3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.

INTERFACIAL CRACK ANALYSIS IN THREE-DIMENSIONAL TRANSVERSELY ISOTROPIC BI-MATERIALS BY BOUNDARY INTEGRAL EQUATION METHOD

The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

TRANSVERSELY ISOTROPIC HYPER-ELASTIC MATERIAL RECTANGULAR PLATE WITH VOIDS UNDER A UNIAXIAL EXTENSION

The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.

A PENNY-SHAPED CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SOLID:MODES Ⅱ AND Ⅲ PROBLEMS

An exact analysis of the modes Ⅱ and Ⅲ problems of a penny- shaped crack in a transversely isotropic piezoelectric medium is performed in this paper.The potential theory method is employed based on the general solution of three-dimensional piezoelasticity and the four harmonics involved are represented by one complex potential.Previous results in potential theory are then utilized to obtain the exact solution that is expressed in terms of elementary functions.Comparison is made between the current results with those published and good agreement is obtained.

TORSIONAL OSCILLATION OF RIGID DISK IN INFINITE TRANSVERSELY ISOTROPIC ELASTIC CYLINDER

In the present analysis torsional oscillation of a rigid disk in an infinite transversely isotropic elastic cylinder is considered. The effects of anisotropy in the stress intensity factor are shown graphically.

DERIVATION OF THE GENERAL FORM OF ELASTICITY TENSOR OF THE TRANSVERSE ISOTROPIC MATERIAL BY TENSOR DERIVATE

In the paper the elasticity tensor and the relation between stress and strain of transverse isotropic material and isotropic material are deduced by tensor derivate. From the derivation the reason why there are two independent elasticity coefficients for isotropic elastic material and five for transverse isotropic elastic material can be seen more clearly.

Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces

This paper deals with a two-dimensional （2D） problem for a transverselyisotropic thick plate having heat sources and body forces. The upper surface of the plate is stress free with the prescribed surface temperature, while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The study is carried out in the context of the generalized thermoelasticity proposed by Green and Naghdi. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying the Laplace and Fourier transforms. The inversion of the double transform is done numerically. Numerical inversion of the Laplace transform is done based on the Fourier series expansion. Numerical computations are carried out for magnesium （Mg）, and the results are presented graphically. The results for an isotropic material （Cu） are obtained numerically and presented graphically to be compared with those of a transversely isotropic material （Mg）. The effect of the body forces is also studied.

Asymmetric Green's functions for exponentially graded transversely isotropic substrate–coating system

By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations.The formulation includes a complete set of transformed stress–potential and displacement–potential relations,with utilizing Fourier series and Hankel transforms.As illustrations,the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions.Because of complicated integrand functions,the integrals are evaluated numerically and for numerical computation of the integrals,a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration.Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions.Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.

A Model for Mechanical Property Evaluation of the Periodic Porous Low-k Materials by SAW

The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.

On the material constants measurement method of a fluid-saturated transversely isotropic poroelastic medium

The fluid-saturated transversely isotropic poroelastic medium could be widely found in nature, e.g., the sedimentary rocks underground. To determine the eight independent material constants for the transversely isotropic poroelastic medium, a series of tests are discussed. Two undrained tests and one drained test are suggested as a set of tests of the least amount. For the verification purpose, two additional drained tests are also introduced as an option. The atmospheric dried test is discussed as a replacement of the traditional infiltrated drained test to save the time waiting for an equilibrium state. Some microscopic material constants, i.e.,the unjacketed bulk coefficients, the porosity, and the compressibility of porous fluid, are measurable but unnecessary to determine the independent material constants of a poroelastic medium.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

基于等效横观各向同性虚拟材料的固定结合部建模方法

为提高固定结合部的建模精度以及通用性,考虑固定结合部在法向和切向的不同特性,提出利用横观各向同性虚拟材料等效的固定结合部动力学参数化建模方法,将固定结合部两接触面的微观接触部分等效为一种等截面的横观各向同性虚拟材料,等效虚拟材料与两侧零件均为固定连接。基于接触分形理论和固定结合部接触刚度分形模型,根据横观各向同性材料弹性常数的定义,理论推导了等效虚拟材料弹性常数以及密度的理论计算模型。在此基础上,对具有固定结合部的试验模型进行了有限元建模与模态分析,进而将理论分析模态与试验模态进行比较,结果表明:试验模型的理论模态与实验模态的前6阶振型完全一致,相应固有频率的相对误差的绝对值在10%以内,说明了建模方法的正确有效性,为数控机床固定结合部动力学建模提供了一种新的方法,实现了固定结合部动力学建模与有限元分析软件的无缝衔接集成。

