Flexural Stress Concentration Near a Hyperboloidal Neck in a Transversely Isotropic Piezoceramic Cylinder

The general solution of the electroelastic problem for a transversely isotropic hyperboloid of revolution is used to find the stress concentration near a hyperboloidal neck in a piezoceramic body subjected to bending. The solution is a sum of four partial solutions for the case where the forces and the normal component of the induction vector on the neck surface are equal to zero. Numerical examples are given for specific external loads and properties of the body. The stress components and normal component of the induction vector near the neck vertex are plotted as a function of the external load and neck curvature     

Anti-plane Shear Deformations in Compressible Transversely Isotropic Materials

Anti-plane shear deformations in a compressible, transversely isotropic hyperelastic material are under investigation. The displacement is assumed to be along the direction of the symmetry axis and is independent of the axial position. The resulting equations of equilibrium form an overdetermined system of partial differential equations for which solutions do not exist in general. Necessary and sufficient conditions are derived for such materials to sustain anti-plane shear deformations in the sense that every solution to the axial equation automatically satisfies the other two in-plane equations. Comparison is made with results for isotropic materials. A weaker version of the conditions specialized to axisymmetric anti-plane shear deformations is also obtained.     

横观各向同性体三维裂纹的瞬态扩展

讨论一对集中力作用下横观各向同性体三维裂纹的瞬态扩展问题,其解答构成三维裂纹瞬态扩展问题的基本解。求解方法是基于积分变换技术,将混合边值问题化为Wiener-Hopf型积分方程,求得了裂纹所在平面应力和位移的封闭形式解。进一步利用Abel定理和Cagniard-de Hoop方法,求得了动态应力强度因子的精确解。最后通过数值结果揭示了横观各向同性材料三维扩展裂纹尖端场的动态特性。     

浅球形双凹坑或多凹坑对应力集中的增强效应

板表面的浅球形凹坑是一种具有代表性的缺陷。本文以光弹性研究成果为基础，结合有限元结果，进一步分析双凹坑或多凹坑对应力集中的增强效应，并确定双凹坑的最不利间距及其对应力集中的影响程度。     

Stress State of a Transversely Isotropic Medium with an Arbitrarily Oriented Spheroidal Inclusion

The stress-concentration problem for an elastic transversely isotropic medium containing an arbitrarily oriented spheroidal inclusion (inhomogeneity) is solved. The stress state in the elastic space is represented as the superposition of the principal state and the perturbed state due to the inhomogeneity. The problem is solved using the equivalent-inclusion method, the triple Fourier transform in space variables, and the Fourier-transformed Green function for an infinite anisotropic medium. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. In special cases, the results are compared with those obtained by other authors. The influence of the geometry and orientation of the inclusion and the elastic properties of the medium and inclusion on the stress concentration is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 33–40, February 2005.     

Exact Analytical Solutions of Static Electroelastic and Thermoelectroelastic Problems for a Transversely Isotropic Body in Curvilinear Coordinate Systems

An approach to the solution of three-dimensional static problems for a transversely isotropic (rectilinear anisotropy) body is expounded and the solutions for piezoceramic canonical bodies are systematized. The result of the study is explicit analytical solutions of three-dimensional problems. Bodies are examined whose boundary surface is the coordinate surfaces in coordinate systems that permit the separation of the variables in the three-dimensional Laplace equation. The stress concentration in bodies near necks, cavities, inclusions, and cracks is investigated. The stress intensity factors of the force field and electric induction near elliptic and parabolic cracks are determined. The contact interaction of a piezoceramic half-space with elliptic and parabolic dies is studied. The bodies are under various mechanical, thermal, and electric loads     

Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

Asymptotic Analysis of Finite Deformation in a Nonlinear Transversely Isotropic Incompressible Hyperelastic Half-space Subjected to a Tensile Point Load

The Boussinesq problem, that is, determining the deformation in a hyperelastic half-space due to a point force normal to the boundary, is an important problem of engineering, geomechanics, and other fields to which elasticity theory is often applied. While linear solutions produce useful Greens functions, they also predict infinite displacements and other physically inconsistent results nearby and at the point of application of the load where the most critical and interesting material behavior occurs. To illuminate the deformation due to such a load in the region of interest, asymptotic analysis of the nonlinear Boussinesq problem has been considered in the context of isotropic hyperelasticity. Studies considering transversely isotropic materials have also been broadly used in the linear theory, but have not been treated within the nonlinear framework. In this paper we extend the nonlinearly elastic isotropic analysis to transverse isotropy, producing a more general theory which also better encompasses applications involving layered media. The governing equations for nonlinearly elastic, transversely isotropic solids are derived, conservation laws of elastostatics are invoked, asymptotic forms of the deformation solutions are hypothesized, and the differential equations governing deformation near the point load are determined. The analysis also develops sequences of simple tests to determine if a transversely isotropic material can possibly sustain a finite deflection under the point load. The results are applied to a variety of transversely isotropic materials, and the effects of the anisotropy considered is demonstrated by comparison of the resulting deformation with similar asymptotic solutions in the isotropic theory. Mathematics Subject Classifications (2000) 74B20, 74E10, 74G10, 74G15, 74G70.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

