黏弹性界面断裂分析的增量“加料”有限元法

提出了一种适用于黏弹性界面裂纹问题的增量“加料” 有限元方法. 利用弹性界面裂纹尖端位移场的解答,通过对应原理和拉普拉斯逆变换近似方法,得到了黏弹性界面裂纹的尖端位移场. 用该位移场构造了黏弹性界面裂纹“加料” 单元和过渡单元位移模式,推导了增量“加料” 有限元方程,求解有限元方程可获得应力强度因子和应变能释放率等断裂参量. 建立了典型黏弹性界面裂纹平面问题“加料” 有限元模型,计算结果表明,对于弹性/黏弹性界面裂纹和黏弹性/黏弹性界面裂纹,该方法都能得到相当精确地断裂参量,并能很好地反映蠕变和松弛特性,可推广应用于黏弹性界面断裂问题的计算分析.     

一维六方准晶弹性层合悬臂梁的解析解

论文利用一维六方准晶的平面本构关系,以及简化为平面问题的物理方程,在悬臂梁的弹性应力解的基础上,假设准晶层和弹性层的应力分布,求出了各自的位移表达式,再利用层间连续条件和放松的边界条件,推导出一维六方准晶层合悬臂梁仅在自由端受集中力作用下声子场和相位子场的位移解析解,为研究准晶涂层材料的力学性质提供参考.     

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。     

分数阶理论下实心球体受热冲击作用的渐进分析

基于分数阶广义热弹性理论,针对实心球体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征,借助于Laplace 正、反变换技术及柱函数的渐进性质,推导了热冲击作用周期内位移场、温度场和应力场的渐进表达式. 通过计算,得到了不同传热能力下受热冲击作用时热波、热弹性的传播规律以及位移场、温度场及应力场的分布规律. 结果表明：分数阶参数取值的不同,热波、热弹性波的传播以及各物理场的分布均有所不同,分数阶参数可视为延迟时间的影响因子,通过改变延迟效应对热弹性行为的影响来改变热冲击的作用效果.     

Winkler地基内磁弹性梁精化理论

结合磁弹性梁和Winkler地基梁精化理论,从线性磁弹性通解出发,利用Lur’e调和函数算子获得了由梁的中线位移、位移梯度和中线上磁场扰动量表示的位移场和应力场;由Winkler地基边界条件和磁场边界条件获得精化理论方程。将应力场分解为关于中线对称和反对称两部分,由反对称部分获得Winkler地基内磁弹性梁的精确挠度方程,磁应力场的对称部分可以分解为纯磁场作用、单向拉伸和超越三部分。     

含有多个涂层压电纤维复合材料的平面问题研究

压电纤维在未来的复合材料结构健康监测中具有重要作用.本文基于横观各向同性压电材料位移和应力连续条件以及经典的复势函数理论,讨论了同时受到平面内机械载荷和出平面电载荷作用时含有多个带涂层压电纤维的无限大线弹性基体的平面力学问题.首先将线弹性基体、涂层和压电纤维的应力场、位移场表示成复势函数,然后通过横观各向同性压电材料和线弹性材料的位移和应力连续条件确定复势函数表达式.将得到的复势函数表达式代入线弹性基体、涂层和压电纤维的的应力场、位移场公式可确定其应力场和位移场.最后,通过定量的案例讨论了涂层的材料属性对线弹性基体应力场的影响.案例分析表明涂层的材料属性对压电复合材料的应力场有重要的影响.     

热释电材料问题的通解与界面裂纹

该文讨论了热释电材料中的热弹性问题的一般解，进而求解了共线界面裂纹问题．利用Ｓｔｒｏｈ方法，把热释电材料的热弹性界面裂纹问题化为一向量形式的Ｈｉｌｂｅｒｔ问题，求出这一Ｈｉｌｂｅｒｔ问题的通解，进而求得了热释电材料热弹性界面裂纹的闭合解，得到了温度、热流、位移、电势、应力和电位移的全场解，得到了裂纹张开位移及电势差的精确表达式．在此基础上，还求得了均匀热释电体中单个热弹性裂纹裂尖场，单个界面裂纹裂尖场以及点热源与界面裂纹的作用．此外，该文还对界面裂纹顶点附近的端部场作了渐近分析．     

平板裂纹前缘三维效应区的弹性力学分析

本文利用Kane和Mindlin关于弹性乎板面内问题位移的基本假设及Fourier变换求解了无限大板的I型裂纹问题,得到了裂纹尖端应力位移场的渐近形式、应力强度因子随板厚的变化规律以及板厚对裂纹前缘三维效应区的影响.研究表明,对线性硬化材料,在塑性切线胰量不太小的情况下,线弹性分析的结果可近似适用于弹塑性材料.     

加层半空间硬币形(Penny—Shaped)交界裂纹的弹性波散射——远场散射波导分析

本文研究了加层半空间硬币形交界裂纹的弹性波散射。文中采用Hankel积分变换,将散射问题转化为求解对偶积分方程,进而变换为奇异积分方程组.应用积分变换,围道积分技术和渐近分析方法,得到了弹性层中散射位移场的远场模式,理论分析表明弹性层中的散射位移场主要由RayLeigh-Like-Mode波组成,该波是弹性层中的散射波导.最后,给出两组弹性常数组合情形下的数值结果及讨论.     