群桩基础的复合体模型建立与应用

在进行建筑物的上下部共同作用研究中,有限元法是一种非常重要的分析手段,但由于需要离散的区域很大,将桩和土体分别划分单元,所需要的单元数量巨大,常常会因受到计算机软件或硬件的限制,分析难以进行。本文按照复合材料力学的处理方法将群桩基础中桩—土体系作等效连续化处理,视为横观各向同性体,建立了桩土等效复合体的本构关系;按“分离模式”和“复合模式”两种情况进行了有限元对比分析,结果表明,等效复合体模型很好地反映出群桩基础的传力机理,对大型群桩基础进行等效连续化处理是完全可行的。采用本文建立的等效复合体模型,可大幅度减少下部基础单元的数量,提高了用有限元法研究建筑物的上下部共同作用的可操作性。

薄层单元基本假设和简化探讨

对薄层单元的基本假设和简化进行了探讨并得到如下结论:薄层单元的本构方程可通过横现各向同性体本构方程采用合理简化得到;薄层单元受拉开裂的本构关系可采用分布裂缝模型模拟开裂简化得到;薄层单元采用的基本假设能在一定程度上保证计算精度及简化计算.

横观各向同性材料中激光超声谱有限元数值模拟

研究了横观各向同性材料中激光超声波的传播特征.基于谱有限元方法,建立了横观各向同性材料中激光超声的数值模型.利用谱有限元方法模拟脉冲激光作用于材料上产生超声波及其传播的过程.讨论了横观各向同性薄板的各向异性及各向同性平面内超声波的传播特征,并分析了材料厚度的变化对产生超声波模态的影响.

横观各向同性压电矩形薄板的非线性振动

由于压电材料在航空航天轻形结构动力控制中的广泛应用 ,压电结构的非线性机理成为工程界急需解决的问题。为了拓广压电结构的理论基础 ,本文对于横观各向同性压电矩形薄板 ,给出了大挠度条件下的应变位移关系 ,利用 Hamilton原理导出了压电矩形薄板的非线性振动方程 ,并用双重 Fourier级数展开和 Galerkin方法获得四边简支压电矩形薄板非线性自由振动的解析解 ,分析了材料参数和几何参数对振动特性的影响。

三维横观各向同性介质界面裂纹的边界积分方程方法

基于两相三维横观各向同性介质的基本解和Somigliana恒等式,对三维横观各向同性介质中的任意形状的平片界面裂纹,以裂纹面上的不连续位移为待求参量建立了超奇异积分_微分方程,界面平行于横观各向同性面.根据发散积分的有限部积分理论,应用积分方程方法研究得到裂纹前沿的位移和应力场的表达式、奇性指数以及应力强度因子的不连续位移表达式.在非震荡情形下,超奇异积分_微分方程退化为超奇异积分方程,与均匀介质的超奇异积分方程形式完全相同.

层状地质材料弹性张量求解及应用

有效弹性张量的确定是土木工程研究者一个重要课题,正确决定宏观有效弹性张量往往是计算结果是否成功的关键。现行主要流行的方法主要有:对弹性张量各元素采用简单体积平均法(方法一)、自洽法(方法二)、Hashin-Strikman法上限(方法三)和Hashin-Strikman法下限(方法四)。利用均匀化技术,在横观各向同性成层地质材料满足位移和应力相等的条件下,获得了宏观弹性张量的具体表达形式(方法五)。在特殊条件下,该表达方程可以简化为自洽法和简单的体积平均法。在实例和应用研究的基础上,对5种方法进行了对比分析。研究结果表明,所提出的方法可以综合描述平行流模型和系列流模型,且弹性张量各组成部分上、下限值不是Hashin-Strikman上下限法所指定的范围,其下限应为自洽法的结果;除元素Ceff1133外,其上限应为Hashin-Strikman上限法结果。这种研究对边坡、坝基等土木工程的计算和分析具有重要作用。