梯度材料中任意形孔对反平面剪切波散射与动应力

该文基于弹性动力学理论,采用复变函数与保角映射方法,研究了指数梯度材料中任意形孔洞对弹性波的散射与动应力集中,给出了问题的解析解.并以求解椭圆孔动应力集中系数为例,分析了入射波数和材料非均匀参数等对椭圆孔动应力分布的影响.     

材料性质对纤维增强复合材料动力学特性的影响

基于弹性动力学理论,对纤维增强复合材料结构中弹性波散射及动应力集中问题进行了分析研究。将非均匀界层区处理为具有相同厚度的多层弹性介质。给出了结构各区域弹性波分析解的表达式。根据位移与应力在界面处的连续条件,确定了弹性波模式系数。给出了界面处动应力集中系数的表达式。作为算例,计算了两种纤维增强复合材料结构中各界面动应力集中系数的数值结果,并分析了界层材料性质以及结构尺寸对各界面动应力集中系数的影响。     

开孔薄板弹性波散射与动应力集中

本文采用边界无法对开孔无限大薄板弹性波的散射与动应力集中问题进行理论分析和数值计算。基于动力学功的互等定理建立了薄板弯曲波动问题的边界积分方程,应用Ｍａｔｈｅｍａｔｉｃａ软件首次推导了各影响系数的计算公式．最后,给出了圆孔附近的动应力集中系数的数值结果。     

出平面线源荷载作用下半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力影响

采用复变函数和多极坐标方法研究了在水平界面承受出平面线源荷载时弹性半空间内浅埋圆孔对半圆形凸起的圆柱形弹性夹杂的动力作用。该问题采用先“分区”再“契合”的思想求解,首先,将整个求解区域分割成两部分,其一为含半圆形凹陷和圆孔的弹性半空间,其二为圆柱形弹性夹杂;其次,构造满足含半圆形凹陷半空间水平界面应力自由和圆孔边界应力自由的散射波,构造满足圆形夹杂上半表面应力自由下半表面应力连续条件的驻波和散射波;最后,在两个区域的“公共边界”上实施“契合”,满足公共边界处位移和应力的连续性条件,同时满足圆孔边界应力自由的边界条件,建立起求解该问题的无穷代数方程组,并就具体算例讨论了圆柱形弹性夹杂周边动应力集中系数的数值结果。结果表明：圆孔的存在对“软”、“硬”夹杂周边动应力集中系数有不同的影响。     

SH波对覆盖层下浅埋圆孔和圆夹杂的散射

利用复变函数法和波函数展开法给出了具有地表覆盖层的弹性半空间内圆形孔洞和圆柱形夹杂在稳态SH波作用下动应力集中问题的解。根据SH波散射的衰减特性,该问题采用大圆弧假定法求解,利用半径很大的圆来拟合地表覆盖层的直边界,将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。借助Helmholtz定理预先写出问题波函数的一般形式解,再利用边界条件并借助复数Fourier-Hankel级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组,截断该无穷代数方程组可求得该问题的近似解析解。最后,通过算例讨论了地表覆盖层及圆孔对浅埋圆柱形夹杂动应力集中的影响。结果表明,覆盖层刚度和厚度的变化及圆孔的存在可显著改变圆夹杂周边动应力集中的分布。     

SH波对界面圆柱体夹杂下半圆脱胶的散射分析

本文采用有限元法研究近场界面圆柱夹杂脱胶结构对瞬态SH波的散射和动应力集中系数问题。用有限元法模拟弹性波在半无限介质中的传播,用ANSYS进行计算,给出了部分节点的位移、应力时程解和夹杂周边的动应力集中系数,讨论圆柱夹杂、介质参数以及波数对动应力集中和各点位移带来的不同影响,并进行对比分析。     