十次对称二维准晶材料的位错动力学问题

论文采用Bak准晶弹性动力学模型研究了十次对称二维准晶材料的位错动力学问题.将Stroh公式推广到了准晶材料动力学问题的研究中,给出了位移和应力一般解的表达式.讨论了位错移动速度、声子场和相位子场耦合弹性常数R对声子场、相位子场位移和应力的影响.     

压电陶瓷中圆币形裂纹在横向剪力下的机－电耦合行为

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。     

ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

I.IntroductionTheplatestructuresonelasticfoundationareofpracticalimportanceinwide-spreadapplicationsinengineering.Basedonrapidprogressofscienceandtechnologyaswellasengineeringconstructions,differentmodelsofeIasticfoundationaredeve1oped,sucha,Winkler,Vlazo…     

Wave propagation through an interface between viscoelastic media in the presence of defects

The propagation of plane harmonic waves through an interface between viscoelastic media is considered using the equations of field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. The reflection and refraction coefficients of elastic displacement waves and the waves of a defect field characterized by a dislocation density tensor and a defect flux tensor are determined. Dependences of the obtained quantities on the parameters of the interfacing media are analyzed.     

An integral equations method for solving the problem of a plane crack of arbitrary shape

The problem of a plane crack of arbibrary shape, subjected to arbitrary loading, is studied. The displacement field is represented by two elastic potentials, the single-layer and the double-layer potential of the second kind. The equations for the crack displacement discontinuities are derived. An approximate analysis of the crack opening displacement under pressure is discussed.     

A Boussinesq–Cerruti Solution Set for Constant and Linear Distribution of Normal and Tangential Load over a Triangular Area

Starting from the elastic solution to a concentrated load on an elastic half space, this paper derives all the required Boussinesq–Cerruti equations for constant, linear and bilinear distributions of normal and tangential load over a triangle area, and presents a solution set to the equations. The surface displacement field in both the normal and tangential direction is obtained. The evaluations of Boussinesq–Cerruti equations are achieved by using various integration techniques. This paper also suggests a composition methodology to construct the solution due to more complicated loading profiles using the principle of superposition.     

Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy

Based on the basic equations for axisymmetric problems of transversely isotropic elastic materials, the displacement components are expressed in terms of polynomials of the radial coordinate with the five involved coefficients, named as displacement functions in this paper, being undetermined functions of the axial (thickness) coordinate. Five equations governing the displacement functions are then derived. It is shown that the displacement functions can be found through progressive integration by incorporating the boundary conditions. Thus a three-dimensional analytical solution is obtained for a transversely isotropic functionally graded disc rotating at a constant angular velocity.The solution can be degenerated into that for an isotropic functionally graded rotating disc. A prominent feature of this solution is that the material properties can be arbitrary functions of the axial coordinate. Thus, the solution for a homogeneous transversely isotropic rotating disc is just a special case that can be easily derived. An example is finally considered for a special functionally graded material, and numerical results shows that the material inhomogeneity has a remarkable effect on the elastic field.     

两微极磁热弹性固体分界面上波的反射与折射

给出了磁场、热场和弹性场多场耦合作用下微极广义热弹性固体的一般控制方程.该方 程既包含了磁场、热场和弹性场的耦合作用,又在其广义热传导方程中涵盖了耦合热弹理论 (C-D)及其5类推广(L-S理论,G-L理论,G-N(II,III)理论和C-T理论).运用该微极广义磁热 弹性控制方程,研究了在定常磁场作用下, 具有均匀初始温度的两理想接触微极弹性介质平面分界面上磁热弹性波的反射和折射现象.给出了分别在缺少磁场、热场作用或不同广义热传 导理论下反射或折射热波、纵向位移波、耦合横向和微旋转波与入射纵向位移波的振幅比随 入射角变化的关系曲线.对缺少磁、热和微极性以及热松弛时间时对应的反射、折射系数进 行了对比.结果表明磁、热和微极性以及热松弛时间对振幅比均有不同程度的影 响,与磁、热和微极性一样,热松弛时间对不同类型波的影响能力差别明显,但对同 一类型的反射波和折射波的影响相似.     

Scattering far field solution of SH-wave by movable rigid cylindrical interface inclusion

The Green's function is used to solve the scattering far field solution of SH-wave by a movable rigid cylindrical interface inclusion in a linear elastic body. First, a suitable Green's function is developed, which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylindrical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface. By using the Green's function, a series of Fredholm integral equations of the first kind which determine the scattering far field can be set up. Then the paper gives the expressions on the far field including the displacement mode of scattering wave and the solution of scattering cross-section. Finally, some examples and numerical results are discussed to analyze the influence of the combination of different media parameters on the answer of far field.     

Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Plate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate. These plate equations are here evaluated by the consideration of a time harmonic 2D vibration problem with finite layers. The boundary conditions at the sides of the layers then have to be considered. Numerical comparisons of the displacement field are made with solutions from two other theories; a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on Fourier series expansions. The two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates.     

On bounds for primary creep in symmetric pressure vessels

The field equations governing primary creep in spherical and incompressible cylindrical pressure vessels subject to a non-decreasing internal pressure are reduced to a single equation in the effective stress. The effects of elastic strains are included. Using this equation, bounds and monotonicity properties are established for the effective stress at any point in the body at any time. It is also shown that these results imply upper and lower bounds for the displacement. These bounds are stated explicitly for the displacement of the outer surface of the vessel.