双材料平面斜裂纹问题超奇异积分方程方法

由双材料平面问题的弹性力学基本解，应用互等功定律和坐标变换，得到双材料平面任意斜裂纹问题位移场及应力分量表达式，经代入裂纹岸应力边界条件，获得以裂纹岸位移间断作为基本未知量的超奇异积分方程组；通过适当的积分变换，用有限部积分原理处理超奇异积分，建立该问题的相应数值算法。文中对任意位置的裂纹问题进行计算，并较为系统地分析界面对裂纹应力强度因子的影响，当裂纹垂直或平行于双材料界面时，计算结果与已有结果一致。     

双材料平面中曲线裂纹问题的超奇异积分方程

基于超奇异积分方程法的基本原理,导出了双材料平面中一般曲线裂纹问题以裂纹岸位移间断为基本未知量的超奇异积分方程组,其奇异积分含一类二阶超奇异积分和一类反映裂纹曲率影响的高斯型奇异积分,正常积分项中也含一类可用幂级数表达的曲率影响项。所得结果使超奇异积分方程法对双材料平面中一般曲线裂纹问题的描述更具一般性。该方程组在曲率半径趋于无穷大和取为定值情况下的退化结果也与关于直线裂纹和圆弧裂纹的已有结果有很好的一致性。针对圆弧裂纹的算例表明,所得方程组适用于曲线裂纹问题的数值计算。     

弹塑性各向异性介质界面断裂的D-B模型

应用傅里叶积分变换方法将裂纹边值问题化为对偶积分方程组，再用逐段积分变换法将问题进一步化为奇异积分方程组，求得双材料各向性弹塑性介质中界面裂纹反平面问题的封闭形式解，并讨论了各向同性问题及单一材料问题。结果表明：裂纹尖端前沿的塑性区尺寸、裂纹的张开位移COD均取决于两种材料流动极限中的较小者及裂纹长度，此外COD还与弹性模量参数有关。     

双相材料平行于界面裂纹问题的超奇异积分方程法

由双相材料平面问题的弹性力学基本解和相应裂纹问题的应力场一般表达式，通过微分运算及极限分析得到平行于界面裂纹问题的超奇异积分方程组，并在有限部积分的意义下建立相应的数值算法，把该问题的计算转化为对一个线性方程组的求解，就典型问题无量纲应力强度因子的计算结果表明，该方法与体力法与边界元分析基本一致。     

三维压电介质界面裂纹的边界积分-微分方程

基于三维两相横观各向同性压电介质的基本解和压电介质的Somigliana恒等式，利用发散积分的有限部理论，建立以裂纹面上的不连续位移和不连续电势为基本未知量的三维压电介质界面裂纹问题的超奇异积分－微分方程组，其中的积分核具有O（1/r^2）阶的奇异性。当两相材料退化为均质材料或单相材料时，方程组中的微分项的系数为零，从而积分－微分方程组退化为已有的均质压电材料的超奇异边界积分方程。     

含共线裂纹功能梯度材料断裂问题分析

应用分层原理分析了具有不同弹性模量含共线双裂纹的功能梯度材料断裂问题。通过积分变换得到嵌入功能梯度材料裂纹的应力场和位移场,结合边界条件、连续条件及单个裂纹的应力场和位移场,将求解该裂纹问题转化为求解奇异积分方程组。通过求解奇异积分方程组得到裂纹的应力强度因子。最后针对材料弹性模量和裂纹几何参数对应力强度因子的影响进行了探讨。结果表明材料弹性模量分布形式对裂纹的应力强度因子影响显著,该结果可为功能梯度材料制备及材料设计等提供理论依据。     

剪切载荷作用下胶接材料界面动应力强度因子的研究

主要研究剪切载荷作用下,胶接材料中弹性和粘弹性界面间Griffith裂纹尖端动态应力强度因子的时间响应.采用积分变换方法,得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式;引入位错密度函数,并通过边界条件和界面连接条件,导出反映裂纹尖端奇异性的奇异积分方程组,采用Gauss积分,并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组,利用配点法进行求解;最后经过Laplace逆变换,求得动态应力强度因子的时间响应.得到Ⅱ型动应力强度因子随着粘弹性材料的剪切松弛参量的增加而增大,膨胀松弛参量的增加而减小;随着弹性材料的剪切模量和泊松比的增加而增大.     

