弹性椭圆夹杂纵向剪切问题

获得纵向剪切下弹性椭圆夹杂问题的精确解。将复变函数的分区全纯函数理论，Cauchy型积分和Riemann边值问题相结合，求得各复势函数之间的解析关系，从而得到问题的封闭形式解，并给出了界面应力的解析表达式。本文解答与已有文献结果一致。本文发展的分析方法，为求解复杂多连通域的平面弹性问题提供了一条有效途径。     

压电材料椭圆夹杂界面开裂问题的电弹性耦合解

本文研究了在反平面剪切和面内电场的共同作用下，压电材料椭圆夹杂的界面开裂问题，假定夹杂是刚性的导体，采用复变函数保角变换和级数展开方法，可确定压电材料基体的复势表达式，进而求得夹杂界面开裂的电弹性耦合的能量释放率。     

含刚性椭圆夹杂的弹性平面奇异解

运用复变函数方法,求解了含刚性椭圆夹杂的无限弹性平面在任意位置作用集中力和集中力偶的问题,导出了界面应力公式,绘出了应力分布曲线。     

横观各向同性介质中椭圆夹杂受非弹性剪切变形引起的弹性场的确定

本文求解了横观各向同性介质中椭圆夹杂内受非弹性剪切变形引起的弹性场。采用各向异性弹性力学平面问题的复变函数解法,结合保角变换,获得夹杂内应变能和基体内边界的应力分布和相应的应变能的表达式。进一步,根据最小应变能原理,获得表征夹杂平衡边界的两个特征剪切应变,从而得到了弹性场的解析解。通过应力转换关系,验证了应力解满足夹杂边界上法向正应力和剪应力的连续条件,表明了该解的正确性。本文解可用于复合材料断裂强度的分析中。     

面向剪切下各向异性三相椭圆夹杂中均匀应力

论证了只要合适选择中间界面层的弹性常数，各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场。讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件。所给出的数值算例显示出该结论的正确性。该方法为纤维增强复合材料的设计提供了一条新途径。     

各向异性介质中的椭圆夹杂问题

本文研究了含椭圆夹杂的弹性体在多项式荷载作用下的二维变形问题，获得了介质和夹杂中的弹性场，证明了夹杂内部的应力变场以荷载的同阶多项式形式出现，而介质中的弹性场也能用椭圆坐标ζ＾－１２的多项式形式表示出来，并在此基础上，以受剪力作用的含夹杂或空孔的悬臂梁为例，求解了梁中的应力扰动现象，并获得了夹杂或空孔周转的环向应力。     

圆内旋轮线形状异质夹杂热弹性问题的解析解

论文研究具有圆内旋轮线型形状夹杂域的平面热弹性体在夹杂域内非均匀温度场作用下对弹性场所产生的影响,其中考虑的夹杂与基体的材料不同但是具有相同的剪切模量。借助黎曼映射理论,将平面光滑闭合曲线外部区域映射到单位圆外部区域,进而利用解析函数性质,结合柯西型积分与Faber多项式,求解得到夹杂域内外场势函数的显式解。通过得到的势函数求出内外场应力,并对应力分布进行分析,结果表明：一般形状异质夹杂时,内场应力值与有限元计算值相吻合;退化到椭圆同质夹杂时,与相关文献中的结果相同,但是更具一般性与实际可操作性。     

椭圆类夹杂分析的杂交应力有限元方法

本文给出了一种分析椭圆类夹杂周边应力场的新型杂交应力有限元方法。基于弹性力学中平面问题的Muskhelishvili复势方法,应用保角变换映射技术,以Laurent级数和Faber级数为工具,借助Hellinger-Reissner原理构建一个能够反映椭圆类夹杂周边弹性现象同时包含椭圆夹杂的多边形超级单元。将该超级单元与标准的4节点杂交应力单元耦合在一起即可建立一种分析椭圆类夹杂周边弹性场的新型特殊杂交应力有限元方法。文中考核算例表明：本文方法不但使用简单、有效,而且精度高、单元少。作为本文方法的一个拓展应用,文章最后给出了一个分析含二个椭圆夹杂无限大各向同性板在远场均布载荷作用下椭圆夹杂周边弹性场的算例,并讨论了椭圆夹杂间距和弹性刚度比对应力集中系数的影响。     

双周期分布圆形弹性夹杂平面热弹性问题

研究了含双周期分布圆形弹性夹杂的无限弹性平面在均匀拉伸和均匀温变下的弹性响应问题．运用Isida的区域单元法和复势函数的级数展开技术,将问题转化为线性方程组的求解．数值结果表明：相邻夹杂问距过大或过小都不利于减小界面应力,当相邻夹杂中心间距与夹杂半径之比为2．2～2．8时,界面剪切应力与环向应力的极大值最小;比值为2．5～3．5时,界面最大径向应力值最小;并且该比值范围不随两相材料弹性模量之比和热膨胀系数之比而变化．     

含界面层圆形夹杂中螺旋位错的弹性分析

研究了复合材料含界面层圆形夹杂内部的一个螺旋位错在夹杂，界面层与基体材料中产生的弹性干涉，将复变函数的分区亚纯函数理论与柯西型积分，罗朗级数相结合，求出了各分区复势的解析关系，化为一个关于界面层复势的函数方程，用显示式表达了问题的结果，揭示了界面层参数对位错干涉能与位错力的影响规律。该解析方法较经典级数方法未知量大量减少，表达式更加简洁，结果的特殊情形包含了若干已有成果。     

Periodic set of the interface cracks with contact zones in an anisotropic bimaterial subjected to a uniform tension–shear loading

A closed form solution to the plane problem of the theory of elasticity for an infinite anisotropic bimaterial space (plane) with a periodic set of the interface cracks with frictionless contact zones near its tips is obtained. By means of the complex function presentation the problem is reduced to the combined Dirichlet–Riemann boundary value problem for a sectionally holomorphic function and solved exactly. The equations for the determination of the contact zone lengths as well as the closed form expressions for the stress intensity factors are carried out. The variation of the mentioned values with respect to the distance between the cracks is illustrated in table and graphical forms.     

