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梯度材料中矩形裂纹的对偶边界元方法分析 总被引:2,自引:0,他引:2
采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解,以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上,面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解,采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比,建议方法可以获得高精度的计算结果. 最后,分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子,讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响. 相似文献
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现存文献关于梯度材料断裂问题的研究大都是假设材料参数为坐标的指数函数或幂函数,而其它函数形式较少采用.本文假设功能梯度材料剪切模量和密度的倒数均为坐标的线性函数,而泊松比为常量,研究功能梯度板条的反平面运动裂纹问题.利用Fourier积分变换技术和传递矩阵法将混合边值问题化为一对奇异积分方程,通过数值求解奇异积分方程获得板条运动裂纹在反平面载荷作用下的动态应力强度因子,并讨论了裂纹运动速度、裂纹相对尺寸、以及材料非均匀性对动态应力强度因子的影响,结果证明梯度参数、裂纹速度和几何尺寸对材料动态断裂行为有显著影响. 相似文献
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功能梯度条共线Griffith裂纹反平面剪切冲击 总被引:1,自引:1,他引:1
研究正交各向异性功能梯度条中多个共线Griffith裂纹的反平面剪切冲击问题.材料两个方向的剪切模量假定按比例同时以特定的梯度变化.采用Laplace和Fourier变换及引进位错密度函数将问题化为求解Cauchy奇异积方程,进而化为代数方程数值求解.考查材料非均匀性、正交性和功能梯度条高度对裂尖动态断裂特性的影响.动应力强度因子的数值结果显示:增加剪切模量的梯度和(或)增加垂直于裂纹面方向的剪切模量,可以抑制动应力强度因子的幅度;若功能梯度条较薄,增大条形域的高度也可抑制裂纹扩展. 相似文献
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基于三维弹性理论和压电理论,对材料系数按指数函数规律分布的功能梯度压电板条中的反平面运动裂纹问题进行了求解。利用Fourier积分变换方法将电绝缘型运动裂纹问题化为对偶积分方程,并进一步归结为易于求解的第二类Fredholm积分方程。通过渐近分析,获得了裂纹尖端应力、应变、电位移和电场的解析解,给出了裂纹尖端场各个变量的角分布函数,并求得了裂纹尖端场的强度因子,分析了压电材料物性梯度参数、几何尺寸及裂纹运动速度对它们的影响。结果表明,对于电绝缘型裂纹,功能梯度压电板条中运动裂纹尖端附近的各个场变量都具有-1/2阶的奇异性;当裂纹运动速度增大时,裂纹扩展的方向会偏离裂纹面。 相似文献
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非均匀复合材料的动态热弹性断裂力学分析 总被引:8,自引:1,他引:7
对非均匀复合材料的动态热弹性断裂力学问题进行了研究,假设材料参数沿厚度方向为变化的,沿该方向将复合材料划分为许多单层,取每一单层材料参数为常数,应用Fourier变换法,在Laplace域内推导出了控制问题的奇异积分方程组,给出了热应力强度因子的表达式,然后利用Laplace数值反演,得出了裂纹尖端的动态应力强度因子.本文的方法具有以下特点:(1)多个垂直于厚度方向的裂纹,(2)材料可以为正交各向异性:(3)考虑了惯性效应.作为算例,研究了带有两个裂纹的功能梯度结构,分析了材料参数的变化对应力强度因子的影响. 相似文献
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DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL 总被引:2,自引:0,他引:2
IntroductionInrecentyears,greatattentionshavebeenpaidtotheresearchofFunctionallyGradedMaterials(FGM).Fromtheviewpointsofappliedmechanics,FGMarenon_homogeneoussolids.Thenon_homogeneityofFGMhasagreatinfluenceontheirmechanicalbehavior,especiallywhenthecomp… 相似文献
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The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack. 相似文献
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The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor. 相似文献
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Pei-Wei Zhang Zhen-Gong Zhou Zeng-Tao Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):411-430
The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this
paper using the generalized Almansi’s theorem. To make the analysis tractable, it was assumed that the shear modulus varies
exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into
two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve
the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi
polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at
the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials;
however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties.
It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. 相似文献
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The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks. 相似文献
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《European Journal of Mechanics - A/Solids》2007,26(2):325-336
Dynamic stress intensity factor for a Griffith crack in functionally graded orthotropic materials under time-harmonic loading is investigated in the present paper. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors of the functionally graded orthotropic materials with a Griffith crack. 相似文献
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研究功能梯度压电带中裂纹对SH波的散射问题,为了便于分析,材料性质假定为指数模型,并假设裂纹面上的边界条件为电渗透型的.根据压电理论得到压电体的状态方程,利用Fourier积分变换,问题转化为对偶积分方程的求解.用Copson方法求解积分方程.求得了裂纹尖端动应力强度因子、电位移强度因子的解析表达式,最后数值结果显示了标准动应力强度因子与入射波数、材料参数、带宽、波数以及入射角之间的关系. 相似文献
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功能梯度板条断裂分析 总被引:2,自引:0,他引:2
现存文献关于功能梯度材料断裂问题的研究大都假设材料性质为坐标的指数函数或幂函数,而对其它函数形式较少采用。本文假设功能梯度材料剪切模量为坐标的双曲函数,而泊松比为常量,研究功能梯度板条的混合型裂纹问题。利用Fourier积分变换技术将混合边值问题转化为一对奇异积分方程,通过数值求解奇异积分方程获得含裂纹功能梯度板条分别在剪切和法向载荷作用下的I型和Ⅱ型应力强度因子,并讨论了材料的非均匀性和裂纹相对尺寸对裂纹尖端应力强度因子的影响。 相似文献
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Jun Liang 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(6):443-464
The dynamic behavior of two parallel symmetric cracks in functionally graded piezoelectric/piezomagnetic materials subjected
to harmonic antiplane shear waves is investigated using the Schmidt method. The present problem can be solved using the Fourier
transform and the technique of dual integral equations, in which the unknown variables are jumps of displacements across the
crack surfaces, not dislocation density functions. To solve the dual integral equations, the jumps of displacements across
the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the electric, magnetic
flux, and dynamic stress fields near crack tips can be obtained. Numerical examples are provided to show the effect of the
functionally graded parameter, the distance between the two parallel cracks, and the circular frequency of the incident waves
upon the stress, electric displacement, and magnetic flux intensity factors at crack tips. 相似文献
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In this paper, the interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material was investigated by using the generalized Almansi's theorem. In the analysis, the electric permittivity of the air inside the crack was considered. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the electric permittivity of the air inside the crack and the gradient parameter of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. 相似文献