平面六节点等参应力奇异单元的精度研究

研究一种平面六节点应力奇异单元的计算精度问题。首先证明该单元具有1/槡r阶奇异性,然后用此单元计算同质材料中的裂纹和双材料界面裂纹的应力强度因子与裂尖应力分布,讨论裂纹尖端奇异单元的尺寸以及在奇异单元与常规单元之间布置一层过渡单元对精度的影响。研究发现,当布置在裂尖的奇异单元边长与裂纹长度的比值在0.1～0.2时,能得到足够精确的解答;而在此范围之外,随奇异单元尺寸进一步增大或减小,精度都会有所下降。对于同质材料中的裂纹以及模量比在10倍之内的双材料界面裂纹,布置过渡单元可以提高精度;而对于模量比大于20倍的界面裂纹,不设置过渡单元的计算结果却与理论解更接近。     

双材料界面裂纹应力强度因子计算

建立不同裂纹长度的双材料界面裂纹模型,用有限元软件计算和分析界面裂纹尖端附近的应力场和位移场.利用裂尖前沿应力和裂纹面相对位移分别计算了界面裂纹尖端的应力强度因子K,两种方法计算的K值完全吻合.通过数值分析,给出一种计算双材料界面裂纹应力强度因子K的经验公式.     

弹性半空间中平片裂纹问题的超奇异积分方程方法

使用边界积分方程方法,在有限部积分的意义下,将弹性半空间中垂于自边界面的平片裂纹归结为一组以裂纹面位移间数为示知函数的超奇异积仞氖限部积分蜞 建立了数值人出了用裂纹面位移间尖力强度因子的公式。通过对圆形、菜和矩形等贡型的平片裂纹问题的计算,分析了自由边界面对裂纹前沿应力强度因子的影响。     

Moving interfacial crack between two dissimilar soft ferromagnetic materials in uniform magnetic field

This paper presents the dynamic magnetoelastic stress intensity factors of a Yoffe-type moving crack at the interface between two dissimilar soft ferromagnetic elastic half-planes. The solids are subjected to a uniform in-plane magnetic field and the crack is opened by internal normal and shear tractions. The problem is considered within the framework of linear magnetoelasticity. By application of the Fourier integral transform, the mixed boundary problem is reduced to a pair of integral equations of the second kind with Cauchy-type singularities. The singular integral equations are solved by means of a Jacobi polynomial expansion method. For a particular case, closed-form solutions are obtained. It is shown that the magnetoelastic stress intensity factors depend on the moving velocity of the crack, the magnetic field and the magnetoelastic properties of the materials.     

Stress concentration analyses of bi-material bonded joints without in-plane stress singularities

The problem of stress concentration in bi-material bonded joint is investigated under the condition of without stress singularities. Disappearance conditions of stress singularity near interface corners and edges are determined based on analyses of eigenvalue equations. Straight-side and curved interface of materials are designed for the bi-material models to avoid singular stress fields around the interface corner and edge. Assuming that one stress component or combined stresses are responsible for failure at or near the interface, the stress concentration becomes critical for the design of bi-material joints with higher interfacial strength. Numerical results show that the stress state near the interface depends strongly on both the interface geometry and the combination of materials, and stress concentration may always occurs at or near the interface. Emphasis is placed on the necessity for geometric optimization of an interface in order to design singularity-free junction with higher interfacial strength.     

任意位置含振子圆板非轴对称振动的积分方程方法研究

运用特殊函数论和富里叶级数理论,采用由贝塞尔函数组成的平方可积空间上的一类完备正交函数系构造圆板的格林函数;应用积分方程和广义函数论,给出在圆板的任意位置带有弹性振子的耦合系统动态特性的积分方程方法.计算实践表明该方法不仅算法简捷、收敛速度快、计算精度高,而且能从整体上对系统的动态特性加以研究,从而为这类结构的优化设计和安全性评估提供有效的途径.     

纤维增强复合材料的刚性圆柱夹杂双周期分布模型的平面问题

对于硬夹杂一软基体的单向纤维增强复合材料，将纤维束看成刚性圆柱状夹杂，考虑夹杂间的相互影响，采用复变函数和坐标变换的方法，构造呈双周期分布且相互影响的刚性圆柱夹杂的复应力函数，同时满足夹杂的边界条件，利用围线积分将求解方程组化为线性代数方程组，推导出受到远场均匀拉应力的作用，双周期分布的刚性圆柱夹杂的界面应力表达式，算例给出双周期夹杂模型的界面应力值，并与单夹杂模型的界面应力最大值进行对比。     

Stress intensity factors and kink angle of a crack interacting with a circular inclusion under remote mechanical and thermal loadings

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular integral equations for edge and temperature dislocation distribution functions are constructed and solved numerically, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.     

Anti-plane moving crack in a functionally graded piezoelectric layer between two dissimilar piezoelectric strips

The dynamic propagation of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layers vary continuously along the thickness. The FGPM layer and two homogeneous piezoelectric layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. The Fourier transform is used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, crack moving velocity, and thickness of the layers. The following are helpful to increase resistance to crack propagation in the FGPM interface layer: (a) certain direction and magnitude of the electric loading, (b) increasing the thickness of the FGPM interface layer, and (c) increasing the thickness of the homogeneous piezoelectric layer to have larger material properties than those of the crack plane in the FGPM interface layer. The DERR always increases with the increase of crack moving velocity and the gradient of the material properties.