横观各向同性弹性地基塞露蒂问题的解析解

根据横观各向同性弹性体半空间问题的基本方程,利用Hankel变换和Bessel函数理论,基于位移法导出的横观各向同性地基空间问题的一般解,得到了材料特征根不相等情况下横观各向同性地基塞露蒂(Cerruti)半空间问题的基本解。该解答经过退化与各向同性Cerruti问题的经典解相吻合。通过算例对两种不同地基内部位移和应力分布进行了对比分析。结果表明,对于给定的算例,两种地基内部沿深度方向的位移分布基本相同,但两种地基内部应力场的差异比较显著。     

任意荷载作用下层状横观各向同性弹性地基的直角坐标解

首次建立了在直角坐标系下层状地基力学问题的通用解法,改变了过去仅能在柱坐标系下进行求解此类的状况。首先将坐标系的原点选在荷载影响范围以外足够远处,从直角坐标系下的横观各向同性弹性问题的基本方程出发,利用Laplace变换及其微分性质,建立了单层横观各向同性弹性地基的状态控制方程,并利用状态空间理论给出了单层地基的解答。然后再利用传递矩阵技术,给出了任意荷载作用下的层状横观各向同性弹性地基的解析解。用提供的方法求解层状横观各向同性地基的非轴对称问题比在极坐标下求解简单、快捷。     

横观各向同性土介质与结构物共同作用的有限元与边界元耦合分析

本文采用有限元与边界元耦合方法对上与结构物进行共同作用的分析．其中上部结构采用有限元子结构法，地基上考虑为横观各向同性特性，应用边界元法，通过基础界面上位移连续、面力平衡的条件进行耦合分析．编制了相应的计算程序，对某高层空间剪力培与地基的共同作用进行了计算，与有限元法和实测结果进行了对比分析，得到了满意的结果．说明：有限元和边界元的耦合方法能充分发挥两者的优越性，不失为共同作用分析的一种有效途径．     

几种常见荷载作用下横观各向同性地基轴对称问题的解析解

通过对各向同性弹性体力学中拉甫位移函数重新修正,应用位移解法,利用Hankel积分变换理论,在象域内得到横观各向同性地基的通解,运用汉克尔积分反演变换得到了半无限地基在几种常见荷载(圆形均布、集中力、刚性承载板)作用下的应力和位移解析解,并给出了数值计算结果。     

层状横观各向同性地基性质对刚性条基摇摆振动的影响

分析了土体的横观各向同性及层状性质对刚性条形基础摇摆振动的影响。首先利用解析层元法得出层状横观各向同性地基的总刚度矩阵。再根据刚性条形基础与地基相互作用的混合边值条件,建立了一组对偶积分方程,并借助Jacobi正交多项式求解了该对偶积分方程,从而得到地基动力柔度系数。计算结果与已有文献的结果吻合较好。同时,算例结果表明:土的水平向与竖向弹性模量比的减小、竖向的剪切模量与弹性模量比的增大,以及水平向泊松比与竖向泊松比比值的增大,都将导致地基动力柔度系数增大;而且,层状地基中上层土的弹性模量的减小使得地基动力柔度系数也增大。     

双层横观各向同性圆柱壳体的弹性理论解

本文是在文献[10]的基础上,进一步分析了双层横观各向同性圆柱壳体在承受轴对称分布载荷时的三维弹性理论解。文中假定壳体的两端为简单支承,研究了壳体的物理参数与几何参数对层间应力分布的影响。本文还给出了双层横观各向同性圆柱壳体在有横向均布压力与轴向等应变(ε₀)拉伸同时作用下的数值计算结果。     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程并得到传递矩阵。进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题。数值算例表明采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的动力特性。     

关于横观各向同性体在其各向同性面内弹性问题的一个常数

研究了在平面应力和平面应变情况下, 横观各向同性材料在其各向同性面内的应力2应变关系以及用位移表达的平衡方程可以被表示成与各向同性材料完全相同的形式。这种等同关系是通过引入一个与横观各向同性材料的泊松比有关的常数得到的。该常数的引入消除了已发表的文献中求解横观各向同性材料平面问题时出现的矛盾。这个常数的引入也便于正确计算单向纤维增强复合材料的横向切变模量。      