双向应力状态下三维球形空穴应力集中的实验研究

用光弹三维应力冻结切片法研究了双向应力状态下球穴附近应力分布和集中问题，介绍了含球穴的三维光弹性模型的尺寸确定、浇注工艺和实现双向应力状态及大面积均匀拉伸加载的方法，分析了在特定平面上的正应力σ，剪应力τ沿球穴边缘的分布及衰减规律。文中对实验数据进行了统计分析处理，证明了实验与理论结果符合一致     

The Stress State of a Transversely Isotropic Ferromagnetic with a Parabolic Crack in a Homogeneous Magnetic Field

The magnetoelastic problem for a transversely isotropic ferromagnetic body with a parabolic crack in the plane of isotropy is solved explicitly. The body is in an external magnetic field, which is perpendicular to the plane of isotropy. The field induces elastic strains and a magnetic field in the body. The characteristics of the stress–strain distribution and induced magnetic field are determined; and their singularities in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented     

螺旋焊线管局部噘嘴应力集中分析

螺旋焊缝局部噘嘴问题是复杂的三维问题，至今没有现成的安全评定公式可以利用，也难以获得纯粹的理论解。应“西气东输”工程之需，本文利用现有直焊缝理论基础，建立了该问题的力学模型，获得了应力集中因子的显式解，给制订螺旋焊线管几保缺陷的安全评定标准提供了理论基础。利用商用有限元工具ABAQUS对螺旋焊线局部噘嘴进行的系统分析显示，本文提供的理论解具有很强的预测能力。     

Stress Concentration in a Soft Ferromagnetic with an Elliptic Inclusion in a Homogeneous Magnetic Field

The paper addresses a stress–strain problem for an infinite soft ferromagnetic body with an elliptic inclusion. The body is in a homogeneous magnetic field B ₀₁. The basic stress–strain characteristics and induced magnetic field in the body and inclusion are determined and their features in the neighborhood of the inclusion are studied. The magnetoelastic and Maxwell stresses are plotted against the ratio of ellipse axes and the latitude angle. Maximum stresses versus magnetic induction and mechanical and magnetic properties of the material are tabulated     

X射线法测试1500m^3乙烯球罐焊接残余应力的现场应用

本文应用Ｘ射线应力仪对ＣＦ－６２钢制乙烯球罐焊接残余应力进行了现场测量，解决了大型球罐的残余应力现场测试过程中的技术问题，结果表明焊后残余应力水平较高而热处理效果良好     

The Stress State of a Piezoceramic Medium with an Elliptic Inclusion under Pure Shear and Pure Bending

Explicit analytical solutions to electroelastic problems for an infinite transversely isotropic medium with a tunnel elliptic inclusion are constructed. At a sufficient distance from the inclusion, the medium is subjected to pure shear or pure bending. It is assumed that the medium and inclusion are dissimilar piezoceramic materials whose axes of symmetry coincide with each other and with the minor axis of the ellipse. The stresses and the projections of the electromagnetic induction vector acting in the medium beyond the inclusion are determined for each case of loading at infinity     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

Elliptic cavity in a three-dimensional anisotropic body with inclined strata deformed by line loads and dislocations

Summary Analytical solutions are proposed for the stress and displacement fields in a quasi three-dimensional elastic anisotropic body containing an elliptic cavity or rigid inclusion. The directions of the principal elastic axes are allowed to be inclined arbitrarily with respect to the axes of the elliptic cavity. As an application, expressions for the stress intensity factors are formulated when the cavity reduces to a colinear crack.     

含孔边非均匀材料圆环的无限大薄板的应力集中系数

对于含圆孔及孔边非均匀材料圆环的无限大薄板，假设非均匀材料的弹性模量沿径向按照指数函数变化，而泊松比为常数，分别导出了双轴拉伸和纯剪切作用时孔边及界面处的应力集中系数的解析解．通过数值算例详细分析了非均匀材料圆环的弹性模量的变化对无限大薄板的孔边及界面处的应力集中系数的影响．研究结果表明，合理选择孔边非均匀材料圆环的材料性能变化参数可有效地缓解薄板的孔边应力集中程度．本文的研究结果可为含圆孔的薄板的设计提供一定的参考．