COMPLETE EIGEN-SOLUTIONS FOR ANTI-PLANE NOTCHES WITH MULTI-MATERIALS BY SUPER-INVERSE ITERATION

In this paper,the super-inverse iterative method is proposed to compute the accurateand complete eigen-solutions for anti-plane cracks/notches with multi-materials,arbitrary opening an-gles and various surface conditions.Taking the advantage of the knowledge of the variation forms ofthe eigen-functions,a series of numerical techniques are proposed to simplify the computation andspeed up the convergence rate of the inverse iteration.A number of numerical examples are given todemonstrate the excellent accuracy,efficiency and reliability of the proposed approach.     

圆形刚性夹杂双周期分布的反平面问题

研究含双周期分布的圆形刚性夹杂在无穷远受纵向剪切的弹性平面问题，遵循复合材料中各夹杂相互影响的重要条件。采用复变函数方法。构造相应模型的复应力函数。通过坐标变换，同时满足夹杂边界位移条件，再利用围线积分将求争方程组化为线性代数方程组。导出了圆形刚性夹杂双周期分布的界面应力解析表达式。算例给出了界面应力最大值与夹杂间距的变化规律。求出了刚性夹杂的合理间距问题，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。     

颗粒增强复合材料的椭圆形刚性夹杂呈双周期分布模型的反平面问题研究

在遵循复合材料中各夹杂相互影响的重要条件下，构造呈双周期分布且相互影响的椭圆形刚性夹杂模型的复应力函数，采用坐标变换和复变函数的依次保角映射方法，达到满足各个夹杂的边界条件，利用围线积分将求解方程化为线性代数方程，推导出了在无穷远双向均匀剪切，椭圆形刚性夹杂呈双周期分布的界面应力解析表达式，最后的算例分析给出了夹杂的形状对界面应力最大值(应力集中系数)的影响规律，并描绘出了曲线。     

非均匀弹性材料中反平面的运动裂纹

用解析方法研究了非均匀弹性材料中反平面运动裂纹问题。首先采用余弦变换求解非均匀材料的基本方程，然后根据混合边值条件建立裂纹运动的对偶积分方程，再把对偶积分方程化为第二类Fredholm积分方程。给出了数值算例，计算结果表明材料的非均匀性对动应力强度因子有较大的影响。     

有限元离散模型中的出平面波动

采用分离变量技术,将二维出平面(Anti-Plane)波动问题的有限元运动方程化为两个联立的一维方程,获得了这一离散模型中波动的解析解,由此对有限元离散模型中出平面波动问题进行了深入的研究。分析了出平面弹性波的频散、截止频率、寄生振荡和有限元离散化引起的波传播的附加的各向异性性质等,同时讨论了时域离散化对出平面波动规律的影响。     

End Effects for Anti-Plane Shear Deformations of Periodically Laminated STrips with Imperfect Bonding

The axial decay of Saint-Venant end effects is investigated for anti-plane shear deformations of semi-infinite generally laminated anisotropic strips. Imperfect bonding conditions are imposed at the interfaces. The analytical approach, using a displacement field which decays exponentially in the axial direction, gives rise to a transcendental equation for the real eigenvalues. The decay rate for the stresses is given in terms of the smallest positive eigenvalue. Laminated strips with periodic layout are then considered. In the presence of imperfect bonding, the effective shear elastic moduli, computed through a homogenization method, depend on the total number of slipping interfaces in the laminate. Numerical examples confirm that the decay lengths computed with effective shear moduli represent the asymptotic values (for an increasing number of layers) for those of periodically laminated strips. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Function of region

The purpose of this paper is to extend points function and interval functions theoretics to an arbitrary region. For this, the new theory, the contraction of a region, and the retraction of a region; the extension of a region, and the kernel-preserving extension of a region are established by the author. Starting from these concepts, the new definitions of a region function is given. And a kernel (i.e. fixed point) of a region function is connected with a stable centre of defining region of such a region function. Thereby, the region theoretics and algorithms are established.In applications, to find a stable centre of a region, the author has utilized the measure theoretics of matrice defined by Hartfiel⁽⁷⁾ and other authors. The measure problems of coefficient matrice of system of equations of linear algebra associated with some region are discussed.     

Solid mechanics of discrete form and the variational principles of the discontinuous form

This paper discusses the fundamental assumptions,the differen-tial equations,and the variational principles of discontinuousform belonging to a new developing branch of science-the solidmechanics of discrete form.The solid mechanics of discrete formbelongs to the branch of science of discrete medium mechanicswhich is the developing direction of the mechanics for the pre-sent.Based on the solid system with discretization and sepa-rability,the unknown functions with discontinuity in definedregions and the defined regions with variable boundaries,themechanics systems to solve the solid displacements,strains andstresses in various cases are called the solid mechanics of dis-crete form.when the unknown functions are sufficiently smooth func-tions in the whole defined region and the effects of the vari-able boundaries are disregarded,the solid mechanics of discreteform will degenerate into the classical solid mechanics belong-ing to continuum.mechanics:Its variational principles will de-generate into the clas