半空间中椭圆夹杂与裂纹对SH波的散射

采用Green函数、复变函数和多极坐标方法求解弹性半空间中椭圆形弹性夹杂与任意方位的裂纹对SH波的散射问题。利用“保角映射”技术求解椭圆夹杂对SH波的散射位移场,并构造适合本问题的Green函数,即含椭圆形弹性夹杂的弹性半空间内任意一点承受时间谐和的反平面荷载作用时的位移基本解,结合裂纹“切割”法构造裂纹,进而得到椭圆夹杂和裂纹同时存在条件下的位移场与应力场。最后,通过具体算例,讨论了不同参数对地表位移、弹性夹杂周边动应力集中系数和裂纹尖端动应力强度因子的影响规律。     

带形介质内SH型导波对圆柱孔洞的动力分析

弹性板壳的反平面运动中由缺陷引起的应力集中问题可以按照带形介质中圆柱孔洞对SH型导波的散射问题来分析。首先,构造带形介质中相容导波的形式,即其满足上、下边界应力自由条件。之后,由波函数展开法给出圆柱孔洞散射波的级数表示,根据累次镜像叠加的方法构造由上、下边界反射所形成的相容的散射导波。最后,给定入射导波,由圆柱孔洞边界应力自由的条件来定解波函数级数的系数。数值算例求解了特定导波对圆柱孔洞的散射,给出了圆柱孔洞边沿的动应力分布,讨论了导波阶数、频率以及孔洞位置的影响。     

基于拉伸振动精确化理论求解含孔厚板弹性波散射问题

针对采用弹性力学平面问题求解波动/振动时常产生较大误差的问题,基于厚板拉伸振动精确化方程,采用复变函数方法对含孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。给出了含椭圆孔厚板拉压弹性波散射与动应力集中的数值结果。研究结果表明:动应力集中系数与分布取决于入射波数、平板厚度、椭圆偏心率等无量纲化参数。     

双相介质半空间椭圆形夹杂与直线裂纹对SH波的散射

利用Green函数法、复变函数法和保角映射法研究了双相介质半空间存在直线裂纹与椭圆形夹杂组成的复合缺陷对SH波的散射问题并给出了解析解。采用保角映射法将椭圆形夹杂外域映射为单位圆外域并利用镜像叠加原理构造了一个能自动满足直角域两个直线边界应力自由边界条件的散射位移场。利用裂纹"切割"技术构造区域I中的直线裂纹,并根据弹性叠加原理得出直角域中同时存在裂纹与椭圆形夹杂时的位移场和应力场。采用"契合"法在界面上添加未知的外力系以满足界面上的应力和位移连续性条件,根据连续性条件建立求解未知力系的定解积分方程组,并通过截断有限项求解。具体算例给出了不同参数条件下椭圆形夹杂的动应力集中系数分布情况,结果表明裂纹将对椭圆形夹杂的动应力集中系数的分布产生影响。     

Multiple scattering of shear waves and dynamic stress from a circular cavity buried in a semi-infinite slab of functionally graded materials

Based on the theory of elastodynamics and employing image method, the multiple scattering and dynamic stress in a semi-infinite slab of functionally graded materials with a circular cavity are investigated. The analytical solution of this problem is derived, and the numerical solutions of the dynamic stress concentration factor around the cavity are also presented. The effects of the distance between the cavity and the boundaries of the semi-infinite slab, the incident wave number and the non-homogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that the dynamic stress around the cavity increases with increasing non-homogeneity parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum dynamic stress and the distribution of dynamic stress around the circular cavity, and the effect increases with increasing incident wave number.     

Non-destructive Detection of a Circular Cavity in a Finite Functionally Graded Material Layer Using Anti-plane Shear Waves

A semi-analytical method is proposed to investigate the non-destructive detection of a circular cavity buried in a functionally graded material layer bonded to homogeneous materials, and the multiple scattering effect of shear waves is described accurately. The image method is used to satisfy the traction free boundary condition at the edge of the functionally graded material layer. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions at the edge and around the cavity. The analytical and numerical solutions of dynamic stress concentration factors around the cavity are presented. The effects of the position of the cavity in the material layer, the incident wave number, and the properties of the two phases of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the buried depth of the cavity and the thickness of the layer are relatively small, the properties of the two phases of materials have great effect on the distribution of dynamic stress around the cavity. In the region of higher frequency, the effects of the position of the cavity and the properties of the two phases of materials on the maximum dynamic stress are greater.     

Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and dynamic stress around a subsurface cylindrical inclusion in a functionally graded piezoelectric material layer bonded to homogeneous piezoelectric materials. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the inclusion. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. Through the numerical solutions of dynamic stress concentration factors around the inclusion, it is found that when the cylindrical inclusion possesses higher rigidity and greater piezoelectric constant than the two phases of functionally graded materials, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion possesses lower rigidity and smaller piezoelectric constant than the two phases of functionally graded materials, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater. The effect of the properties of the inclusion on the dynamic stress around the inclusion is greater than that on the electric field. The effects of wave frequency on the dynamic stress and electric field are also examined.     

Dynamic stress from a subsurface cylindrical inclusion in a functionally graded material layer under anti-plane shear waves

The multiple scattering of shear waves and dynamic stress resulting from a subsurface cylindrical inclusion in a functionally graded material (FGM) layer bonded to homogeneous materials are investigated, and the analytical solution of this problem is derived. Image method is used to satisfy the traction free boundary condition of the FGM layer. The analytical solutions of wave fields around the actual and image inclusions are expressed by employing wave functions expansion method, and the expanded mode coefficients are determined by satisfying the continuous boundary conditions around the inclusions. Through the numerical solutions of dynamic stress concentration factors (DSCFs) around the inclusion, the effects of the position of the inclusion in the material layer, the properties of the inclusion, and the properties of the two phases of composites on the DSCFs are analyzed. Analyses show that when the cylindrical inclusion is stiffer than the two phases of FGMs, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion is softer than the two phases of FGMs, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater.     

双相压电介质中界面附近圆孔的动态性能分析

采用Green函数法研究界面附近含圆形孔洞的双相压电介质对时间谐和SH波的散射问题。首先利用复变函数的方法构造出适合于本文问题的位移Green函数和电场Green函数。然后利用契合思想，根据界面上的连续性条件建立起求解问题的第一类Fredholm型积分方程，得到了圆孔孔边周向剪应力的动应力集中系数和周向电场强度集中系数的解析表达式。最后作为算例，给出了界面附近圆孔边界的两组集中系数随入射波频率、材料的几何参数和物理参数变化的计算结果图，部分计算结果与已有文献进行了比较。     

功能梯度材料亚表面缺陷的热波多重散射问题

基于热传导波动模型,采用波函数展开法,研究了半无限功能梯度材料亚表面球形缺陷的热波多重散射.给出了热波散射的一般解.温度波由调制光束在材料表面激发,球形缺陷表面的边界条件为绝热,非均匀参数为指数函数变化.分析了结构几何参数和物理参数对温度分布的影响,并给出了温度变化的数值结果.本研究可为功能梯度材料的分析研究、物理反问题和红外热波成像等提供理论基础和参考数据.     

Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves

Considerable efforts have been devoted to the characterization of the strength at the surfaces/interfaces of piezoelectric nanocomposites. In this paper, the multiple scattering of electro-elastic waves from two piezoelectric nano-fibers in piezoelectric matrix is considered and the dynamic stress at the interface is obtained. A decoupling function is introduced to solve the governing equation in piezoelectric materials. The displacement and electric potential are described by a wave function expansion method. The addition theorem for cylindrical wave function is used to obtain the total coupling wave field. The conventional surface/interface model of Gurtin and Murdoch is extended to the case of coupling stress and electric displacement. The dynamic stress concentration factor around two nano-fibers is obtained. Through numerical analysis, it is found that the interaction between the two nano-fibers has a significant effect on the coupling of stress and electric displacement at the interface, especially in the region of high frequency. The interacting effect of the two piezoelectric interfaces is also related to the properties of the nano-fibers and interface. To show the validity of the dynamic model, comparison with existing results is also given.     

Scattering of SH-waves by an interface cavity

Summary. The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.