具裂纹的功能梯度压电压磁复合材料的SH波散射问题

讨论了具裂纹功能梯度压电压磁复合材料的SH波的散射问题,通过Fourier积分变换,把混合边值问题转化为对偶积分方程,并利用Copson方法将时偶积分方程转化为第二类Fredholm积分方程求解,得到了裂纹尖端的应力强度因子、电位移强度因子和磁通量强度因子,最后通过数值计算讨论了材料梯度参数,入射角等因素对标准动应力强度因子的影响．     

SH波在正交各向异性功能梯度材料直裂纹处的散射

研究了正交各向异性功能梯度材料中直裂纹对SH波的散射问题,材料两个方向的剪切模量和密度假定为指数模型,通过积分变换-积分方程方法,建立数学模型,化为对偶积分方程,用Copson方法求解对偶积分方程,最后得到动应力强度因子,并且给出了数值算例,讨论了在SH波作用下,裂纹尖端的动应力强度因子与入射波的频率,入射角的关系．     

具周期裂纹半无限大功能梯度压电材料的热应力分析

讨论了无限长功能梯度压电板中双裂纹尖端热响应分析,用Fourier积分变换把混合边值问题转化为以裂纹面上位移为未知量的对偶积分方程,利用Schmidt方法对其求解,最后通过数值算例考察了温度变化及材料系数对应力强度因子的重要影响.     

各向同性功能梯度材料反平面弹性断裂力学分析

研究了无限大平面各向同性功能梯度材料在反平面剪切荷载作用下裂纹问题。材料剪切模量假定为指数模型,通过采用积分变换和对偶积分方程方法,求得裂纹尖端应力强度因子。结果表明:裂纹尖端应力具有奇异性,材料模量梯度越大,应力强度因子越低。     

弹性材料夹杂含裂纹梯度材料的接触问题

研究弹性材料夹杂含裂纹功能梯度材料的接触问题．利用Fourier积分变换,将问题转化为关于未知位错密度函数的奇异积分方程,再用配点法对奇异积分方程进行数值求解．获得了裂纹尖端标准应力强度因子．数值结果显示了标准应力强度因子与梯度材料非均匀参数、摩擦系数、裂纹长度以及裂纹距刚性压头中心水平距离的关系．     

SH波在功能梯度压电带拼接半无限大压电材料中共线双裂纹处的散射问题

分析了SH波在功能梯度压电带拼接半无限大压电材料中共线双裂纹处的散射,基于功能梯度压电材料参数指数模型,在裂纹面电渗透性边界条件下,利用Fourier积分变换将问题转化成对偶积分方程,并利用Copson方法对问题进行了求解,最后通过数值算例表明了右裂纹尖端的动应力强度因子受波数和梯度参数的影响情况.     

功能梯度材料平面I型裂纹尖端应力场分析

功能梯度材料是一种新型的非均匀材料,因为其材料常数是连续变化的,其力学基本方程和一般的弹性材料不同,断裂问题的求解也比一般弹性材料要复杂的多。结合弹性材料I型裂纹问题的求解,采用指数模型,研究了功能梯度材料平面I型裂纹尖端应力场,首先引入应力函数,将平面I型裂纹问题转化为四阶常系数偏微分方程,然后给出问题的精确解答,讨论了梯度系数和应力强度因子的关系。     

功能梯度材料平面Ⅰ型裂纹尖端应力场分析

功能梯度材料是一种新型的非均匀材料，因为其材料常数是连续变化的，其力学基本方程和一般的弹性材料不同，断裂问题的求解也比一般弹性材料要复杂的多。结合弹性材料Ⅰ型裂纹问题的求解，采用指数模型，研究了功能梯度材料平面Ⅰ型裂纹尖端应力场，首先引人应力函数，将平面Ⅰ型裂纹问题转化为四阶常系数偏微分方程，然后给出问题的精确解答，讨论了梯度系数和应力强度因子的关系。     

含裂纹梯度材料与均匀材料粘接接触问题

基于功能梯度材料和均匀弹性材料本构方程,探讨了含裂纹半无限大功能梯度材料与均匀弹性材料粘接的接触问题.通过借助Fourier变换技术,将所要研究的问题转换为关于未知位错密度函数的奇异积分方程,并把位错密度函数表示为Chebyshev多项式,最终将奇异积分方程转换为线性代数方程组进行配点数值求解.数值结果以图表的形式显示非均匀参数、裂纹几何性对裂纹尖端应力强度因子的影响.     

