Elasticity solutions of spherically isotropic cones under concentrated loads at apex

Based on the Ref. [9], the displacement and stress distributions in a spherically isotropic cone subjected to concentrated loads at apex are studied. The displacement and stresses are given explicily for the cone in compression torsion and bending cases, respectively, based on the situation of the concentrated forces and moments. Finally, the hollow cone problems are discussed. Project supported by National Natural Science Foundation of China     

磁电弹性圆锥顶端作用集中荷载的解析解

当磁电弹性材料特征根互异时，用5个势函数表示的通解出发，对圆锥顶端作用集中扭矩Mx的扭转、集中力Px和点电荷Q的压缩、集中力Px和集中力矩My的弯曲变形问题，用一些调和函数的线性组合分别构造了势函数，并根据边界条件求出了势函数中的待定系数从而确定势函数，再将势函数代入通解得到磁电弹性圆锥顶端作用集中载荷时的位移、电势、磁势、应力、电位移和磁感应强度的三维解析解。此解形式简单便于应用。当圆锥角2α=π时，可退化得到半空间问题的解。     

The general solution of spherically isotropic magnetoelectroelastic media and its applications

A general solution of the three-dimensional equilibrium problem of spherically isotropic magnetoelectroelastic media is presented. Base on the obtained general solution, exact and compact form solutions are obtained for (1) a spherically isotropic magnetoelectroelastic cone subjected to concentrated force, concentrated couple, a point charge and a point electric current at its apex; (2) a spherically isotropic magnetoelectroelastic space with a concentrated force at the origin; (3) a spherical shell under spherically symmetric deformation; and (4) stress concentration around a spherical cavity subjected to remote uniform tensile force, electric charge and electric current.     

集中力拉伸作用下的不可压缩橡胶类锥体

分析了受集中力拉伸作用下不可压缩橡胶类锥体尖端附近的应力分布及形变行为。给出了锥体尖端应力场的渐近解，当锥角为１８０°时，即为非线性的Ｂｏｕｓｓｉｎｅｓｑ问题的解。     

Analysis of a rubber cone tensioned by a concentrated force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180°, the solution becomes that of non-linear Boussinesq's problem for tension case.     

土体触探静力加载试验的FLAC模拟模型选择

本文将触探静力加载试验作为轴对称问题处理,建立了两种不同FLAC轴对称模型,等荷载模型和等位移模型。研究表明,两种模型的FLAC模拟结果基本一致,一般条件下,应用简化的、运算速度快的等荷载模型可以满足试验要求。     

Elasticity solutions for a piezoelectric cone under concentrated loads at its apex

IntroductionTheproblemofaconesubjectedtoconcentratedloadsatitsapexisaclassicalprobleminthetheoryofelasticity.AnumberofscholarshavestUdiedtheproblem.LovereportedthesolutionstotheproblemofanisotropicconeunderconcentfatCdforcesatitsapex['].Lur'estudiedthisclassofproblemssystematicallybymeansofPapkovich-Neubergeneralsolution[2].LekniskiiandHu,byusingtheirrespectivegeneralsolutions,studiedcompressionandbendingproblemsofatransverselyisotropicconesubjectedtoaxialconcentfatedforcesandtfansverseconc…     

Second mode unstable disturbance measurement of hypersonic boundary layer on cone by wavelet transform

Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel.Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance.Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space.The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbanceThe generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique.The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space.Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition.It is demonstrated that,at hypersonic speeds,the dominant flow instability is the second mode,which governs the course of laminar-turbulent transition of sharp cone boundary layer.     

圆柱、圆锥和圆台的平衡裕度分析

提出了平衡裕度的新概念,并给出了保守力场中物体或系统静力平衡裕度的定义。以此为基础,分析计算了圆柱、圆台和圆锥体的静平衡裕度,并讨论了各几何参数的变化对平衡裕度的影响。文中提出了对静力平衡系统平衡状态差别的定量评价问题,并给出了利用平衡裕度对系统平衡状况进行定量分析的方法。文中提出的研究思路是一种新的系统安全评价方法,对其它系统的研究也有借鉴意义,研究结果对工程安全设计也有启发。     

板锥网壳结构的连续化分析

板锥网壳结构是一种受力性能合理，技术经济效益良好的新型空间结构形式。本文将板锥网壳结构连续化为能共同作用的特殊形式的三层薄壳，按薄壳理论建立其位移法和混合法的基本微分方程。通过对微分方程的求解，计算其整体位移及结构内力。该法具有一定的精度，可宏观地了解结构的力学性能，并可用于板锥网壳结构的初步设计。     

