Scattering of SH waves by a scalene triangular hill with a shallow cavity in half-space

In this study,a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface.The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables.Based on the complex function,multi-polar coordinate method,and region-matching technique,algebraic equations are established at auxiliary boundaries and free boundaries conditions in a complex domain.The auxiliary circle is used to solve the singularity of the reflex angle at the triangle corner.Then,according to sample statistics,the least squares method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary.Numerical results show that the continuity of the auxiliary boundaries and the accuracy of the zero-stress boundaries are adequate,and the displacement of the free surface and the stress of the circular hole are related to the shape of the triangle,the position of the circular hole,the direction of the incident wave,and the frequency content of the excitation.Finally,time-domain responses are calculated by FFT based on the frequency domain theory,and the results reveal the wave propagation mechanism in a complicated structure.

Dynamic Response of Tunnel Structures in Inhomogeneous Medium Under SHWave:Shear Modulus in Quadratic Functional Form

The task of thiswork is to study the scattering of SHwaves by homogeneous tunnel structures in an unbounded inhomogeneous medium.The shear modulus is assumed to be a function of coordinates(x,y).Atwo-dimensional scattering model is established.Selecting different inhomogeneous parameters,the medium has different properties,expressed as a rigid variation.The stress concentration phenomenon of the structure is analyzed for material design.Based on the complex function theory,the expressions of wave field in the tunnel are derived.The stress concentration phenomenon on the tunnel is discussed with numerical examples.The distribution of dynamic stress concentration factor on the inner and outer boundaries is analyzed under different influencing factors.Finally,it is found that the distribution of dynamic stress concentration factor is significantly affected by the inhomogeneous parameters and reference wave numbers of the medium.

Notch fatigue of Cu50Zr50 metallic glasses under cyclic loading:molecular dynamics simulations

Molecular dynamics simulation is performed to simulate the tension–compression fatigue of notched metallic glasses(MGs),and the notch effect of MGs is explored.The notches will accelerate the accumulation of shear transition zones,leading to faster shear banding around the notches’root causing it to undergo severe plastic deformation.Furthermore,a qualitative investigation of the notched MGs demonstrates that fatigue life gradually becomes shorter with the increase in sharpness until it reaches a critical scale.The fatigue performance of blunt notches is stronger than that of sharp notches.Making the notches blunter can improve the fatigue life of MGs.

出平面剪切波作用下弹性非均匀材料中圆孔受刚度影响的力学分析

基于复变函数理论,研究了出平面剪切波在非均匀直角域内的传播特性.介质的非均匀性体现在剪切模量是与空间坐标有关的函数.引入一个位移辅助函数和一对映射函数用以辅助推导控制方程.同时,在复坐标系下可以更方便的进行坐标变换.使用镜像法构造了介质内反射波和散射波的波场表达式.根据圆孔处的边界条件求解了散射波中的未知系数,并给出了直角域空间内波场的解析表达式.在动力学分析中,刚度可以用剪切模量来表示.在算例分析中,讨论了位移幅值和动应力集中系数对非均匀参数,参考波数以及圆孔位置的依赖关系.