Effect of Temperature Sensitivity and Inelastic Behavior of Phase Materials on the Bearing Capacity of Plane Structures with Uniformly Stressed Reinforcement

An inelastic problem of uniformly stressed reinforcement of plane temperature-sensitive composite structures is formulated. Analytical solutions are obtained for the thermoelastic and inelastic cases. On the basis of these solutions, it is shown that the bearing capacity for inelastic projects can be increased severalfold as compared to thermoelastic projects, and reinforcement can be substantially saved in the inelastic case under fixed loading. Despite the worsening of strength characteristics of the composition phases, the bearing capacity of the structure remains almost unchanged upon heating in the inelastic case and can even increase in the thermoelastic case.     

PLANE ELASTIC PROBLEM ON RIGID LINES ALONG CIRCULAR INCLUSION

The plane elastic problem of circular-arc rigid line inclusions is considered. The model is subjected to remote general loads and concentrated force which is applied at an arbitrary point inside either the matrix or the circular inclusion. Based on complex variable method, the general solutions of the problem were derived. The closed form expressions of the sectionally holomorphic complex potentials and the stress fields were derived for the case of the interface with a single rigid line. The exact expressions of the singular stress fields at the rigid line tips were calculated which show that they possess a pronounced oscillatory character similar to that for the corresponding crack problem under plane loads. The influence of the rigid line geometry, loading conditions and material mismatch on the stress singularity coefficients is evaluated and discussed for the case of remote uniform load.     

Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses. The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation (20040350712)     

Analytical model of thermal striping for a micro-cracked solid

Using the formal asymptotic approximation of the Mode I stress intensity factor for an edge crack in a thermoelastic half plane containing several small voids obtained in [Nieves, M.J., Movchan, A.B., and Jones, I.S., 2011. Asymptotic study of a thermoelastic problem in a semi-infinite body containing a surface-breaking crack and small perforations. QJMAM 64 (3), 349–369] we investigate the effect of micro-cracks on this stress intensity factor. In numerical examples, we show how the behaviour of the stress intensity factor as a function of crack depth is affected by micro-cracks of different orientations occurring in the half space.     

Thermoelastic surface waves on an exponentially graded half-space

In this paper, we consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space, in which all thermoelastic characteristic parameters exponentially change along the depth direction. The propagation condition is established in the form of a bicubic equation whose coefficients are complex numbers while the analytical solutions (eigensolutions) of the thermoelastodynamic system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is subsequently expressed as a linear combination of the three eigensolutions while the secular equation is established in an implicit form. The explicit secular equation is written when an isotropic and homogeneous thermoelastic half-space is considered and some numerical simulations are given for a specific material.     

Thermally conductive elliptic inhomogeneities in 2D anisotropic solids

The problem of a thermally conductive elliptic hole embedded in an anisotropic thermoelastic solid under a remote uniform heat flow is considered. For the plane problem, solutions are derived by the use of an extended thermoelastic version of the Stroh formalism. The hoop stress around the elliptic hole is obtained in an explicit real form. We analyze the influence of the interior thermal conductivity and the cavity thickness on the temperature and stress on the boundary points of the hole. By comparison with the thermally insulated cavity, we show that the consideration of the interior conductivity may lead to significantly different thermomechanical behaviors. Ana Ursescu on leave from Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie no. 13, Bucharest, Romania.     

Rayleigh surface waves in the theory of thermoelastic materials with voids

In this paper we analyze the behavior of plane harmonic waves and Rayleigh waves in a linear thermoelastic material with voids. We take into account the damped effects of the thermal field upon the propagation waves. Consequently, the propagation condition is established in the form of an algebraic equation of 9th degree whose coefficients are complex numbers while the eigensolutions of the thermoelastodynamic with voids system are explicitly obtained in terms of the characteristic solutions. We show that the transverse waves are undamped in time and they are not influenced by the thermal and porous effects while the longitudinal waves are all damped in time and they are coupled with the thermal and porous effects. The related solution of the Rayleigh surface wave problem is expressed as a linear combination of the eigensolutions in concern. The secular equation is established in an implicit form and afterwards an explicit form is written for an isotropic and homogeneous thermoelastic with voids half-space. Furthermore, we use the numerical methods and computations to solve the secular equation for a specific material.     

A half-space problem in the theory of generalized thermoelastic diffusion

In this work we consider the problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and subjected to a time dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques.The temperature, displacement, stress and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.     

Numerical and analytical study of the propagation of thermoelastic waves in a medium with heat-flux relaxation

The thermoelastic problem of laser exposure of metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally.