Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.The project supported by the National Natural Science Foundation of China(10272009 and 10472030) and the Natural Science Foundation of Hunan Province(02JJY2014)     

Sudden Blocking of a Supercritical Open‐Channel Flow

This paper reports results of experiments in which a steadystate nonuniform supercritical openchannel flow was suddenly blocked by a rapidly falling gate at a downstream distance of about one hundred critical depths. This results in a hydraulic jump propagating upstream. Experimental data on the shape, height, and propagation speed of its leading front are given. It is shown that the parameters of the jump differ significantly from the values found using a quasistationary approach.     

FLEXURAL WAVE PROPAGATION IN NARROW MINDLIN''''S PLATE

Appling Mindlin's theory of thick plates and Hamilton system to propagation of elastic waves under free boundary condition, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin. Based on the two kinds of theories, the dispersion curves show great difference in the region of short waves, and the cutoff frequencies are higher in Hamiltonian systems. However, the dispersion curves are almost the same in the region of long waves.     

带裂纹的椭圆孔口问题的应力分析

断裂现象与材料和结构中的孔洞、缺口或裂纹等缺陷密切相关,这是因为缺陷附近的应力集中明显.该文利用复变方法,通过保角映射研究了带裂纹的椭圆孔洞的平面弹性问题,给出了应力强度因子的解析解.并由此计算了两互相垂直的裂纹问题.     

四参数全范围da/dN曲线测定方法研究

机械结构设计的损伤容限分析,需要使用材料疲劳裂纹扩展速率曲线性能。在总结传统疲劳裂纹扩展曲线的基础上,本文讨论了四参数全范围da/dN曲线公式;基于断裂力学原理,分别给出了此公式中材料裂纹扩展门槛值ΔKth,断裂韧性K1C和张开函数f的测定方法;利用多元线性回归法对试验数据进行了曲线拟合,得到了四参数全范围da/dN曲线公式的参数估计式;将此公式运用于不同应力比下的裂纹扩展速率试验数据拟合,通过试验数据的拟合结果可以看出:四参数全范围da/dN曲线公式,能够充分有效合理地表征全范围裂纹扩展速率的物理特性和宏观数据规律,且参数估计简便,拟合精度高;从而验证了四参数全范围da/dN曲线公式的有效性和合理性,并将得到广泛应用。     

直立顺层边坡的黏弹性稳定分析

直立边坡的失稳与岩体的流变性质密切相关，其在一定载荷作用下失稳表现出延迟特性。采用自重作用下的梁柱力学模型，考虑岩石的流变性，给出了不同材料模型下直立边坡的极限坡高及其分析方法。     

V型缺口裂端的三维应力状态及约束分析

利用三维有限元方法，研究了有限厚度板中V型缺口根部穿透裂纹前沿的三维弹性应力场。对不同厚度、不同缺口张开角和裂纹长度对应力强度因子及裂尖附近的三维约束程度的影响进行了分析，同时还讨论了三维约束区的大小。研究结果显示：当缺口张开角小于60度时，不同缺口的应力强度因子和离面约束因子的分布基本一致，角度的影响不明显。应力强度因子是厚度的函数，板中面的应力强度因子随厚度的增加逐渐减小趋近干平面值，最大为1．08倍的平面值。当板厚超过15倍的缺口深度时，应力强度因子最大值将从中面转移至接近自由表面位置，距中面约0．4倍板厚。三维约束非常明显的区域在裂尖前沿约0.45倍厚度的范围内．二维到三维的过渡区在裂尖前沿1.5倍厚度的区域内；在中面上三维效应影响区最大，随着离中面距离的增加逐渐减小，在自由表面上降为0。     

混凝土破裂过程的三维数值模型

利用混合同余法产生了随机变量,将混凝土中的骨料简化为球体,采用循环比较法将随机变量赋给球心坐标(X,Y,Z),实现了混凝土骨料的空间随机分布,最终建立了三维混凝土数值模型。对模型整体进行单元剖分,将骨料、砂浆、界面层分别投影到该有限元网格中,采用多次网格划分技术完成模型网格划分。通过对算例进行有限元计算,结果表明该模型基本上反映了混凝土骨料分布的实际情况,较好地模拟了混凝土的不均匀性与各向异性,验证了建立该模型的方法是可行的。     

A DECAGONAL QUASICRYSTAL WITH AN ARC-SHAPED CRACK

A decagonal quasicrystal,which is weakened by an arc-shaped crack penetratingthrough the solid in the period direction,and which is subjected to remote uniform phonon stresses,is investigated by applying the complex variable method which is just developed by the authors.It is found that the phonon and phason stresses near the crack tips exhibit inverse square rootsingularities.The four complex stress functions characterizing the phonon and phason fields arederived.Explicit expressions for the phonon and phason stress intensity factors,crack openingdisplacements and energy release rate are also presented.     

Fixed Final Time Optimal Control via Simple Cell Mapping

A cell mapping strategy based on Bellman'sPrinciple of optimality (BP) is proposed to solve the fixed final time optimalcontrol of strongly nonlinear systems with state and control bounds. Thefixed final time problem is transformed into a fixed final time-fixed finalstate optimal control problem by reversing the time. This transformationallows to solve the problem in the framework of the BP. Backward searchingalgorithms within the cell mapping context are used to obtain the solution ofthe new problem. This approach reduces considerably the computational effortrequired for the original problem when it is solved by a forward searchingapproach. The vibration control problem of damped and undamped variablestiffness oscillators with bounded stiffness tuning range is studied todemonstrate the effectiveness of the approach. A numerical study on theconvergence of the method is also presented.