Effect of nonhomogenous material properties on transverse vibrations of elastic cantilevers

In this paper, the method of the influence functions and the method of partial discretization are proposed to solve the boundary-value problem of free transverse vibrations of a nonhomogenous cantilever with a concentrated mass attached to the free end. In order to demonstrate the possibilities of the methods, the case of a cantilever in the form of a sharp cone, a frustum of a cone, and a linear wedge made of two different materials is treated in detail. The general characteristic equations which allow one to take into consideration the nonhomogeneous material properties and the cross-sectional geometry of cantilever are introduced. The expressions for the first three terms of the characteristic series are obtained in closed form using the method of Cauchy influence functions. The results of calculations of the first two frequencies of free transverse vibrations are presented for selected material combinations and various cantilever geometries. There is very good agreement between the numerical results obtained using the method of partial discretization and the analytical results obtained using the method of influence functions. The high accuracy of the proposed methods and agreement with known theoretical data and with the experimental results obtained by the authors in the homogeneous cantilever case are shown. Presented at the International Conference on the Theory of Machines and Mechanisms, Poland, 1996. Published in Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 103–110, June, 1999.     

静电雾化锥射流模式下液锥形态的研究

本文分析了静电雾化锥射流模式下液锥表面静电应力、表面张力应力分布特性,基于应力平衡建立了液锥力学模型,并对流量、荷电电压及针形喷嘴的内半径等参数对液锥结构形态的影响进行了预测。首先设计了针形喷嘴静电雾化实验装置,应用高速摄影技术观测了静电雾化的典型雾化模式和液锥形态演化特性。实验结果表明:锥射流雾化模式仅在一定的荷电电压范围内才会出现;针形喷嘴的流量增加,液锥锥角减小,液锥长度增长;随着荷电电压或针形喷嘴内半径的增加,液锥锥角增大,液锥长度缩短。实验结果与液锥力学模型的预测结果一致。     

弹性层内部有集中力的精确解

利用Ｈａｎｋｅｌ变换及矩阵理论，获得了位于水平刚性基础上的弹性层在其内部受垂直于边界的集中力作用了的精确率，推广了已有的结论。Ｋｅｌｖｉｎ解，Ｍｉｎｄｌｉｎ解及弹性层表面受集中的用的解都是其特殊情形下的结论。     

Direct Numerical Simulation of Hypersonic Boundary-Layer Flow on a Flared Cone

The forced transition of the boundary layer on an axisymmetric flared cone in Mach 6 flow is simulated by the method of spatial direct numerical simulation (DNS). The full effects of the flared afterbody are incorporated into the governing equations and boundary conditions; these effects include nonzero streamwise surface curvature, adverse streamwise pressure gradient, and decreasing boundary-layer edge Mach number. Transition is precipitated by periodic forcing at the computational inflow boundary with perturbations derived from parabolized stability equation (PSE) methodology and based, in part, on frequency spectra available from physical experiments. Significant qualitative differences are shown to exist between the present results and those obtained previously for a cone without afterbody flare. In both cases, the primary instability is of second-mode type; however, frequencies are much higher for the flared cone because of the decrease in boundary-layer thickness in the flared region. Moreover, Goertler modes, which are linearly stable for the straight cone, are unstable in regions of concave body flare. Reynolds stresses, which peak near the critical layer for the straight cone, exhibit peaks close to the wall for the flared cone. The cumulative effect appears to be that transition onset is shifted upstream for the flared cone. However, the length of the transition zone may possibly be greater because of the seemingly more gradual nature of the transition process on the flared cone. Received 20 March 1997 and accepted 21 May 1997     

Shock tensors and shock polars

A refraction law for the velocity at an oblique shock in a compressible fluid is derived in dyadic form similar to that for refraction of light rays at an interface. The shock tensor embodies only the assumptions of conservation of mass and equality of tangential velocity components. Given the shock inclination and density ratio, a quadratic equation in the ratio of the flow speeds can be found with flow turning angle as a parameter. Analysis of the two solutions shows that they lie on a circle in the polar plane, a result independent of the equation of state or other conservation laws. If the density ratio is allowed to vary, a pencil of circles is generated in the hodograph plane ; or, equivalently a right, elliptic cone with two nappes appears in the three-space formed when the density ratio coordinate is added at right angles to the hodograph plane. The further requirements that momentum and energy be conserved taken together with weak restrictions on the functional form of the equation of state are sufficient to permit the development of a general theory of shock polars. The allowed shock states are seen to lie on the space curve formed by intersection of a surface called the Hugoniot cylinder with the elliptic cone. The projection of this space curve on the hodograph plane is the shock polar. The theory is applied to the special case of a polytropic gas by way of illustration.     

细长体背风面横向非对称分离的研究

用数值模拟方法研究了超声速情况下，无限长细长体背风面的涡结构。数值模拟的出发方程和计算格式分别为全Ｎ－Ｓ方程和二阶空间精度的ＴＶＤ格式。数值结果给出了圆锥、半球柱体和椭圆锥在不同攻角下的流场结果。结果表明圆锥在攻角α＝１５°，２０°和２５°时背风面呈现明显的稳定非对称横向分离，而半球柱体和椭圆锥在３２．５°和２５°时背风面均未出现非对称的横向分离结构。     

静力触探锥头阻力的近似理论与实验研究进展

锥头阻力在静力触探试验中扮演着十分重要的角色.从不同角度,对触探中锥头阻力的研究进行简要阐述,对承载力理论、空洞膨胀理论、应变路径法及运动点位错法等几种理论分析方法进行了回顾.另外,对数值分析和实验研究的进展情况进行了叙述.并对各种方法的适用性进行了比较.承载力理论虽然简单,但忽略了土的压缩性和探杆周围初始应力的增加,所以不能精确地模拟锥头的深层贯入.空洞膨胀理论提供了一个分析锥头阻力的简单而较精确的方法,它考虑了土的压缩性(或膨胀性)和锥头贯入过程中锥杆周围应力增加的影响.但这种方法是将锥头贯入与空洞膨胀之间做了一个等效模拟,所以不同的模拟方法,得到的结果差别较大.应变路径法能够有效解决饱和粘土中的不排水贯入,但不适用于砂土.运动点位错法因为考虑了部分排水,所以能较好地预测固结系数,但采用了线弹性分析,故位错法在其他方面的应用还需要大量的试验验证.有限元法在处理锥头贯入这类慢侵彻问题时缺乏一种很好的处理技术,导致它在进行破坏荷载计算时有显著的误差和数值计算困难.标定槽试验将在验证和建立锥头阻力与土的性能关系方面继续起到一个重要作用,但其结果需经过校正后才可应用到现场.最后对该领域的研究趋势进行了讨论.      

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

The fundamental solution for the axi-symmetrictranslational motion of a microstretch fluid due to a concentrated point body force is obtained.A general formula for thedrag force exerted by the fluid on an axi-symmetric rigid particle translating in it is then deduced.As an application to theobtained drag formula,this paper has discussed the problemof creeping translational motion of a rigid sphere in a microstretch fluid.The slip boundary condition on the surfaceof the spherical particle is applied.The drag force and theother physical quantities are obtained and represented graphically for various values of the micropolarity and slip parameters.     

高超声速再入体表面热流计算

运用非结构网格计算外部无粘流场,并结合边界层内粘性主导区域的工程算法,计算高超声速飞行器的气动加热。通过求解三维Euler方程确定复杂外形飞行器的边界层外缘参数,在理论与经验公式的基础上,利用局部相似性解的方法计算了钝锥和钝双锥外形有攻角再入的表面热流,并与国内外文献的NS方程数值计算结果和风洞试验结果进行了对比,三者的结果吻合较好。     

水位变化对正倒锥体冰载荷影响的离散元分析

在海冰与锥体海洋结构的相互作用过程中,潮汐水位变化时海冰作用于锥体结构的位置改变对冰载荷具有显著影响.本文采用具有粘结破碎功能的离散元方法计算海冰与锥体作用的破坏过程.同时考虑海冰上下表面温度差异对海冰强度的影响,将离散元计算冰载荷及海冰破坏模式与渤海现场实测数据进行对比验证.离散元结果表明,海冰与正锥和倒锥碰撞时均发生弯曲破坏,且冰载荷均随水线处锥径的增大而增大.在水线处锥径相同的情况下,正锥冰载荷大于倒锥冰载荷,而正锥作用下海冰的断裂长度则较小.基于离散元计算结果和渤海现场观测资料分析了海冰与正锥、倒锥作用时冰载荷和断裂长度差异的主要原因.海冰与正倒锥交界线处作用时,一般发生弯曲破坏.当冰层中心高度与正倒锥交界线的高度相同时,海冰才会发生局部挤压破碎,但冰荷载并没有明显升高.由此可见,倒锥体结构可有效降低冰载荷从而具有较好的抗冰性能.以上研究表明离散元方法可确定海冰与锥体结构作用时的海冰破碎规律和冰载荷特性,为海洋工程结构的抗冰设计提供参考依据.