Anti-plane elastodynamic analysis of orthotropic planes weakened by several cracks

Stress analysis is carried out in an orthotropic plane containing a Volterra-type dislocation, the distributed dislocation technique is employed to obtain integral equations for an orthotropic plane weakened by cracks under time-harmonic anti-plane traction. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.     

Elastodynamic analysis of a cracked orthotropic half-plane

The solution of elastodynamic volterra-type dislocation in an orthotropic half-plane is obtained by means of the Fourier transforms. The distributed dislocation technique is used to construct integral equations for an orthotropic half-plane weakened by cracks where the domain is under time-harmonic anti plane traction. These equations are of Cauchy singular type at the location of dislocation which is solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determine stress intensity factors for multiple smooth cracks. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.     

Anti-plane elastodynamic analysis of cracked graded orthotropic layers with viscous damping

Stress analysis is carried out in a graded orthotropic layer containing a screw dislocation undergoing time-harmonic deformation. Energy dissipation in the layer is modeled by viscous damping. The stress fields are Cauchy singular at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks with any location and orientation in the layer. These equations are solved numerically thereby obtaining the dislocation density function on the crack surfaces and stress intensity factors of cracks. The dependencies of stress intensity factors of cracks on the excitation frequency of applied traction and material properties of the layer are investigated. The analysis allows the determination of natural frequencies of a cracked layer. Furthermore, the interactions of two cracks having various configurations are studied.     

Antiplane elastodynamic analysis of a strip weakened by multiple defects

The method of images is utilized to derive the solution of a screw dislocation under time-harmonic conditions for an elastic strip from the solution of infinite planes. The displacement and stress components are obtained for a strip under concentrated antiplane, time-harmonic traction. The dislocation solution is employed to formulate integral equation for a strip weakened by cracks and cavities. The effects of load frequency and crack orientation on the stress intensity factors are studied.     

Anti-plane analysis of an orthotropic strip weakened by several moving cracks

In this paper several finite cracks with constant length (Yoffe-type crack) propagating in an orthotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an orthotropic strip containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in an orthotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by moving cracks. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the orthotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically.     

Anti-plane stress analysis of dissimilar sectors with multiple defects

In this article, the anti-plane deformation of a typical dissimilar sector consists of two sub-sectors attached to each other on one circular edge is studied. The solution of a Volterra type screw dislocation problem in the sector is obtained through finite Fourier cosine transform. Exact closed-form solutions for the displacement and stress fields are also presented. Next, using a distributed dislocation method, integral equations of the sectors weakened by cracks and cavities under an anti-plane traction are obtained. The defects are assumed to be located only in one of the sub-sector regions. The obtained equations for the latter problem are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the efficiency and applicability of the proposed solution procedure. The geometric and force singularities of the stress field are studied and compared to those reported in the literature.     

Stress analysis of orthotropic planes weakened by cracks

The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

圆形孔口裂纹的反平面剪切问题的解析解

利用复变函数方法,通过构造保角映射,研究了带裂纹的圆形孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子.在极限情形下,求得Griffith裂纹在裂纹尖端处应力强度因子,这与已有的结果完全一致.最后数值算例给出了半经和裂纹长度对应力强度因子的影响.     

On arcs sharing the maximum number of points with ovals in cyclic affine planes of odd order

The sporadic complete 12‐arc in PG(2, 13) contains eight points from a conic. In PG(2,q) with q>13 odd, all known complete k‐arcs sharing exactly ½(q+3) points with a conic 𝒞 have size at most ½(q+3)+2, with only two exceptions, both due to Pellegrino, which are complete (½(q+3)+3) arcs, one in PG(2, 19) and another in PG(2, 43). Here, three further exceptions are exhibited, namely a complete (½(q+3)+4)‐arc in PG(2, 17), and two complete (½(q+3)+3)‐arcs, one in PG(2, 27) and another in PG(2, 59). The main result is Theorem 6.1 which shows the existence of a (½(q^r+3)+3)‐arc in PG(2,q^r) with r odd and q≡3 (mod 4) sharing ½(q^r+3) points with a conic, whenever PG(2,q) has a (½(q^r+3)+3)‐arc sharing ½(q^r+3) points with a conic. A survey of results for smaller q obtained with the use of the MAGMA package is also presented. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 25–47, 2010     

The nonexistence of projective planes of order 12 with a collineation group of order 8

In this article, we prove that there does not exist a symmetric transversal design which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. As a corollary of the result, we prove that there is no projective plane of order 12 admitting a collineation group of order 8. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 411–430, 2008     

点群6一维六方准晶椭圆孔口与半无限裂纹反平面弹性问题的解析解

导出了点群6-维六方准晶反平面弹性问题的控制方程.利用复变方法,给出了点群6-维六方准晶在周期平面内的反平面弹性问题的应力分量以及边界条件的复变表示,通过引入适当的保角变换,研究了点群6-维六方准晶中带有椭圆孔口与半无限裂纹的反平面弹性问题,得到了椭圆孔口问题应力场的解析解,给出了半无限裂纹问题在裂纹尖端处的应力强度因子的解析解.在极限情形下,椭圆孔口转化为Griffith裂纹,并得到该裂纹在裂尖处的应力强度因子的解析解.当点群6-维六方准晶体的对称性增加时,其椭圆孔口与半无限裂纹的反平面弹性问题的解退化为点群6mm-维六方准晶带有椭圆孔口与半无限裂纹的反平面弹性问题的解。     

Effective elastic moduli of two-dimensional solids with multiple cracks

An accurate method which directly accounts for the interactions between different microcracks is used for analyzing the elastic problem of multiple cracks solids. The effective elastic moduli for randomly oriented cracks and parallel cracks are evaluated for the representative volume element (RVE) with microcracks in infinite media. The numerical results are compared with those from various micromechanics models and experimental data. These results show that the present method is simple and provides a direct and efficient approach to dealing with elastic solids containing multiple cracks. Project supported by the National Natural Science Foundation of China (Grant No. 19704100), and the National Natural Science Foundation of Chinese Academy of Sciences (Project KJ951-1-201).     

Free in-plane vibration analysis of a curved beam (arch) with arbitrary various concentrated elements

In the existing literature, the information regarding the exact solutions for free in-plane vibrations of the curved beams (or arches) carrying various concentrated elements is rare, particularly for the case with multiple attachments including eccentricities and mass moments of inertias. For this reason, this paper aims at presenting an effective approach to tackle the title problem. First of all, the un-coupled equation of motion for the circumferential displacement of an arch segment is derived. Next, based on the value of the discriminate parameter for a cubic equation, the exact solutions for the three types of roots of the un-coupled equation are determined and, corresponding to each type of roots, all displacement functions for the arch segment in terms of the real numbers (instead of the complex ones) are obtained. Finally, use of the compatible equations for the displacements and slopes together with the equilibrium equations for the forces and moments at each intermediate node and two ends of the entire curved beam, a frequency equation of the form ∣H(ω)∣ = 0 is obtained. It is found that the conventional approach by using the condition “∣H(ω^t)∣ ? ε” to search for the approximate value of ω^t is difficult even if the convergence tolerance ε is greater than 10⁺³ (i.e., ε > 10⁺³) instead of less than 10^?3 (i.e., ε < 10^?3), however, the half-interval method is one of the effective tools for solving the problem if all coefficients of the determinant ∣H(ω)∣ are the real numbers. In addition to comparing with the existing literature, most of the numerical results obtained from the presented method are compared with those obtained from the conventional finite element method (FEM) and good agreement is achieved.     

Vibration analysis of rotating systems with open and breathing cracks

This paper is concerned with vibration analysis of rotating systems containing cracks. The flexibility matrix of cracked element is calculated with modified integration limits which is more accurate than conventional methods. The effect of this modification on the coefficients of flexibility matrix is presented for a simple rotor system containing open crack. To model the crack breathing behavior, a new finite element approach is introduced and implemented. Then, the dynamic response of a rotor with a breathing crack is evaluated by using the frequency/time domain approach (short time Fourier transform). The ability of short time Fourier transform to detect small cracks is investigated and compared with the transient response. The results provide a possible basis for an on-line monitoring system.     

Exact analysis of queueing networks with multiple job classes and blocking-after-service

Two models of closed queueing networks with blocking-after-service and multiple job classes are analyzed. The first model is a network withN stations and each station has either type II or type III. The second model is a star-like queueing network, also called a central server model, in which the stations may have either type I or type IV, with the condition that the neighbors of these stations must be of type II or type III such that blocking will be caused only by this set of station types. Exact product form solutions are obtained for the equilibrium state probabilities in both models. Formulae for performance measures such as throughput and the mean number of jobs are also derived.This work was supported by the National Science Foundation (NSF) under Grant No. CCR-90-11981.     

含多重时滞非线性系统的分数阶迭代学习控制的收敛性分析

本文研究了含多重时滞非线性系统的分数阶迭代学习控制(FOILC).它包含了外部干扰和输出控制噪音,通过引入λ—范数,获得在开环和闭环迭代学习控制作用下,系统控制输入以及跟踪误差收敛的充分条件.最后,通过数值仿真验证所提方法的有效性.     

The assessment of the information quality with the aid of multiple criteria analysis

The virtual business work flow depends on the information quality (IQ) which is essential attribute of information. The IQ depends strongly on organization of the information system (IS) and how the information is processed. In our approach we incorporate the four-aspect representation of IQ: (1) intrinsic, (2) contextual, (3) representational, and (4) accessibility. These four-aspects are divided into several criteria at the next level of hierarchy. The weights, representing the relative importance of criteria, have been assessed by pair-wise comparisons made by group of experts. Based on discussion with experts, six alternative strategies, that could be used for improving the IQ, were designed. For each given criterion, the group of subjects revealed the opinion about the level of achievement of every alternative. The set of scores, assigned to the alternative by different subjects, formed the discrete distribution that is used for a comparison of alternatives with the aid of stochastic dominances. In analogy to the Electre I methodology, the simple algorithm for the aggregate evaluation of analyzed alternatives was proposed. The benefits of proposed approach were demonstrated in a case study of the semiconductor industry. The results of our study suggest, that in case of matured company, the external strategies, that point out to the information exchange and strategic networked alliance with customers and suppliers, are preferred to the internal ones. The latter ones might be of greater importance for the new set up or for a young company.     

Controllability analysis of linear time-varying systems with multiple time delays and impulsive effects

In this paper, the issue of controllability for linear time-varying systems with multiple time delays in the control and impulsive effects is addressed. The solution of such systems based on the variation of parameters is derived. Several sufficient and necessary algebraic conditions for two kinds of controllability, i.e., controllability to the origin and controllability, are derived. The relation among these conditions are established. A numerical example is provided to illustrate the effectiveness of the proposed methods.