三维压电介质界面裂纹的边界积分-微分方程

基于三维两相横观各向同性压电介质的基本解和压电介质的Somigliana恒等式，利用发散积分的有限部理论，建立以裂纹面上的不连续位移和不连续电势为基本未知量的三维压电介质界面裂纹问题的超奇异积分－微分方程组，其中的积分核具有O（1/r^2）阶的奇异性。当两相材料退化为均质材料或单相材料时，方程组中的微分项的系数为零，从而积分－微分方程组退化为已有的均质压电材料的超奇异边界积分方程。     

计算平面Ⅰ、Ⅱ型复合应力强度因子的半权函数法

给出计算一般平面裂纹问题应力强度因子的半权函数方法。该方法引入两个满足裂纹面零应力条件、平衡方程以及裂尖位移具有r^-1/2奇异性的虚拟位移与应力函数的解析表达式，即半权函数。从功能互等定理出发，结合从裂纹下缘到上缘绕裂尖任意路径的位移与应力的近似值，得到Ⅰ、Ⅱ复合型应力强度因子KⅠ和KⅡ积分形式的表达式。由于在积分中避开了裂尖的奇异性，因此即使采用较粗糙的模型或方法得到的近似值，也可以得到精度较高的KⅠ、KⅡ。相对于权函数法，本方法的限制条件较少，半权函数易于获得，实用性强；相对于有限元法计算量小，模型建立简便。     

计算Reissner理论各向异性板应力强度因子的半权函数法

由功能互等定理导出用半权函数表示的各向异性板应力强度因子的解析表达式，并给出基于Reissner板理论含裂纹的各向异性板受弯曲、扭转和剪切作用的半权函数。计算含中心裂纹四边自由受纯弯曲作用板的应力强度因子，并与有关的结果进行比较，表明此方法简便、可靠。     

任意复杂多回路平面机构及操作手奇异分析的模块法

提出了求解任意复杂多回路平面连杆机构及操作手奇异位置分析的模块法。即一个复杂机械可看作是由输入一个或多个零自由度的基本运动键组成,对这些数量有限的基本运动链进行奇异分析,然后将灾看作是复杂机构和操作手奇异分析的基本模块;仅当一个基于运动键达到奇异位置时,复杂机构即处于奇异位置。还得到了任意复杂多回咱平面机构产生奇异位置的奇异性条件总数的计算公式。因此,该方法可求解所有复杂的多回路平面机构及操作手的     

6-PUS并联机器人的奇异性分析

本文对6-PUS并联机器人的奇异位形进行了分析。在运动学分析的基础上得出了该类并联机器人的运动学方程。将并联机器人的奇异条件表示为矢量的混合积形式,然后根据矢量混合积与并联机器人腿在空间的几何关系,给出了6-PUS并联机器人几种出现奇异位形的腿的几何条件。     

Elastodynamic response of a crack perpendicular to the graded interfacial zone in bonded dissimilar materials under antiplane shear impact

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of antiplane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.     

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only-0.621％;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is-11.29％.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05％.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.     

Solution of analytical-variational method on bi-material interface crack and its comparison with experiment

An analytical method is developed to describe the fields of stress and displacement in a bi material strip with an edge interfacial crack. All of the basic governing equations, boundary conditions on crack surfaces, and conditions of continuity along the interface are satisfied by the eigen-function expansion method. The other boundary conditions will be satisfied by the generalized variational principle. Good convergence of generalized stress intensity factors is obtained, and the values of crack opening displacement and energy release rate obtained by this method are close to the experimental results. Some problems regarding oscillatory singularity, contact zone and energy release rate are discussed. Finally, the effects of modulus, thickness and crack length to mode mixity are presented.     

平面刚性夹杂问题的边界积分方程方法

研究了含刚性夹杂的平面弹性力学问题。由Ｓｏｍｉｇｌｉａｎａ公式出发，将问题归结为一组混合型边界积分方程的求解。其中外侧边界仍为常规的边界积分方程，而夹杂线上则是典型的Ｃａｕｃｈｙ型奇异积分方程，结合使用边界元及奇异积分方程算法［１］．本文对若干具有工程意义的例子作了数值计算，得到了其应力强度因子；有关结果还与文［２］作了比较，从而证明本文方法是完全可靠的，它可进一步用于解决更一般的问题。     