高铁荷载下横观各向同性CFG桩桩土复合路基减振特性研究EI北大核心CSCD

基于2.5D有限元法基本原理,推导横观各向同性地基2.5D有限元控制方程,利用等代桩墙对水泥粉煤灰碎石(cement fly-ash gravel, CFG)桩桩土复合路基进行简化,建立高铁荷载下横观各向同性CFG桩桩土复合路基2.5D有限元分析模型。考虑不同车速,分析横观各向同性地基土体刚度比n对高铁荷载下地面振动的影响,研究CFG桩桩土复合路基的减振机理,探讨桩径、桩间距、面积置换率m对其减振特性的影响。结果表明:高铁荷载下地面振动随横观各向同性地基土体刚度比n的提高而减小;CFG桩能更多地将高铁运行引起的动荷载沿深度方向传导至复合路基深处,从而显著减小地面振动,且减振效果随与轨道中心距离逐渐增强;CFG桩桩土复合路基的减振效果随桩径增大或桩间距减小而增强,当桩径大于等于0.5 m或桩间距小于等于4倍桩径时,进一步增大桩径或缩短桩间距难以显著提高减振效果;振动衰减系数FVR随CFG桩桩土复合路基面积置换率m的增大而减小,当面积置换率m≥0.06时,继续增大面积置换率m对减振效果的影响较小。     

等效介质理论数值法计算复合材料的热膨胀系数

本文用一套等效介质理论的数值方法计算了球状微粒掺杂之各向同性复合材料及单向纤维增强之横观各向同性复合材料之线热膨胀系数,得到合理的结果,并与Schapery式、Kerner式之计算及实验值作出比较,显示了等效介质理论于复合材料热弹性能计算之适用性.      

A soil damage model expressed by a double scalar and its applications

Poroelasticity refers to the study of the mechanics of porous elastic materials that are saturated with compressible or incompressible fluids. When considering saturated poroelastic geomaterials, their consolidation response can be influenced by the evolution of damage in the porous skeleton. The objective of this paper is to examine the problem of consolidation response of damage-susceptible poroelastic geomaterials. Firstly, a new constitutive model of soft soils expressed by isotropic double scalar damage variables is developed and incorporated into Biot’s consolidation finite element equations via EDAPD program. Then, the EDAPD program is applied to analyze a soft subgrade reinforced by surcharge preloading technology. The comparison between the numerical predictions and the experimental data shows that the isotropic double scalar damage model presented in this paper is effective and feasible in analyzing the consolidation problem of damaged porous media.     

Stress in Thin Films;Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transvers isotropy is expected,owing to the limited dimenionlity .The usually applied models for the calculation of elstic constants of polycrystals from single crystal elastic contants(so-called grain interaction models)erroneously predict macroscopic isotropy for an(untextured) thin film.This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically anisotropic behaviour (shown by non-linear sin^2φ plots).A new grain interaction model,predictin the macroscopically anisotropic behaviour of thin films,is proposed.     

Effect of Constitutive Parameters on Cavity Formation and Growth in a Class of Incompressible Transversely Isotropic Nonlinearly Elastic Solid Spheres

Cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres are described as a bifurcation problem, for which the strain energy density is expressed as a nonlinear function of the invariants of the right Cauchy-Green deformation tensor. A bifurcation equation that describes cavity formation and growth is obtained. Some interesting qualitative properties of the bifurcation equation are presented. In particular, cavitated bifurcation is examined for a solid sphere composed of an incompressible anisotropic Gent-Thomas material model with a transversely isotropy about the radial direction. The effect of constitutive parameters on cavity formation and growth is then carried out. It is proved that a cavity forms in the interior of the sphere earlier or later than that in the isotropic Gent-Thomas sphere as the anisotropic parameter takes certain values. The condition for the bifurcation to the left or to the right of the cavity solution is proposed. The stability and the catastrophe of the equilibrium solutions are discussed by using the minimal potential energy principle. Whereas, in contrast to other isotropic nonlinear elastic spheres, cavitated bifurcation in the isotropic Gent-Thomas sphere is quite different, it is proved that the cavity solution can bifurcate locally to the left. The growth of a pre-existing micro-void in the sphere is examined, which interprets the physical implications of the preceding bifurcation problem.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