热机荷载下含梯度涂层的弹性条中裂纹问题(英文)

研究了热机荷载作用下含功能梯度材料涂层的裂纹弹性底层条问题,提出一些新的边界条件,假设裂纹面上的温度降低是由通过裂纹的控制热传导的因子造成,利用傅里叶积分变换,将热弹性混合边值问题转化为一组奇异积分方程,奇异积分方程组可以利用Chebyshev多项式逼近方法近似求解.给出了温度、位移场和热应力强度因子的数值计算方法.通过算例分析了不同几何参数下裂纹表面标准温度的分布,并讨论了裂纹位置和热弹性非均匀参数对Ⅰ、Ⅱ型裂纹尖端标准热应力强度因子的影响.结果表明:弹性底层厚度不变时,梯度涂层厚度对裂纹表面的温度分布有重要的影响;梯度涂层厚度的变化对底层的裂纹有重要的影响.研究结果有助于对梯度涂层结构热机行为的理解.     

Analysis of a functionally graded piezothermoelastic hollow cylinder

INTRODUCTION Piezoelectric symmetric structures always play an important role in the use of piezoelectric materials (Olesiak and Pyryev, 1995; Ding et al., 2003; Wu et al., 2003). To improve the durability of this kind of piezoelectric structures, functionally gradient piezo- electric materials (FGPM) have been developed and used to produce these devices such as sensors and actuators (Hauke et al., 2000; Zhu et al., 1995). For the case when a rectangular plate made of function- ally gr…     

3D thermoelasticity solutions for functionally graded thick plates

Thermal-mechanical behavior of functionally graded thick plates, with one pair of opposite edges simply supported, is investigated based on 3D thermoelasticity. As for the arbitrary boundary conditions, a semi-analytical solution is presented via a hybrid approach combining the state space method and the technique of differential quadrature. The temperature field in the plate is determined according to the steady-state 3D thermal conduction. The Mori-Tanaka method with a power-law volume fraction profile is used to predict the effective material properties including the bulk and shear moduli, while the effective coefficient of thermal expansion and the thermal conductivity are estimated using other micromechanics-based models. To facilitate the implementation of state space analysis through the thickness direction, the approximate laminate model is employed to reduce the inhomogeneous plate into a homogeneous laminate that delivers a state equation with constant coefficients. The present solutions are validated by comparisons with the exact ones for both thin and thick plates. Effects of gradient indices, volume fraction of ceramics, and boundary conditions on the thermomechanical behavior of functionally graded plates are discussed.     

热载荷下梯度结构硬质合金的弹塑性响应

采用有限元方法模拟了热载荷下梯度结构硬质合金的弹塑性响应．样品几何模型为二维梯度结构的轴对称圆柱体．通过引入约束因子构建了梯度材料的弹塑性本构方程．数值模拟表明：当材料温度从初始无应力的800℃下降到0℃时,在样品表面出现了压应力而在富钴区出现了拉应力;表面压应力的最大值为254MPa,富钴区拉应力的最大值为252MPa;在钴相浓度差等于或大于0．3时,钴相梯度区出现了明显的塑性流动;当温度从0℃上升到800℃时,总的塑性应变达到0．0014．塑性流动有利于降低材料内部的热应力集中．     

Thermoelastic stresses in a uniformly heated functionally graded isotropic hollow cylinder

The axisymmetric themoelastic problem of a uniformly heated, functionally graded isotropic hollow cylinder is considered. An analytical form of solution is proposed. For the case when the Young's modulus and thermal expansion coefficient have a power-law dependence on the radial coordinate, explicit exact solution is obtained. For the degenerated case, i.e. when the cylinder is homogeneous and isotropic, no stresses will occur provided it is subjected to a uniform temperature. Numerical results are finally given and some important inclusions are obtained. Project (No.10002016) supported by the National Natural Science Foundation of China (NSFC).     

Optimization design and residual thermal stress analysis of PDC functionally graded materials

INTRODUCTION Polycrystalline diamond compacts (PDC), con-sisting of a polycrystalline diamond (PCD) layer on a WC-Co substrate, and having high hardness and abrasive resistance, are used in a variety of drilling and machining applications (Farhad, 2001; Sadi and Muzaffer, 2001). However, due to differences of thermal and mechanical properties in diamond and WC-Co substrate, residual thermal stresses develop in regions near the interfaces during fabrication. The diamond coating exhib…     

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

INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu…     

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.     

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.     

The analytical solutions for orthotropic cantilever beams (II):Solutions for density functionally graded beams

INTRODUCTION Functionally graded materials (FGM) possesselastic constants and density that vary gradually withlocation within the material. In one kind of FGM,only the elastic constants vary continuously along oneor more directions, and in the other kind, only thedensity varies gradually with location. We call thelater one density functionally graded materials. Functionally graded materials have attractedmuch interest. Tutuncu and Ozturk (2001) obtainedclosed-form solutions…