基于自适应LMS的导波雷达液位计回波识别与校正

非平稳及多奇异点的雷达回波信号包含虚假回波,影响液位回波信号的识别与液位测量.为解决雷达液位计的虚假回波干扰问题,提高液位识别与测量精度,提出一种回波识别与校正方法.将短时幅度函数与短时过零率函数结合,利用函数逐帧地对回波信号计算,识别液位回波信号;通过自适应最小均方误差进行系统的权矢量迭代,更新权系数,对回波信号进行处理,进行抑制虚假回波干扰.实验结果表明:该方法能够准确识别液位回波信号;液位测量精度可达到0.42％F.S,相比于其他去噪方法,该方法在抑制噪声的同时能较好地保留信号奇异性特征,有较好的鲁棒性.     

All planar parallel manipulators with cylindrical singularity surface

In this article we give the complete list of all non-architecturally singular parallel manipulators of Stewart Gough type with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations. The presented list has only two entries containing the necessary and sufficient geometric conditions of the corresponding manipulator designs possessing such a singularity surface. These manipulators have the advantage that their singularity set can easily be visualized as curve by choosing p as projection direction. Moreover the computation of singularity free zones reduces to a 5-dimensional task. We close the paper by formulating a conjecture for the non-planar case.     

弹性半空间中平片裂纹问题的超奇异积分方程方法

使用边界积分方程方法,在有限部积分的意义下,将弹性半空间中垂于自边界面的平片裂纹归结为一组以裂纹面位移间数为示知函数的超奇异积仞氖限部积分蜞 建立了数值人出了用裂纹面位移间尖力强度因子的公式。通过对圆形、菜和矩形等贡型的平片裂纹问题的计算,分析了自由边界面对裂纹前沿应力强度因子的影响。     

Stress field near transverse cracks under extension or in-plane shear in cross-ply composite laminates

Based upon the method of eigenfunction expansion and Leknitskii’s complex-variable potentials for the generalized plane deformation, the singular stress field near transverse cracks is examined for cross-ply composite laminates under two types of deformation, extension and in-plane shear. The stress singularity for each deformation is obtained from the eigenvalue equation resulting from appropriate near field conditions. It is found that the stress singularity for in-plane shear deformation is much stronger than for extension. To compute the stress intensity, use is made of the asymptotic representation for the stress and displacement field in conjunction with the singular hybrid finite element method. The numerical results are confirmed through comparison to those from other numerical techniques such as the boundary collocation method.     

Interface crack of two dissimilar bonded functionally graded strips with arbitrary distributed properties under plane deformations

In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack with material properties varying arbitrarily is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. A multi-layered model is employed to model arbitrary variations of material properties based on two linear-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. Numerical results show that fracture behavior of materials can be greatly affected by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited.     

机械振动信号中突变信息检测的新方法研究

提出利用时间序列重构的吸引子轨迹矩阵奇异值分解的方法检测信号中的突变信息。针对２组数值信号,利用该方法进行检测,并将检测结果与小波变换结果进行比较。结果表明,该方法是可行的,从而为信号奇异性检测撮一种有效工具。     

巨型运输车结构强度轴对称位势边界元法的预测

巨型运输车辆的结构系统的应力分布通常是三维的,从轴对称位势问题的边界积分方程出发,论述精确预测其结构强度需使用三维数值方法,对系数矩阵计算中柯西主值积分的奇异性与对数积分中的奇异性分别进行了研究,对柯西奇异积分部分提出一种解析的表达形式;而将对数积分中的奇异性进行了降阶处理．通过与有解析解的算例进行比较表明,本方法在减少计算量的情况下仍能较好地保证精度,对材料的奇异应力捕捉更为有效．     

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.     

一种求解复杂平面机构奇异位置的分析图解法

提出了复杂多环路平面机的奇异位置分析的一种简明的分析图解方法,即先将机的分解为基本运动链,再导出基本运动链的奇异性条件,后由其相应的奇异几何图形,解出其机构的奇异位置。揭示了机构奇异分析的三个重要结论。还给出了任意复杂多环路平面机构可能产生奇异位置的上限计算公式。最后举例说明了一个双环复杂机构的奇异位置求解过程,此外提出的方法可推广至空间机构的奇异性分析。     

Anti-plane shear behavior of an arbitrarily oriented crack in bonded materials with a nonhomogeneous interfacial zone

The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper. The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of modeIII stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.