零级次弹性圆柱杆在常速度拉伸时的惯性效应

本文给出了一个零级次弹性圆柱杆在常速度拉伸时有限变形的解析解,由其解发现在不同拉伸速度下应力-应变曲线的不同,完全是由于惯性力而引起,它使轴向应力几乎是随着拉伸速度比值的平方而增加。     

Limit angular velocities of variable thickness rotating disks

Elastic and plastic limit angular velocities are calculated for rotating disks of variable thickness in power function form. Analytical solution is obtained and used to calculate elastic limit angular velocities of variable thickness rotating annular disks and annular disks with rigid inclusion. An efficient numerical solution procedure is designed and used to obtain the elastic limit angular velocities of variable thickness rotating solid disks. Von Mises yield criterion and its flow rule is used to estimate plastic limit angular velocities. Both linear and nonlinear hardening material behaviors are treated numerically. The results are verified by comparing with those of uniform thickness rotating solid disks available in the literature. Elastic and plastic limit angular velocities are found to increase with the reduction of the disk thickness at the edge as well as the reduction in the disk mass due to the shape of the profile.     

Casson Fluid Flow Due to Non-Coaxial Rotation of a Porous Disk and the Fluid at Infinity Through a Porous Medium

The flow of the Casson fluid due to non-coaxial rotation of a disk and the fluid at infinity is investigated. Partial differential equations are made dimensionless and coupled. The exact solution of the resultant nonlinear initial-boundary-value problem is solved by applying the Laplace transform. The shear stresses at the disk surface and the steady state stresses are computed. The effects of dimensionless parameters on the dimensionless primary and secondary velocities are analyzed.     

Radiation emitted by a constant load moving uniformly in a circle on an elastically supported membrane

Wave radiation is studied which is due a constant load moving with a constant speed along a circular path over an unbounded membrane on a elastic foundation. The steady-state solution of the problem is obtained, showing that the radiation occurs for all load velocities. It is shown that the elastic field radiated by the supercritically moving load is confined in a spiral-like apex. The membrane displacements at the boundaries of this apex are discontinuous. The radiated energy per period of load rotation is calculated showing a discrete energy spectrum. For increasing load velocities, the total amount of radiated energy becomes larger. It also turns out that the major part of the radiated energy follows the direction of the load motion.     

Stress fields and Eshelby forces on half-plane inhomogeneities with eigenstrains and strip inclusions meeting a free surface

The stress field due to a half-plane inhomogeneity with plane eigenstrain is obtained by a limiting procedure from the one of a circular Eshelby inhomogeneity/inclusion. This field, which requires tractions to be applied at infinity to be sustained, has minimum strain energy versus any other superposed homogeneous one, and is the Eshelby solution inside plus the Hill jump conditions. By superposition, the stresses due to an infinite strip (Eshelby property domain) inhomogeneity with eigenstrain are obtained, and, by superposition periodic strips or laminates can be obtained. By cancelling the stresses on a free-surface, strips of inclusions meeting a free surface are solved. They exhibit tensile stresses under the free surface, and logarithmic singularities in the tensile stress at the vertex, which may initiate cracking. The Eshelby self-forces on the boundary of circular and half-plane inhomogeneities are computed.     

横观各向同性油气藏水力压裂裂纹扩展规律研究

针对横观各向同性与各向同性油气藏水力压裂裂纹扩展的差异性,基于扩展有限元法建立水力压裂力学模型,通过ABAQUS子程序开发了各向同性和横观各向同性岩体的起裂判据。在各向同性岩体数值模拟结果与解析解以及现场压裂典型曲线对比吻合的基础上,得到了包含层理构造的横观各向同性岩体水力压裂过程中裂纹扩展规律。层理类岩体水力压裂的裂缝扩展方向由地应力状态、层理方向以及岩体与层理界面抗拉强度共同决定;水力压裂过程中,注水压力在裂纹尖端产生应力集中,层理面法向分量先达到界面抗拉强度时,裂纹沿层理方向开裂,反之裂纹沿垂直最小地应力的方向扩展;裂纹扩展速度随层理抗拉强度的增加而降低;由于地层的滤失,随压裂液的注入,裂纹长宽尺度增长速率降低。     

