Dynamic Stress around Two Interacting Cylindrical Nano-Inhomogeneities with Surface/Interface Effects

On the basis of continuum surface elasticity, two interacting cylindrical nano-inhomogeneities with surface/interface effect in a small-sized solid under anti-plane shear waves are investigated, and the dynamic stress around the nano-inhomogeneities is analyzed. The wave function expansion method is used to expressed the wave field around the two nano-inhomogeneities. The total wave field is obtained by the addition theorem for cylindrical wave function. Through analysis, it is found that the distance between the two nano-inhomogeneities shows great effect on the dynamic stress in nano composites. The effect of the distance is also related to the properties of the nano-inhomogeneities and the interface, the wave frequency, and the incident angle of shear waves. To show the accuracy of the results for certain given parameters, comparison with the existing results is also given.     

Dynamic stress in a semi-infinite solid with a cylindrical nano-inhomogeneity considering nanoscale microstructure

In this paper, the dynamic stress around a cylindrical nano-inhomogeneity embedded in a semi-infinite solid under anti-plane shear waves is investigated. The surface/interface stress effects around the nano-inhomogeneity and at the straight edge of the semi-infinite solid are both considered. The boundary condition at the straight edge of the semi-infinite solid with surface/interface effects is satisfied by the image method. The incident, scattered and refracted displacement fields in the nano-sized composites are expressed by employing the wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two semi-infinite solids. Analyzes show that the effect of interface properties, especially that at the straight edge, on the dynamic stress is significant, and the effect increases noticeably due to the nanoscale of the structure. The incident frequency and angle of waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show a pronounced effect on the dynamic stress distribution if the semi-infinite solid shrinks to nanoscale.     

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.     

Interface Effect on the Dynamic Stress around an Elliptical Nano-Inhomogeneity Subjected to Anti-Plane Shear Waves

In the design of advanced micro- and nanosized materials and devices containing inclusions, the effects of surfaces/interfaces on the stress concentration become prominent. In this paper, based on the surface/interface elasticity theory, a two-dimensional problem of an elliptical nano-inhomogeneity under anti-plane shear waves is considered. The conformal mapping method is then applied to solve the formulated boundary value problem. The analytical solutions of displacement fields are expressed by employing wave function expansion method, the expanded mode coefficients are determined by satisfying the boundary conditions at the interfaces of the nano-inhomogeneity. Analyses show that the effect of the interfacial properties on the dynamic stress is significantly related to the wave frequency of incident waves, the shear modulus ratio of the nano-inhomogeneity and the matrix, and the dimensions of the elliptical nano-inhomogeneity. Comparison with the previous results is also presented.     

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.     

SH波入射双相介质半空间浅埋任意位置圆形夹杂的动力分析

采用Green 函数及复变函数方法研究了SH 波入射到双相介质半空间时,浅埋任意位置圆形夹杂的动力响应问题。首先,利用“镜像”法构造满足直角平面自由边界条件的散射波场解答,进而求出该文所需的Green函数;其次,利用“契合”思想,将模型沿着垂直界面剖分为两个直角域,并利用界面连续性条件及Green函数建立待解外力系的第一类Fredholm 积分方程组;最后,通过具体算例给出了圆形弹性夹杂周边的动应力集中系数。结果显示:界面、自由边界、圆形夹杂、入射波数等因素均对动应力集中系数有影响。     

柱面SH波作用下管道的动应力集中研究

在地下工程爆破开挖过程中,爆破地震波对管道安全的影响是十分重要的。为了更好的研究柱面SH波作用下管道的动应力集中情况,以爆破地震波中的柱面SH波作为研究对象,推导了柱面SH波作用下管道内壁上动应力集中系数(DSCF)的解析解。通过宝通禅寺地下通道爆破开挖工程,讨论了归一化爆心距r^*和入射波频率f对DSCF的影响。结果表明,由于管道与周围土层剪切模量差异较大,管道上的动应力集中系数普遍较大;从DSCF分布的角度来讲,当r*和入射波频率f对DSCF的影响。结果表明,由于管道与周围土层剪切模量差异较大,管道上的动应力集中系数普遍较大;从DSCF分布的角度来讲,当r^*<5时,柱面波与平面波的差异较大,但当r*<5时,柱面波与平面波的差异较大,但当r^*>5时,柱面SH波基本可以认为与平面SH波等价;低频入射波对管道的安全更为显著,特别是入射波频率与管道自振频率接近时,管道受到的影响最为严重。     

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。     

Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.     

Study on the Propagation of Interface Crack of Young Concrete Lining and Rock Under Blasting Load

在水利水电工程施工中,经常会遇到爆破开挖对混凝土衬砌的影响,尤其是新浇混凝土衬砌结构。新浇筑混凝土内部随机分布很多微裂隙,这些裂纹在爆破冲击荷载作用下容易扩展连通,特别是衬砌混凝土与基岩粘结面裂纹扩展更应引起注意。本文在考虑混凝土龄期的基础上,对混凝土与岩石粘结面裂纹的动态应力强度因子进行了计算,找出了不同应力波入射角度对裂纹扩展机理的影响。在应力波的垂直入射情况下,混凝土粘结面裂纹扩展主要是应力波在自由面反射形成拉伸应力,致使衬砌混凝土粘结面裂纹拉裂。在应力波的水平入射情况下,混凝土粘结面裂纹扩展形式受混凝土龄期影响。随着混凝土龄期的增加,混凝土与岩石的弹性模量差值逐渐减小,裂纹由剪切破坏变为受压缩张开破坏。     

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.     