On the thermodynamic requirement of elastic stiffness anisotropy in isotropic materials

In general, thermodynamic admissibility requires isotropic materials develop reversible deformation induced anisotropy (RDIA) in their elastic stiffnesses. Taking the elastic potential for an isotropic material to be a function of the strain invariants, isotropy of the elastic stiffness is possible under distortional loading if and only if the bulk modulus is independent of the strain deviator and the shear modulus is constant. Previous investigations of RDIA have been limited to applications in geomechanics where material non-linearity and large deformations are commonly observed. In the current paper, the degree of RDIA in other materials is investigated. It is found that the resultant anisotropy in materials whose strength does not vary appreciably with pressure, such as metals, is negligible, but in materials whose strength does vary with pressure, the degree of RDIA can be significant. Algorithms for incorporating RDIA in a classical elastic-plastic model are provided.     

Ductile penny-shaped crack in a transversely isotropic cylinder

The problem of a penny-shaped crack contained in a transversely isotropic cylinder of elastic perfectly-plastic material is considered for the case when the crack is extended by an axial load. The problem is reduced to solving numerically a Fredholm integral equation of the second kind for the width of the plastic zone. Graphical results are presented showing the effect of transverse isotropy upon the width of the plastic zone and these are compared with the results for isotropic materials.     

A new lamination theory for layered textile composites that account for manufacturing induced effects

This paper is concerned with the development of a new lamination theory for layered textile composites that can account for manufacturing induced effects. The theory can be used for the calculation of the effective linear elastic extensional and bending stiffnesses of laminated textile composite panels. A representative unit cell (RUC) of the textile architecture is first identified along with its constituents. Tow geometry is represented analytically taking account of tow undulation. Each tow is modeled as a transversely isotropic linear elastic solid and the contribution from each tow to the RUC elastic bending stiffness is obtained by volume averaging, taking account of the volume fraction of each constituent. The formulation is amenable to the incorporation of geometric changes to the textile architecture that occurs through manufacturing induced consolidation. Predictions of the elastic bending stiffness are compared against experimental data, showing a strong correlation between the analytical model and the experimental results.     

Green's functions for the isotropic or transversely isotropic space containing a circular crack

Summary Green's functions for an infinite three-dimensional elastic solid containing a circular crack are derived in terms of integrals of elementary functions. The solid is assumed to be either isotropic or transversely isotropic (with the crack being parallel to the plane isotropy).     

The influence of elastic anisotropy on the propagation of fracture

The model of a propagating crack introduced by Craggs for an isotropic solid is extended to the case of general elastic anisotropy. The general theory for propagation under tensile or shear stresses is derived. As for most two dimensional problems in anisotropic elasticity, the solution involves the roots of a sixth degree polynomial so that it is necessary to proceed numerically at some stages. A computer program has been written to do this. This is used to show that the shape of the square cracks which are produced in the interior of silicon-iron by the internal pressure of electrolytic hydrogen may be due to elastic anisotropy. On this basis, predictions can be made as to the shape of cracks in other metals, in particular molybdenum, vanadium and tantalum. These metals are representative of the four combinations of fracture plane and deviation from isotropy. Explicit formulae are given for the special orientations where the sixth degree polynomial can be explicitly factorized.     

Elastic properties of powders during compaction. Part 2: elastic anisotropy

Isotropy in the elastic properties of powders undergoing uniaxial compaction in a cylindrical die was evaluated from in situ measurements of elastic wave speed. Shear and bulk longitudinal wave speeds were measured in both the axial (pressing) and radial directions. For the five different metal powders studied, wave speeds were generally higher in the axial direction. As such, the powder body was best described as a transversely isotropic material; complete isotropy was approached only when the powder was close to the loose packed state, or completely solid. Transversely isotropic elastic moduli analogous to the common isotropic ‘engineering’ moduli (Young’s modulus, Poisson’s ratio, etc.) were calculated by combining elastic wave speed measurements with the Saint-Venant approximation. Pseudo-isotropic elastic moduli (calculated from axial wave speed measurements and assuming elastic isotropy) were found to be only qualitatively similar to transversely isotropic elastic moduli for the axial plane.