二维切口问题完备特征解的研究现状与进展

简要回顾和介绍了文献中常见的几种求解二维切口问题特征根的方法,评述这些方法 的特点及其求解范围．重点介绍了在求解二维切口问题完备特征根方面的一些进展,包括特征 根的求解方法、特征根的重根探讨以及相应的特征函数计算,这一问题基本上得到了解决．为 基于特征展开研究二维断裂问题打下了基础．      

Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading

The behaviour of a bi-piezoelectric ceramic layer with a centre interfacial crack subjected to anti-plane shear and in-plane electric loading has been studied. The dislocation density functions and the Fourier integral transform method have been employed to eliminate the problem of singular integral equations. The normalized energy release rate, stress and electrical displacement intensity factors, G/G₀,K_III/K_III0 and K_D/K_D0, respectively, were determined for different geometric and property parameters by use of two different crack surface electric boundary conditions, i.e. impermeable and permeable. It has been shown that the effects of the thickness and material constants of the piezoelectric layer on all the three parameters, i.e. G/G₀,K_III/K_III0 and K_D/K_D0 were significant.     

Singular integral equations and boundary element method of cracks in thermally stressed planar solids

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A generalization of Fan’s results: Distribution of cycle lengths in graphs

Fan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187-202] proved that if G is a graph with minimum degree δ(G)≥3k for any positive integer k, then G contains k+1 cycles C₀,C₁,…,C_k such that k+1<|E(C₀)|<|E(C₁)|<?<|E(C_k)|, |E(C_i)−E(C_i−1)|=2, 1≤i≤k−1, and 1≤|E(C_k)|−|E(C_k−1)|≤2, and furthermore, if δ(G)≥3k+1, then |E(C_k)|−|E(C_k−1)|=2. In this paper, we generalize Fan’s result, and show that if we let G be a graph with minimum degree δ(G)≥3, for any positive integer k (if k≥2, then δ(G)≥4), if d_G(u)+d_G(v)≥6k−1 for every pair of adjacent vertices u,v∈V(G), then G contains k+1 cycles C₀,C₁,…,C_k such that k+1<|E(C₀)|<|E(C₁)|<?<|E(C_k)|, |E(C_i)−E(C_i−1)|=2, 1≤i≤k−1, and 1≤|E(C_k)|−|E(C_k−1)|≤2, and furthermore, if d_G(u)+d_G(v)≥6k+1, then |E(C_k)|−|E(C_k−1)|=2.     

M x /G/1 Queue with Multiple Vacations

Abstract

In this article, we study a queueing system M ^x /G/1 with multiple vacations. The probability generating function (P.G.F.) of stationary queue length and its expectation expression are deduced by using an embedded Markov chain of the queueing process. The P.G.F. of stationary system busy period and the probability of system in service state and vacation state also are obtained by the same method. At last we deduce the LST and mean of stationary waiting time in the service order FCFS and LCFS, respectively.     

疲劳裂纹扩展柔度法测量系统研究

为了寻求高温高压环境介质下的疲劳裂纹扩展的测量方法,本文研制了基于柔度法的疲劳裂纹扩展系统。根据显微镜的标定结果,验证该计算机自动测量系统给出了可信的测量结果。其中,位移由涡流位移传感器测得,载荷由试验机自带的标准传感器测得。计算机实时采集并处理测试信号,给出裂纹扩展速率。文中介绍了该系统的功能及应用前景。作为应用实例,给出了４２ＣｒＶ和ＩＲ３Ｍｏ等钢种的疲劳裂纹扩展速度及门槛值。     

光弹贴片法研究砼在疲劳荷载作用下裂缝扩展过程

为了研究疲劳荷载作用下砼裂缝扩展过程,本文采用光弹贴片法对尺寸为200mm×200mm×200mm的楔入劈拉试件预制裂缝稳定扩展直至失稳破坏全过程进行了系统的研究,并采用照相机拍摄了光弹贴片所显示的裂缝扩展全过程,得到了砼裂缝长度随疲劳次数的增加而稳定扩展的完整而直观的观测结果．根据光弹贴片所显示的彩色条纹序列,还测得了疲劳荷载作用下砼裂缝尖端附近的主剪应变差分布．试验表明,采用光弹贴片法可有效地测定疲劳荷载作用下砼裂缝扩展过程．     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

Experimental study on crack curving propagation in bending beams under impulsive load

Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen, the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the stress intensity factors for the cracks running in varying curvature paths under bending stress wave. The project supported by the National Natural Science Foundation of China and the Scientific Commission of Yunnan Province of China     

同输入M/M/∞排队群的联合队长过程

本提出一个偏微分方程方法，用这一方法研究同输入M/M／∞排队群中的联合队长分布。在任意初始条件下，给出了瞬时联合队长分布的多元母函数，也讨论了稳态队长的联合分布及各排队系统之间的相关性。