炸药参数对高锰钢爆炸硬化性能的影响

为了研究炸药参数对高锰钢爆炸硬化效果的影响,对两种不同密度的炸药进行爆速测试,并利用该炸药分别对高锰钢试样进行爆炸硬化实验,测试了从硬化表面向材料内部的硬度、抗拉强度和冲击韧性随深度的变化。测试结果表明:高锰钢试样在相同深度下,经过密度1.38 g/cm3炸药3次爆炸硬化得到的硬度大于密度1.48 g/cm3炸药2次爆炸硬化后的硬度,而冲击韧性小于密度1.48 g/cm3炸药作用后的冲击韧性;从爆炸硬化表面向下15 mm内,经过密度1.38 g/cm3炸药3次爆炸硬化得到的抗拉强度大于密度1.48 g/cm3炸药2次爆炸硬化后的抗拉强度,但深度大于15 mm时,经过密度1.38 g/cm3炸药3次爆炸硬化得到的抗拉强度小于密度1.48 g/cm3炸药2次爆炸硬化后的抗拉强度。从硬化后试件的硬度、抗拉强度以及冲击韧性这3方面考虑,使用单次爆炸冲量较小的炸药进行多次爆炸硬化效果较好。     

Laminar flow through a channel with uniformly porous walls of different permeability

Summary The steady laminar flow of a viscous incompressible fluid through a two-dimensional channel, having fluid sucked or injected with different velocities through its uniformly porous parallel walls is considered. A solution for small suction Reynolds number has been given by the authors in a previous paper. The purpose of this paper is to present a solution valid for large Reynolds numbers for the cases of (i) suction at both walls, and (ii) suction at one wall and injection at the other. A technique of matching outer and inner expansions is used to obtain an asymptotic solution for both of these cases. Further a perturbation solution for the case of suction at one wall and injection at the other is obtained by choosing the difference between two wall velocities as the perturbation parameter. Both asymptotic and perturbation solutions are confirmed by exact numerical solutions. As expected, the resulting solutions show the presence of the usual suction boundary layers in both types of flow considered in this paper.     

丙烯酸盐喷膜防水材料在酸碱浸润和冻融循环条件下的耐久性试验分析

丙烯酸盐喷膜防水材料在酸碱溶液浸润和冻融条件下的耐久性能是该类材料在工程应用中较难回避的实际问题,论文采用酸性介质(0.2%的H2SO4溶液)和碱性介质(0.1%NaOH+饱和Ca(OH)2溶液)对该材料进行饱和浸泡并进行冻融循环后,研究了该材料的吸水性、断裂拉伸强度和拉断伸长率的变化规律。试验结果表明:喷膜防水材料在侵蚀-冻融循环作用下,其拉断伸长率和断裂拉伸强度显著降低,且酸性介质对材料拉伸性能的影响较大;材料耐低温冰冻能力较强,耐高温能力较差。反映出丙烯酸盐喷膜防水材料在低温冰冻和碱性介质中耐久性较好,不建议在高温和酸性介质条件下使用。     

Investigation of high elastoplastic straining of shells of revolution under complex tensile and torque loading

A method of the numerical solution of nonlinear unsteady problems of axisymmetric elastoplastic straining of shells of revolution with allowance for torque loading at high strains is proposed. The method is based on the geometrically nonlinear theory of the Timoshenko shells and the plasticity theory with due allowance for combined isotropic and kinematic hardening. The problem is solved with the use of the variational difference method. Results of numerical and experimental investigations of elastoplastic straining of cylindrical shells under proportional and sequential kinematic tensile and torque loading are reported.     

三类锚杆受拉作用解析解的统一表达式

利用点荷载作用于半无限空间的Mindlin位移解,根据位移协调条件得出内锚式锚杆受拉作用的解析解,然后推导出全长粘结锚杆、压力型锚杆的解析解,建立了这3类锚杆受拉作用解析解的统一表达式.利用所求得的解析解,研究了锚杆类型、土体弹性模量、锚杆孔径对锚杆应力分布的影响.结果表明:(1)3类锚杆的剪应力都是单峰值的曲线;(2)土体弹性模量增大,则锚杆剪应力峰值增大,但分布范围减小;(3)锚杆孔径增大,则锚杆剪应力峰值减小,但对其分布范围几乎没有影响.     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

Ultrasonic Measurements of Residual Stresses Caused by Severe Thermomechanical Deformation during FSW

In engineering processes, residual stresses can be intense once high plastic deformation and temperature gradient are involved. This is exactly the case for friction stir welding (FSW) in which both rotational and translational movements of the tool induce extreme temperature gradient and plastic deformation. In this research, the extents of longitudinal and transverse residual stresses are measured within the AA7075-T6 plates welded through FSW process using ultrasonic method. According to the obtained results, it can be found that the residual stress is of the tensile type adjacent to the welding line whereas it is of the compressive type far from the welding line. Another observation is that the longitudinal residual stresses are considerably greater than the transverse residual stresses. Furthermore, with the aim of investigating the effects of rotation and traverse velocities of the tool on residual stress, experiments are carried out at three different rotation and traverse velocities. Based on the acquired results, it is observed that upon increasing the rotation and traverse velocities, the longitudinal and transverse residual stresses decrease and increase, respectively.     

