冲击载荷下两裂纹间的连通规律

脆性材料内部含有大量裂纹,当某一裂纹扩展时,其他裂纹会对扩展裂纹产生影响。为了研究冲击载荷下,脆性材料内两裂纹的相互影响、连通规律及裂纹尖端应力强度因子的变化规律,利用有机玻璃板制作了含非平行双裂纹的实验试件,利用落板冲击设备进行了中低速冲击实验,结合有限元分析软件ABAQUS计算出裂纹尖端应力强度因子,利用有限差分软件AUTODYN进行了动态数值模拟研究,并将其模拟结果与实验结果进行对比分析。实验及模拟结果表明：裂纹破坏形态与AUTODYN数值模拟破坏形态基本一致;试件的断裂形态随着两裂纹间距不同而不同;裂纹间的相互影响程度随着裂纹间间距增大而减小;裂纹尖端应力强度因子K_I随着裂纹间距的增大而减小,而K_II随着裂纹间距增大而增大。

     

A penny shaped crack in a transversely isotropic material under non-axisymmetric impact loads

A solution is given for problems involving non-axisymmetric dynamic impact loading of a penny shaped crack in a transversely isotropic medium. Laplace and Hankel transforms are used to reduce the equations of elasticity to integral equations, and solutions are obtained for the three modes of fracture. The stress intensity factors are determined for a penny shaped crack loaded by concentrated normal impact forces and concentrated radial shear impact forces. The integral equations are solved by numerical methods, and the results are plotted showing how the dynamic stress intensity factors are influenced by the asymmetric loading.     

冲击作用下含预制裂纹梁柱试件的动态断裂

利用焦散线实验系统,进行了冲击加载下含预制裂纹梁柱试件的断裂实验,研究了梁柱试件的梁柱节点、梁上和柱端裂纹的扩展轨迹、扩展速度和应力强度因子的变化规律。实验结果表明:受冲击后,试件首先在梁柱节点处开裂,并在裂纹扩展过程中发生明显的曲裂运动,证明梁柱节点处最容易受到破坏。预制裂纹条数越多,梁柱节点处开裂越晚,说明裂纹条数少,能量可以在裂纹尖端积聚得更集中、更快。含柱端预制裂纹的试件,2条裂纹的开裂相隔时间要长于含梁上预制裂纹的试件;同时,试件的第2条裂纹优先在梁上裂纹处开裂,说明固端支座比简支梁断裂需要更多的能量。随着预制裂纹的增多,梁上裂纹在扩展过程中的曲裂现象减弱, 由于部分能量在柱端裂纹处积聚,用于推动梁上裂纹扩展的能量相应地减少。并且由于柱端裂纹的存在,梁上裂纹受到的拉应力分量减小,导致裂纹尖端受到弯矩变小,影响了裂纹的曲裂运动。     

控制棒驱动机构步跃提升碰撞的动力学建模

控制棒驱动机构(CRDM)在步跃提升时,钩爪部件会与承压壳体上的提升磁极发生面面碰撞。本文基于混合坐标法建立控制棒驱动机构有限元离散的刚-柔耦合动力学方程,用罚函数法计算了钩爪部件与承压壳体之间的碰撞力和应力分布情况。结果表明,刚柔耦合多体方法在仿真小变形碰撞时可以提高计算效率,同时又能达到与有限元方法同等的精度。进一步对碰撞模型不同区域的网格疏密和尺寸大小做了定量分析,得到了降低有限元网格数量的方法,可为工程中碰撞模型的网格划分提供参考。     

Predicting the behaviour of structures under impact loads using geometrically distorted scaled models

When a scaled structure (model or replica) is used to predict the response of a full-size compound (prototype), the model geometric dimensions should relate to the corresponding prototype dimensions by a single scaling factor. However, owing to manufacturing technical restrictions, this condition cannot be accomplished for some of the dimensions in real structures. Accordingly, the distorted geometry will not comply with the overall geometric scaling factor, infringing the Π theorem requirements for complete dynamic similarity. In the present study, a method which takes geometrical distortions into account is introduced, leading to a model similar to the prototype. As a means to infer the performance of this method, three analytical problems of structures subjected to dynamic loads are analysed. It is shown that the replica developed applying this technique is able to accurately predict the full-size structure behaviour even when the studied models have some of their dimensions severely distorted.     

