ABSTRACT

In this paper, the problem of dynamic stress concentration in the process of anti-plane motion caused by a single circular cavity in a strip medium and the non-circular cavity in a porous strip medium is studied. In the case of only a single circular cavity, a numerical calculating example is presented to solve scattering around a circular cavity with a given SH guided wave and describe dynamic stress distribution at the edge of a circular cavity. Then, the results of the finite element method and analytical method are used to verify each other. Firstly, a compatible guided wave is constructed in the elastic strip, which satisfies stress-free conditions in upper and lower boundaries. Secondly, the scattering of waves around a circular cavity is expressed as series form by the employed wave function expansion method, and compatible scattering guided waves resulting from the reflection of waves off the boundaries of the elastic strip is constructed by repeated image superposition. Lastly, the coefficients of the wave function expansion are determined based on the stress-free condition of circular boundaries with pre-given incident guided waves. In the case of the non-circular cavity in the medium, the scattering of guided waves from the cavity is solved by finite element analysis, the dynamic stress distribution factor around the edge of the cavity is given, and to discuss influences of wave frequency and cavity position. The conclusions of this paper are of great reference value to the selection and ultrasonic non-destructive testing of anti-seismic materials.

摘要

本文研究了带状介质中的单个圆形空腔和多孔带状介质中的非圆形空腔在反平面运动过程中引起的动应力集中问题。在只有单个圆形腔的情况下，给出了一个数值计算例子，以求解给定SH导波的圆形腔周围的散射，并描述圆形腔边缘的动态应力分布。然后，利用有限元法和解析法的结果相互验证。首先，在弹性条中构造兼容的导波，满足上下边界的无应力条件。其次，波在圆形腔周围的散射通过所采用的波函数展开方法表示为级数形式，通过重复图像叠加构建由弹性条边界反射波产生的兼容散射导波。最后，基于预先给定入射导波的圆形边界无应力条件确定波函数展开系数。在介质为非圆形空腔的情况下，通过有限元分析求解导波从空腔中的散射，给出了空腔边缘周围的动应力分布因子，并讨论了波频率和波频率的影响。腔体位置。本文的结论对抗震材料的选择和超声无损检测具有重要的参考价值。