共查询到14条相似文献,搜索用时 171 毫秒
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利用两相材料中集中力的基本解,建立了求解曲线型刚性线夹杂和两相材料界面相交问题的弱奇异积分方程。通过Cauchy型奇异积分方程主部分析方法,得出穿过两相材料界面的曲线型刚线性在交点处的奇性应力指数及交点处角形域内的奇性应力,并利用奇性应力定义了交点处的应力奇异因子。通过对弱奇异积分方程的数值求解,得出了刚性线端点和交点处的应力奇异因子。 相似文献
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和界面接触的刚性线夹杂对SH波的散射 总被引:2,自引:0,他引:2
利用积分变换方法,得出了两相材料中单位简谐力的格林函数。根据简谐集中力的格林函数得出了和界面接触的刚性线的散射场。利用无穷积分的性质,把和界面接触刚性线的散射场分解为奇异部分和有界部分。通过分解后的散射场建立了和界面接触剐性线在SH波作用下的Cauchy型奇异积分方程。根据所得奇异积分方程和刚性线的散射场得到了刚性线端点的奇异性阶数及奇性应力。应用刚性线端点的奇性应力定义了刚性线端点的应力奇异因子。对所得Cauchy型奇异积分方程的数值求解,可得刚性线端点的应力奇异因子。 相似文献
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与两相材料界面接触的裂纹对SH波的散射 总被引:1,自引:0,他引:1
利用积分变换方法得出了两相材料中作用简谐集中力时的格林函数.根据所得的格林函数并利用Betti-Rayleigh互易定理得出了与界面接触裂纹的散射波场.裂纹的散射波场可分解为两部分,一部分为奇异的散射场,另一部分为有界的散射场.利用分解后的散射场,可得裂纹在SH波作用下的超奇异积分方程.根据裂纹散射场的奇异部分和Cauchy型奇异积分的性质得出了裂纹和界面接触点处的奇性应力指数和接触点角形域内的奇性应力.利用所得的奇性应力定义了裂纹和界面接触点处的动应力强度因子.对所得超奇异积分方程的数值求解可得裂纹端点和接解点处的应力强度因子。 相似文献
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折线型裂纹对SH波的动力响应 总被引:1,自引:0,他引:1
利用Fourier积分变换方法,得出了无限平面中用裂纹位错密度函数表示的单裂纹散射场.根据无穷积分的性质,把单裂纹的散射场分解为奇异部分和有界部分.利用单裂纹的散射场建立了折线裂纹在SH波作用下的Cauchy型奇异积分方程.根据折线裂纹散射场和所得的积分方程讨论了裂纹在折点处的奇性应力及折点处的奇性应力指数.利用所得的奇性应力定义了折点处的应力强度因子.对所得Cauchy型奇积分方程的数值求解,可得裂纹端点和折点处的动应力强度因子。 相似文献
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研究两种材料界面上的刚性线与其它任意位置处直线裂纹弹性干涉的反平面问题。基于界面上刚性线与任意位置处螺型位错干涉的基本解,运用连续位错密度模型法将问题转化为奇异积分方程。用半开型积分法求解奇异积分方程,得到位错密度函数的离散值,计算裂纹尖端处的应力强度因子。算例说明该方法可用于工程实际问题。 相似文献
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利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。 相似文献
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Lu Jianfei Zhang Xiaofang Wang Jianhua Shen Weiping 《Acta Mechanica Solida Sinica》2000,13(2):119-124
The interaction between multiple curved rigid line and ciruclar inclusion in antiplane loading condition is considered in
this paper. By utilizing the point force elementary solutions and taking density function of traction difference along curved
rigid lines, a group of weakly singular integral equations with logarithmic kernels can be obtained. After the numerical solution
of the integral equations, the discrete values of density functions of traction difference are obtainable. So the stress singularity
coefficient at rigid line tips can be calculated, and two numerical examples are given. 相似文献
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The weakly singular integral equation used to solve the problem of the curved crack crossing the boundary of the antiplane
circular inclusion is presented. Using the principal part analysis method of the Cauchy type integral equation, the singular
stress index at the intersection and the singular stress of angular regions near the intersection are obtained. By using the
singular stress obtained, the stress intensity factor at the intersection is, defined. After the numerical solution of the
integral equation, the stress intensity factors at the end points of the crack and intersection are obtainable.
The research is supported by National Natural Science Foundation of China (No. 59879012) and is the project of Chinese Foundation
of State Education Commission (No. 98024832). 相似文献
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Y. A. Bogan 《Journal of Elasticity》2011,103(2):269-280
By definition, the principal problem of the two-dimensional theory of elasticity consists in solving the equation for the
Airy’s stress function in a region with its first order derivatives assigned at a boundary. In this paper, an indirect formulation
of this problem based on integral equations with weakly singular kernels is proposed. In a bounded region with a Lyapunov
boundary it is reduced to the solution of weakly singular integral equations. Differential properties of its solution are
investigated. 相似文献
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The problem of a rigid punch contacting with a finite graded layer on a rigid substrate is investigated within the framework of steady-state plane strain thermoelasticity, in which heat generated by contact friction is considered with a constant friction coefficient and inertia effects are neglected. The material properties of the graded layer vary according to an exponential function in the thickness direction. Fourier integral transform method and transform matrix approach are employed to reduce the current thermocontact problem to the second kind of Cauchy-type singular integral equation. Distributions of the contact pressure and the in-plane stress under the prescribed thermoelastic environment with different parameter combinations, including ratio of shear moduli, relative sliding speed, friction coefficient and thermal parameters are obtained and analyzed, as well as the stress singularity and the stress intensity factors near the contact edges. The results should be helpful for the design of surfaces with strong wear resistance and novel graded materials for real applications. 相似文献