Identification of horseshoes chaos in a cable-stayed bridge subjected to randomly moving loads

In this paper, the dynamic response of cable-stayed bridge loaded by a train of moving forces with stochastic velocity is investigated. The cable-stayed bridge is modelled by Rayleigh beam with linear elastic supports. The stochastic Melnikov method is derived and the mean-square criterion is used to determine the effects of stochastic velocity and cables number on the threshold condition for the inhibition of smale horseshoes chaos in the system. The results indicate that the intensity of the random component of the loads velocity can be contributed to the enlargement of the possible chaotic domain of the system, and/or increases the chances to have a regular behavior of the system. On the other hand, the presence of cables in cable-stayed bridges system increases it degree of safety and paradoxically can be contributed to its destabilization. Numerical simulations of the governing equations are carried out to confirm the analytical prediction. The effect of loads number on the system response is also investigated.     

不同高应变率冲击荷载作用下混凝土试样的能量耗散分析

针对混凝土材料在冲击荷载作用下能量耗散和破碎程度关联性难确定的问题,采用分离式霍普金森压杆(SHPB)完成了混凝土试块冲击试验,通过对冲击后碎块的筛分试验和应力波传播过程中应变的测试,得到了试块的能量耗散规律和破碎特征。结果表明,(1) 入射应力波的加载时间约为380 μs,入射能、反射能和吸收能随冲击气压的增大而增大;同一气压下,反射能最早达到平衡; (2) 平均应变率越大,入射能和吸收能也越大;当平均应变率为300/s左右时,能量利用率为最低值; (3) 随着入射能的增加,吸收能的增长率越来越大,当入射能达到2100 J时,吸收能近乎线性增长; (4) 随冲击气压增大,试样由拉裂破坏逐渐转移为压碎破坏,且随着材料吸收能的增大,平均破碎尺寸越来越小。当吸收能大于700 J时,吸收能对试样的平均破碎尺寸减小的影响较小。     

Behavior of a three-layer cylindrical shell under the action of locaized loads

Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 10, pp. 36–40, October, 1992.     

Modelling turbulence around and inside porous media based on the second moment closure

To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier–Stokes equations, there appear three unknown covariant terms in the momentum equation. They are namely the dispersive covariance, the macro-scale and the micro-scale Reynolds stresses, in the present study. For the macro-scale Reynolds stress, the TCL (two-component-limit) second moment closure is applied whereas the eddy viscosity models are applied to the other covariant terms: the Smagorinsky model and the one-equation eddy viscosity model, respectively for the dispersive covariance and the micro-scale Reynolds stress. The presently proposed model is evaluated in square rib array flows and porous wall channel flows with reasonable accuracy though further development is required.     

Steady state and stability of a beam on a damped tensionless foundation under a moving load

In the first part of this paper we study the effect of damping on the multiple steady state deformations of an infinite beam resting on a tensionless foundation and under a point load moving with a sub-critical speed. Due to the non-linear characteristics of the problem, a guess on the deformed shape has to be made before a numerical search can be initiated. It is found that when the damping is present, all the steady state solutions are asymmetric. As the damping approaches zero, some of the steady state solutions become symmetric, while some others remain asymmetric. In the second part of the paper we propose to test the stability of these steady state deformations by a transient analysis on a long finite beam. Our numerical experiment indicates that among all these multiple steady state solutions only one of them is stable. This stable steady state deformation reduces to a symmetric solution when the damping approaches zero. Furthermore, it is found that this stable solution is also the one among all steady state solutions closest in shape to the linear solution based on a bilateral foundation model.     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

