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。     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。     

横观各向同性热弹性多孔介质板的精化理论

研究了孔隙水压力作用下横观各向同性热弹性多孔介质板的精化理论。在不做任何预先假设的情况下,利用 Lur’e 方法和横观各向同性热弹性多孔介质的通解,得到了横观各向同性热弹性多孔介质板的精化理论。首先,根据调和函数的sin算子函数表达式,得到了用5个二维待定函数表示的位移场和应力场;其次,在非齐次边界条件下,利用基本的数学算法,得到了在孔隙水压力载荷作用下热弹性多孔介质板的精化方程;最后,通过舍弃高阶项,得到了位移场和应力场的近似解。     

横观各向同性介质中弹性波的吸收边界条件

在数值求解固体中的弹性波动问题时，常需引入吸收边界条件来限制大范围或无边界的求解区域，使数值计算得以顺利进行。本文通过合成简单的一阶偏微分算子，给出了横观各向同性介质中弹性波的吸收边界条件，其中每个单一的算子均可完全吸收沿某一角度出射的平面波。文中还基于弹性波的势函数理论，导出了准Ｐ波和准Ｓ波在吸收边界处的反射系数公式，用以检验其吸收能力。本文所给出的吸收条件，形式简单，且算例表明吸收效果良好，因     

柱面受温度载荷的轴对称横观各向同性压电热弹性圆柱的精化理论

将精化理论的研究方法推广到轴对称横观各向同性压电热弹性圆柱的研究中,利用压电热弹性问题的轴对称通解以及准调和函数的Bessel算子函数表示方法,获得了该圆柱在柱面受温度载荷作用下的精确耦合场;当柱面受到随轴向Z增大而逐渐减小的轴对称量纲为一的温度载荷时,绘制出圆柱在半径r 分别为0.2、0.4、0.6、0.8、1.0时的位移分量、电势、温度增量沿轴向z的分布。结果表明：圆柱在同一高度的情况下,径向位移和轴向位移随半径增大而增大,电势的绝对值也随半径的增大而增大,而温度增量随半径的变化则不明显。此外,本文还通过算例验证了该精化理论应用的正确性。     

横观各向同性热弹性梁的精化理论

本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。     

纵向剪切下含共焦刚性核弹性椭圆夹杂中的螺型位错干涉

研究了无穷远纵向剪切下无限大基体中含共焦刚性核弹性椭圆夹杂内任意位置螺型位错的干涉问题.运用复变函数保角映射、解析延拓等方法,获得了基体与夹杂区域的应力场的级数形式精确解,并得出了位错像力的解析表达式,导出了纵向剪切下两椭圆界面最大应力及其比值公式.在此基础上,分析和讨论了夹杂内部刚性核对位错与夹杂之间干涉的扰动效应,以及椭圆夹杂尺度对位错像力的影响规律.     

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。     

横观各向同性圆柱体端部问题的三维弹性理论解

从位移的通解出发，用分离变量法得到横观各向同性圆柱体的位移和应力的特征函数展开式，并把位移势函数的解用付里叶积分的形式表示。利用留数运算，该积分解可以转换成类似于特征函数的展开式。通过混合端部边界问题，得到与特征函数解成双正交关系的另一组函数。利用这种双正交关系，可以处理不同的端部边界问题。     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论,研究了横观各向同性液体饱和多孔介质中平面波的传播特性．首先导出了波传播的特征方程并给出其解析解,结果显示：有４种不同波速的平面体波传播：第一准纵波（ＱＰ１）、第二准纵波（ＱＰ２）、准横波（ＱＳＶ）和反平面横波（ＳＨ）．文中给出了波速和衰减的解析表达式,数值计算了频散曲线和衰减曲线,并讨论了各类准体波位移之间的耦合关系．最后分析了Ｒａｙｌｅｉｇｈ波的生成条件和传播特性．文章详细讨论了介质异性对波传播特性的影响     

End Effects in Anti-plane Shear for an Inhomogeneous Isotropic Linearly Elastic Semi-infinite Strip

The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and, in particular, to functionally graded materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

Saint-Venant Decay Rates for an Isotropic Inhomogeneous Linearly Elastic Solid in Anti-Plane Shear

The purpose of this research is to investigate the effects of material inhomogeneity on the decay of Saint-Venant end effects in linear isotropic elasticity. This question is addressed within the context of anti-plane shear deformations of an inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation with variable coefficients on a semi-infinite strip. The elastic coefficients are assumed to be smooth functions of the transverse coordinate. The estimated rate of exponential decay with distance from the loaded end (a lower bound for the exact rate of decay) is characterized in terms of the smallest positive eigenvalue of a Sturm–Liouville problem with variable coefficients. Analytic lower bounds for this eigenvalue are used to obtain the desired estimated decay rates. Numerical techniques are also employed to assess the accuracy of the analytic results. A related eigenvalue optimization question is discussed and its implications for the issue of material tailoring is addressed. The results of this paper are applicable to continuously inhomogeneous materials and, in particular, to functionally graded materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.