Unsteady layered vortical fluid flows

An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette flow. Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered. These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed. It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary.     

Random vibrations of a rotating shaft with non-linear damping

Bending vibrations of a rotating shaft due to external random excitation are considered for the case of potential instability of the shaft's linear model due to the presence of internal or “rotating” damping. A two-degree-of-freedom model is studied which accounts for non-linearity in external or “non-rotating” damping. An explicit expression is obtained for a stationary joint probability density of displacements and velocities as an exact analytical solution to the corresponding Fokker-Planck-Kolmogorov equation. The results are used to develop criterion for on-line detection of instability for the operating shaft from its measured response.     

Stress distributions from interference fits and uniaxial tension

Machine assemblies can be prestressed (1) to eliminate stress gradients and (2) to increase fatigue life. Where prestressing is used to reduce stress gradients, the geometry is usually simple and good mathematical models are available for design purposes. The instances where fatigue life is the prime consideration are difficult to analyze because of asymmetry and variable boundary conditions. However, the interference prestress can be determined from an approximate model. The approximate solution indicates that the normal stress at the interface of a bolt-hole assembly varies almost linearly with diametral interference. When a tensile field is added to an interference prestress, even approximate techniques falter. Quantitative agreement with strain-gage data can be made at a point and for the initial loading cycle only. After several cycles, the experimental value of cycle-stress variation at the interface approximates the average applied tensile stress. The calculated value is twice as great. Stresses due to interference fits can be predicted, and prestressed bolted joints designed with greater confidence.     

Transient free convection flow of a viscoelastic fluid over vertical surface

In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The gov-erning equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a compari-sion. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.     

Dynamics of taut strings traveled by train of forces

This paper analyzes the dynamical response of taut strings crossed by systems of traveling forces at constant velocity. Starting from the classic solution for the single moving load, the effect of trains of forces having a step equal to the string length is dealt with. The response is formulated in terms of a linear map, whose reiteration furnishes the discrete-time response, and enables the investigation of the asymptotic behavior of the system. The analytical solution highlights the presence of many critical velocities, for which an instability phenomenon by response accretion may occur. The presence of damping inhibits the onset of instability but also allows to attain large displacements, especially in correspondence of the first critical velocities of the undamped string. Finite-difference numerical solutions confirm the full validity of the proposed analytical solutions. A simple procedure to deduce an improved solution for the problem of the single moving force is outlined in the Appendix.     

Finite Element Analysis of Dynamically Loaded Homogeneous Viscous Beams

The paper is concerned with impulsively loaded beams in which the material is treated as homogeneous viscous as an approximation of a rigid-viscoplastic constitutive relation. As opposed to the standard displacement method finite element formulation, where interpolation functions describing the velocity field across elements is given, a mixed formulation is used in which nodal velocities and nodal moments are carried as parameters. At each instant the accelerations (by the Tamuzh principle) and the rates of change of moment (by a virtual velocities formulation) are found, and velocities and moments are integrated forward independently. The properties of the mode solution are also introduced, and the forward integration is carried through only for the difference between the mode solution and the actual solution. This leads to a very efficient scheme for the numerical solution of a cantilever beam problem shown as an illustration.     

Numerical modeling of the free rise of an air bubble

The results of a numerical investigation of the dynamics of a single air bubble rising in water are presented. The bubbles, 1, 2.5, 3, 5, 8, and 10 mm in diameter, are considered. An analysis is based on the numerical solution of the complete three-dimensional system of Navier–Stokes equations for a two-phase medium using an implicit approach with the automatic tracking of the gas-water interface by means of separating the volume fractions. Emphasis is placed on an examination of the local physical characteristics of the motion. The calculated mean rise velocities are compared with experimental data. The rising bubble trajectories are shown to be periodic, zigzag or helical in shape, which is due to the variation in their form and the generation of a characteristic turbulent wake behind them. The bubble rise velocities are correlated with the forces acting on the bubbles.