Growth of a main crack under the influence of gas moving inside it

The motion of a gas or liquid in a growing main crack is examined in connection with the problem of the hydraulic fracture of an oil-bearing bed [1, 2] and evaluation of the quantity of gaseous products escaping from the cavity formed by the underground explosion into the atmosphere by way of the crack [3]. The studies [1, 2] formulated and solved a problem on the quasisteady propagation of an axisymmetric crack in rock under the influence of an incompressible fluid pumped into the crack. An exact solution was obtained in [4] to the problem of the hydraulic fracture of an oil-bearing bed with a constant pressure along the crack. The Biot consolidation theory was used as the basis in [5] for an examination of the growth of a disk-shaped crack associated with hydraulic fracture of a porous bed saturated with fluid. A numerical solution to a similarity problem on the motion of a compressible gas ina plane crack was obtained in [6]. Here we examine the problem of the propagation of a main crack (plane and axisymmetric) under the influence of a gasmoving away from an underground cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 116–122, July–August, 1986.We thank V. M. Entova for his remarks, which helped to improve the investigation.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling solitons under the hydrostatic and Boussinesq approximations

An examination of solitary waves in 3D, time‐dependant hydrostatic and Boussinesq numerical models is presented. It is shown that waves in these models will deform and that only the acceleration term in the vertical momentum equation need be included to correct the wave propagation. Modelling of solitary waves propagating near the surface of a small to medium body of water, such as a lake, are used to illustrate the results. The results are also compared with experiments performed by other authors. Then as an improvement, an alternative numerical scheme is used which includes only the vertical acceleration term. Effects of horizontal and vertical diffusion on soliton wave structure is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

Statistics of the deformation of the front of a tunnel-crack propagating in some inhomogeneous medium

We present a statistical analysis of some geometrical features of the front of a tensile tunnel-crack propagating quasistatically, according to some Paris-type law, in some elastic solid with spatially varying Paris constant. The work is based on an earlier formula of the authors, which provides the first-order change of the distribution of the mode I stress intensity factor along the front of a tunnel-crack, arising from some small but otherwise arbitrary in-plane perturbation of this front. The quantities studied include the power spectrum and the autocorrelation function of the deviation of the two parts of the front from reference straight lines, the autocorrelation function of the derivative of this deviation in the direction of the crack front, the mean squared fluctuation of the deviation, and its correlation distance. The various measures of the magnitude of the deviation of the front from straightness are all found to increase in time at a considerable rate, which means in some sense that the “wavyness” of the front continuously grows. However, the correlation distance of the deviation also increases, which mitigates the preceding conclusion, since it means in another sense that the crack front tends to “straighten back” in time. Also, comparisons are made with the cases of a semi-infinite crack propagating quasistatically or dynamically, using some results of Rice and coworkers for the latter case. The rate of growth of the various measures of the magnitude of the deviation from straightness is much larger for the tunnel-crack than for the semi-infinite one. This is because the finite width of the tunnel-crack induces a “destabilizing” effect of the straight configuration of the front for sinusoidal perturbations with large wavelengths, which is typical of such finite crack geometries.     

Behavior of rigid-plastic polygonal plates with a rigid insert under blast loads

A method based on a perfect rigid-plastic body model is developed to analyze the dynamic behavior of hinged or clamped polygonal plates that have a perfectly rigid insert and rest on a viscoelastic foundation with supports. The plate is subject to an arbitrary blast load of high intensity uniformly distributed over the plate surface. Two cases of plate deformation are examined. In each of the cases, equations of motion are derived and realization conditions are analyzed. Analytic expressions for the deformation time and the maximum residual deflection are derived in the case of an arbitrary load of medium intensity and in the case of high-intensity load described by a rectangular function. Examples of numerical solutions are given __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 99–110, January 2008.     

某输电线路铁塔覆冰条件下的失效模式分析

建立了覆冰荷载作用下寻找输电铁塔主要失效模式的方法,该方法以覆冰厚度为控制量,可以方便地获得铁塔的主要失效模式及其相应的极限覆冰厚度。分析了南方某既有输电线路铁塔在两种工况下的主要失效模式,指出该类铁塔的薄弱处位于挂导线处、上曲臂以及塔身上部。同时指出如果存在20％不平衡纵向张力,挂导线处及上曲臂的极限覆冰厚度接近于该...