Effect of surface stress and irregularity of the interface on the propagation of SH-waves in the magneto-elastic crustal layer based on a solid semi space

The object of the present paper is to investigate plane SH waves through a magneto-elastic crustal layer based over an elastic, solid semi space under the influence of surface stress on the free surface of the crustal layer and irregularity of the interface. Two types of irregularities of the interface namely, rectangular and parabolic have been considered. Modulations of wave velocity due to the presence of surface stress, irregularity and the magnetic field have been studied separately. Their combined effect has also been investigated. Graphs are drawn to highlight some important peculiarities. It is observed that surface stress, irregularity and magnetic field have their respective role to play in the propagation of SH waves in the crustal layer. Further modulation of wave velocity occurs due to their combined effect.     

基于能量法研究刚性质量块轴向撞击圆柱壳的屈曲

基于能量法,考虑应力波效应,研究了刚性质量块撞击圆柱壳的屈曲问题。建立拉格朗日函数,将其和计算获得的符合边界条件的准试函数代入第二类拉格朗日方程,得到二阶线性偏微分方程,分析方程解的特性,得到刚性质量块撞击圆柱壳屈曲临界速度的解析表达式。算例分析讨论了临界长度、冲击质量、轴向模态数、环向模态数、径厚比对屈曲的影响。结果表明:应力波效应、初始冲击动能、径厚比对圆柱壳的动力屈曲有明显影响;高速冲击易激发屈曲的高阶模态、也容易在径厚比较小时激发圆柱壳的屈曲。     

出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射

采用复变函数法和Green函数法,求解出平面线源荷载对半空间中半圆形凸起的圆柱形弹性夹杂的散射。首先,给出在含有半圆形凸起的圆柱形弹性夹杂的弹性半空间中,水平表面上任意一点承受时间谐和的出平面线源荷载作用时的位移函数,取该位移函数作为Green函数;然后,采用分区的思想,分别构造出夹杂内的驻波和夹杂外的散射波,满足"公共边界"处位移和应力的连续性条件,建立起求解该问题的无穷代数方程组;最后,给出了动应力集中系数和水平地面位移幅值的数值结果,并进行了讨论。     

Scattering of vertical shear waves by a cluster of nanosized cylindrical holes with surface effect

This study considers the multiple scattering of vertical shear waves (SV-waves) by a cluster of nanosized cylindrical holes. When the radius of the holes shrinks to nanometers, surface effects play an important role in their mechanical performance, and the surface elasticity theory is adopted to analyze diffraction phenomena. By using the displacement potential method and wave functions expansion method, the scattering fields around the holes are derived. Both the dynamic stress concentration around the holes and the scattering cross section are calculated to illustrate the effect of surface effects on the multiple scattering of an SV-wave.     

地下双洞室在SV波入射下动力响应问题解析解

采用波函数展开法给出了地下双洞室在平面SV波入射下动力响应二维问题的一个解析解，数值结果表明：当两个洞室之间距离较近时，洞室之间的相互作用对地下双洞室的动应力集中具有显著的放大作用，两个洞室情况动应力集中系数可能达到单个洞室的5．2倍以上，动应力集中系数的峰值位于两个洞室相对的区域内。     

双向耦合地震作用下含软弱层岩质边坡锚固界面剪切作用

为研究地震作用下锚固岩质边坡锚杆-砂浆界面和砂浆-岩体界面上的剪切作用,利用FLAC~(3D)软件构建锚固含软弱层岩质边坡数值模型,对水平向和竖向地震波耦合作用下的全长黏结锚杆锚固边坡两锚固界面上的剪切作用进行了深入研究。研究结果表明:两锚固界面上的剪应力分布很不均匀,界面处于弹性变形阶段时,两峰值剪应力紧邻中性点,随锚固界面脱黏破坏的发展,两峰值剪应力不断地向锚杆两端转移;双向耦合地震波较单向和双向未耦合地震波对锚固界面剪应力影响更为显著。考虑双向地震波耦合作用的锚固边坡抗震设计更为合理。研究结果可为边坡锚固抗震设计提供参考。     

On the influence of a bimaterial interface on dynamic stress intensity factors

Summary The method of dynamic Green's function and the integral transforms are applied to investigate the elasto-dynamic stress intensity factor of a crack straddling an interface of a bimaterial composite. The crack which extends to infinity on one side is assumed to extend an arbitrary distancea on the other side of the interface. Anti-plane line loads are suddenly applied at timet=0 on either side of the crack surface at arbitrary distancesl ₁ andl ₂ from the interface. The effect of the interface on the dynamic stress field near the crack tip is studied. It is found that the transmitted wave through the interface and reflected wave from the interface serve to increase or decrease the stress field in the vicinity of the crack tip depending on the elastic properties of the two materials.     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究。研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的。扩展速度最大值达到210m/s,裂纹扩展加速度最大值为9.47Mm/s2,切口端部动态应力强度因子KdⅠ最大值为0.6MN/m3/2。     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的.扩展速度最大值达到210m/s,裂...