Singularity characteristics for a lip-shaped crack subjected to remote biaxial loading

In this paper, the conformal mapping method was adopted to solve the problem of an infinite plate containing a central lip-shaped crack subjected to remote biaxial loading. A kind of leaf-shaped configuration was also constructed in order to solve the problem. The analytical result showed that the singularity order of the stress field at the tip of a lip-shaped crack remains -1/2, despite the difference in notch-crack width.

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat how direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre-matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.

基于贝塞尔曲线的WSN等值线绘制算法

从无线传感器网络(WSN)环境数值监测应用的实际需求出发,提出了一种应用于该类场景中的等值线绘制(CMBC)算法.CMBC算法基于图形学中常用的贝塞尔(Bezier)曲线理论,通过选择部分节点提供信息给网关节点绘制等值线.此方法有效解决了监测应用场景中对最终监测精度的需求与大量报告节点所引发的高流量负载和网络能耗之间的矛盾.仿真结果表明,CMBC算法和已有研究工作相比能够使用更少的汇报节点完成高精度等值线的绘制,因此CMBC算法能够节省节点的能量,延长网络的生存期.

Two-Point Closure Strategy in the Mapping Closure Approximation Approach

A two-point closure strategy in mapping closure approximation (MCA) approach is developed for the evolution of the probability density function (PDF) of a scalar advected by stochastic velocity fields. The MCA approach is based on multipoint statistics. We formulate a MCA modeled system using the one-point PDFs and two-point correlations. The MCA models can describe both the evolution of the PDF shape and the rate at which the PDF evolves.

Mapping Closure Approximation for Reactive Scalars in Random Flows

The Mapping Closure Approximation (MCA) approach is developed to describe the statistics of both conserved and reactive scalars in random flows. The statistics include Probability Density Function (PDF), Conditional Dissipation Rate (CDR) and Conditional Laplacian (CL). The statistical quantities are calculated using the MCA and compared with the results of the Direct Numerical Simulation (DNS). The results obtained from the MCA are in agreement with those from the DNS. It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.

Dynamic phase-mapping of domain nucleation on MgO : LiNbO3 crystal by digital holographic interferometry

The quantitative phase-mapping of the domain nucleation in MgO:LiNbO3 crystals is presented by using the digital holographic interferometry. An unexpected peak phase at the beginning of the domain nucleation is observed and it is lowered as the spreading of the domain nucleus. The existence of the nucleus changes the moving speed of the domain wall by pinning it for 3s. Such in-situ quantitative analysis of the domain nucleation process is a key to optimizing domain structure fabrication.

Phase mapping of domain kinetics in lithium niobate by digital holographic interferometry

The phase mapping of domain kinetics under the uniform steady-state electric field is achieved and investigated in the LiNbO3 crystals by digital holographic interferometry. We obtained the sequences of reconstructed three-dimensional and two-dimensional wave-field phase distributions during the electric poling in the congruent and near stoichiometric LiNbO3 crystals. The phase mapping of individual domain nucleation and growth in the two crystals are obtained. It is found that both longitudinal and lateral domain growths are not linear during the electric poling. The phase mapping of domain wall motions in the two crystals is also obtained. Both the phase relaxation and the pinning-depinning mechanism are observed during the domain wall motion. The residual phase distribution is observed after the high-speed domain wall motion. The corresponding analyses and discussions are proposed to explain the phenomena.

Mapping chromosomal homologies between humans and two langurs (Semnopithecus francoisi and S-Phayrei) by chromosome painting

Chromosomal homologies were established between human and two Chinese langurs (Semnopithecus francoisi, 2n=44, and S. phayrei, 2n=44) by chromosome painting with chromosome-specific DNA probes of all human chromosomes except the Y. Both langur species showed identical hybridization patterns in addition to similar G-banding patterns. In total, 23 human chromosome-specific probes detected 30 homologous chromosome segments in a haploid langur genome. Except for human chromosomes 1, 2, 6, 16 and 19 probes, which each gave signals on two non-homologous langur chromosomes respectively, all other probes each hybridized to a single chromosome. The results indicate a high degree of conservation of chromosomal synteny between human and these two Chinese langurs. The human chromosome 2 probe painted the entire euchromatic regions of langur chromosomes 14 and 19. Human chromosome 1 probe hybridized to three regions on langur autosomes, one region on langur chromosome 4 and two regions on langur chromosome 5. Human 19 probe hybridized on the same pattern to one region on chromosome 4 and to two regions on langur chromosome 5, where it alternated with the human chromosome 1 probe. Human 6 and 16 probes both hybridized to one region on each of the two langur autosomes 15 and 18. Only two langur chromosomes (12 and 21) were each labelled by probes specific for two whole human chromosomes (14 and 15 and 21 and 22 respectively). Comparison of the hybridization patterns of human painting probes on these two langurs with the data on other Old World primates suggests that reciprocal and Robertsonian translocations as will as inversions could have occurred since the divergance of human and the langurs from a common ancestor. This comparison also indicates that Asian colobines are karyotypically more closely related to each other that to African colobines.