三维双材料结构的应力奇异性分析

应用有限单元法子模型技术，对具有不同界面角的三维双材料结构的应力奇异性进行了分析。结果表明，应用子模型技术估算三维双材料结构的应力奇异性指数是有效的。然后分析了界面端线和界面端点处附近奇异性指数，得到了一些重要而有趣的结果。最后对消除三维双材料结构应力奇异性的几何条件进行了讨论。     

基于界面端奇异性理论的单纤维拔出试验的试件设计

在单纤维拔出试验中，由于试件的界面端存在应力奇异性，这使试验所得到的界面剪切强度数据失去合理性[1]。但从文献[1]关于微珠脱粘试验研究的结论中可以发现当基体的楔形角小于某临界角度后，微珠试件界面端应力奇异性几乎消失。由此启发我们设计出一种楔形角小于该纤维／基体系统临界角的锥面的拔出试件，这样即可以防止出现传统拔出试件在界面端的强应力奇异性，又可以避免微珠脱粘试验自身的缺陷。界面端具有任意楔形角的轴对称模型被用于分析和确定纤维／基体系统的临界角，对方程进行渐近展开和分离变量处理，根据边界条件可以得到关于特征值λ的特征方程，针对确定的纤维／基体系统可以得到特征值和楔形角的关系曲线，我们把应力奇异性指数等于-0．005时所对应的楔形角定义为临界角，以及根据临界角设计锥面拔出试件的方法。     

各向异性复合材料的应力奇异性

本文根据各向异性材料的特征值与特征函数理论,用极其简单的矩阵形式,建立了复合楔形和裂纹止于两材料界面等情况下确定应力奇异阶次的特征方程,讨论了应力奇异性的一些特性,计算了各种情况下的应力奇异阶次。     

Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10⁻¹¹ to 10⁰ by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.     

Singular behaviour and asymptotic stress field of a crack terminating at a bimaterial interface

A crack terminating at an interface of two dissimilar elastic materials is investigated. It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part being characterized by one singularity. The detailed relation of the two singularities with the bimaterial properties is given for some special cases of the crack.     

Stress singularities near the apex of a cylindrically polarized piezoelectric wedge

Summary In this paper, the stress singularities for a cylindrically polarized piezoelectric wedge are investigated. The characteristic equations are derived analytically by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is polarized in the radial, circular or axial direction, respectively. Similar to the rectilinearly polarized piezoelectric problem, the inplane and antiplane stress fields are uncoupled. The results show the variations of the singularity orders with the changes of the wedge angle, material constants, polarized direction, and the boundary conditions.     

电磁波导的奇异元与对偶有限元分析

基于电磁波导的对偶变量变分原理以及Hamilton正则方程,将含有奇异性的电磁场问题导入Hamilton体系下进行分析,通过分离变量及共轭辛本征函数向量展开法,构造出可以表征电磁场奇异性的奇异解析元。奇异元的采用克服了普通单元处理含有导电劈和介质楔的波导问题的困难,同时能够方便地与电磁对偶元相结合,保持了有限元方法的灵活性,具有较高的精度。     

大散射角散斑场中有关相位奇异新特性的研究

利用散斑场和参考光的干涉提取散斑场复振幅和相位, 研究了不同散射角下散斑场相位的分布规律以及相位奇异处光波复振幅实部零值线和虚部零值线夹角、光强等值线离心率的统计特性. 在大散射角散斑中发现了一种新的相位奇异现象, 即相位奇异线; 研究了相位在跨越奇异线时的突变规律及涡旋状相位的分布特征, 发现在相位奇异线处存在着呈双曲线或抛物线状的光强等值线.     

The multiplicity of abelian covers of splice quotient singularities

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.     

Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality