定性增大;随着岩层厚度的增大,不稳定岩层的范围基本保持不变,但是岩层的抗滑稳定区域随着厚度增加逐渐向坡脚移动,厚度越大,坡脚处的抗滑稳定性越大。实例分析验证了本文理论的合理与可行性,研究结论对工程实践具有一定指导意义。     

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。     

Local structure of a binary finely dispersed fluidized bed

Results are given of calculations of the quantities characterizing the random pseudoturbulent motions of the phases in a homogeneous fluidized bed consisting of particles of two sorts, differing in size. The dependence of the coefficients of pseudoturbulent diffusion of the particles, the mean-square velocities of the pulsations, etc., on the partial concentrations of the particles, the ratio of their sizes, and other parameters is evaluated. For granular beds, fluidized by a gas or a drop-type liquid, intense chaotic fluctuations of both phases are characteristic; these determine to a considerable degree the observed macroscopic properties of the bed and affect its effectiveness as a working body in various types of heat exchangers and chemical reactors. Such random (pseudoturbulent) motions are particularly considerable for beds of small particles under homogeneous fluidization conditions, where mixing due to the rise of cavities in the bed, filled only with the fluidizing medium, is practically absent. A similar situation is encountered in reactor and regenerating units for catalytic cracking [1, 2], in beds with a drop-type liquid phase, in rarefied two-phase systems under the conditions of strong fluidization or of the transport of bulk materials in a dilute phase, etc. The characteristics of pseudoturbulence in locally homogeneous flows of monodisperse two-phase systems have been investigated, for example, in [3–5]. However, real fluidized beds are generally polydis-perse; the presence of particles of different sizes in the bed has a very considerable effect, on the intensity of the pulsations, the effective diffusion coefficients of the phases of the bed, the effective viscosities, etc. [1, 6]. In addition, the chaotic mixing in polydisperse beds determines some of the technological characteristics, specifically, the rate of entrainment of small particles by the flow of the fluidizing medium and the settling of large particles, the degree of separation of the fractions of the disperse phase, which is very important in determination of the limits of the existence of the fluidized state, and in the modeling of numerous processes of the separation of particles with respect to size or density [1, 6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 118–126. March–April, 1976.     

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.      

数值模拟油井射孔器作用过程方法研究及应用

提高射孔器性能是射孔弹厂家面临的和油田用户关心的主要问题。油井聚能射孔器的作用过程涉及爆轰波的形成、传播、爆轰波与其他介质的相互作用等爆轰问题,射流的形成、延展等界面碰撞问题,射流对靶的侵彻、靶的成坑和动态响应等侵彻问题,作用过程复杂。为了研究油井聚能射孔器的作用过程和机理,降低设计成本,缩短研制周期,本文介绍了模拟石油射孔器从炸药起爆,射流形成,射流侵彻钢靶、井液、混凝土靶的整个作用过程的欧拉数值方法,包括数学模型、离散方法、相应的本构模型,以及为节省计算机时采用的计算和理论分析耦合的模拟方法,并将数值模拟结果与实验进行了比较。研究结果表明,数值模拟结果与实验结果符合的较好,说明方法是有效的和可行的。     

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     

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.