含有随机夹杂的统计非均匀弹性介质参数的分析

本文提出了随机点场理论用于研究含有随机夹杂的统计非均匀介质。本文不同于其它作者,一般均将随机理论建立在Eshelby的等效夹杂原理之上,而这里是建立在Kunin的微结构理论基础之上。作为理论的一个应用,本文对复合材料的有效模量及夹杂内部及周围微观场进行了计算。     

弹性薄板与层状无限非均匀介质的耦联分析

本文采用一维离散、二维解析的半解析单元法研究弹性薄板与无限介质静力相互作用问题,为工程上解决具有复杂材料特性的无限土体介质与明置结构的耦联分析提供一种简便、实用、有效的方法。文中还对耦联问题中介质特性效应、相对刚度效应、板件形状效应、土层深度效应以及非均质性影响等作了较为全面的分析。     

非均匀损伤介质中波传播的数值解

对弹性波在非均匀损伤介质中的传播理论进行了研究。通过将非均匀损伤区域离散成分层均匀的区域,结合相邻区域交界面处的连续条件,推导出了以右行波、左行波为状态向量的波动方程和传递矩阵。对几种非均匀损伤介质中波的传播进行了实例数值计算,并和其解析解的结果进行了比较,讨论了弹性波在非均匀损伤介质中传播的一般性质。     

径向非均匀介质中圆形夹杂的动应力分析

基于复变函数理论,研究了径向非均匀弹性介质中均匀圆夹杂对弹性波的散射问题. 介质的非均匀性体现在介质密度沿着径向按幂函数形式变化且剪切模量是常数. 利用坐标变换法将变系数的非均匀波动方程转为标准亥姆霍兹(Helmholtz) 方程. 在复坐标系下求得非均匀基体和均匀夹杂同时存在的位移和应力表达式. 通过具体算例分析了圆夹杂周边的动应力集中系数(DSCF). 结果表明:基体与夹杂的波数比和剪切模量比,基体的参考波数和非均匀参数对动应力集中有较大的影响.      

松质骨弹性模量计算的均匀化方法

对松质骨建立了六种单胞微观结构模型，采用均匀化方法和有限元方法计算松质骨的宏观等效弹性模量。给出了六种单胞模型的松质骨弹性模量与材料密度(体分比）的关系，与实验数据进行了对比，分析了不同微观结构模型在不同骨骼中的应用。结果表明，本文方法及六种单胞模型可以对松质骨微观结构和材料性能进行有效的模拟计算。同时本文又着重对松质骨的宏观等效弹性模量与体分比的指数关系进行了探讨。     

大延伸非均匀介质中地震波全弹性散射理论I-弹性波单次散射理论

所描述的工作聚焦于大延伸非均匀介质中非均匀弹性地震波散射问题的研究。应用Born近似及等效源原理,推出了来自连续横向无界非均匀层的弹性散射波的通解。这一工作是解决大延伸非均匀介质的弹性地震波多次散射问题的基础。在上述通解的基础上,建立了适用于大延伸非均匀介质的全弹性散射理论。该理论可包容小尺度非均匀体,大延伸非均匀介质全弹性波单次弱散射理论及标量波单次弱散射理论,因此可视其为一个更为广义和统一的弱散射理论。     

非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内，通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法，给出了一种计算非均匀吸收同中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型，可模拟任意震源及所产生的各种体波、面波，数值结果表明具有很高的计算精度。     

非均匀介质有限元法

提出适合非均匀介质应力分析的有限元法．文中在有限单元内部采用等参变换方法模拟材料特性的变化，算例表明该法计算效率高，计算精度好．     

非均匀调制随机激励下系统的非平稳响应分析

基于时域复模态分析，提出一种非均匀调制随机激励下系统非平稳响应特性的解析解法，用Ｎｉｉｇａｔａ地震激励模型作了说明．算例与仿真结果吻合良好．     

M积分与夹杂/缺陷弹性模量的显式关系

M积分在材料构型力学中表征着缺陷自相似扩展的能量释放率,而有效弹性模量下降量在传统损伤力学中是一个具有内变量属性的损伤参数. 探讨了两者之间的特定关系,以此为材料构型力学与损伤力学搭建桥梁.借助穆斯海里什维利（Muskhelishvili）复势函数方法获取无限大弹性平面含圆形夹杂的弹性场解,根据M 积分的复势函数解析表达式得到M 积分与夹杂弹性模量的显式表达式. 随后通过有限元分析,对含复杂缺陷群的弹塑性材料进行数值模拟,结果表明内部缺陷区域的有效弹性模量下降与M 积分存在着特定关系. 基于此,提出利用材料构型力学中的外变量参数（M 积分）来替代损伤力学中的内变量参数（弹性模量下降量）描述材料的缺陷演化.      

Bounds for the Effective Elastic Properties of Completely Random Planar Polycrystals

Bounds have been developed for the elastic moduli of completely random planar polycrystals, the shape and crystalline orientations of the constituent grains of which are supposed to be uncorrelated. Explicit results for the aggregates of orthotropic crystals are demonstrated. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Existence of Longitudinal Plane Waves in General Elastic Anisotropic Media

We give a new proof of Kolodner's result that longitudinal waves can propagate in at least three directions in a hyperelastic anisotropic medium. We give examples of an orthotropic hyperelastic tensor with exactly three such directions, of a monoclinic elastic (but not hyperelastic) tensor with only one, and of a monoclinic elastic (elliptic, but not uniformly elliptic) tensor with no direction for longitudinal waves. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effective elastic moduli of an inhomogeneous medium with cracks

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material. The project supported by the National Education Committee for Doctor     

Propagation of Elastic Waves in Periodically Inhomogeneous Media

The structural theory of waves and vibrations in periodically inhomogeneous media is set out. Relevant research results are presented. Emphasis is on the principles of the theory, surface waves, and other surface effects     

Prediction of the overall moduli of a cylindrical short-fiber reinforced composite

With respect to obtaining the effective elastic moduli of the composite, the present theory differs from both Eshelby's equivalent inclusion method and Hill's self-consistent one, both of which only consider the mechanical properties of the matrix and inclusions (fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes, sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others^[7,8]. Finally, numerical results are given.     

拉压不同弹性模量薄板上圆孔的应力分析

采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题．采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式．算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算．     

不同模量壳体理论广义弹性定律的普遍表达式

本文研究了拉伸和压缩不同模量材料制成的壳体弱矩理论的本构关系,导出了广义弹性定律的普遍表达式,即中曲面法向坐标的各任意幂次项系数的公式,并指出文献[1]中最终公式保留的线性项,仅为本文普遍表达式的一个较简单的特殊情形,因此,可以不顾文献[1]中关于应力沿壳厚按线性规律变化的基本假设。     

多圆形刚性夹杂的反平面问题

构造任意分布且相互影响的多个圆形刚性夹杂模型的复应力函数，采用复变函数方法，达到满足各个夹杂的边界条件，利用坐标变换和围线积分将求解方程组化为线性代数方程组，推导出了圆形刚性夹杂任意分布的界面应力解析表达式，算例对多夹杂与单夹杂两种模型的界面应力最大值进行了对比，同时还给出了界面应力最大值随夹杂间距的变化规律，求出了刚性夹杂的合理间距。本文发展的分析方法为研究夹杂材料的细观机理探索了一条有效的分析途径。     

Effective elastic moduli of inhomogeneous solids by embedded cell model

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites. The project supported by the National Natural Science Foundation of China (No. 19704100) and the National Natural Science Foundation of Chinese Academy of Sciences (No. KJ951-1-201)     

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

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