Abstract

Materials and structures in practical engineering inevitably subject to dynamic loads. Surface and internal discontinuities have signification effects on wave propagation and may cause dynamic stress concentration in the vicinity of them. Thus, it is of great significance to determine the dynamic response of materials and structures with surface and internal features under elastic waves. In this article, based on the wave function expansion method, the image method and the complex function method, an analytical solution is presented for the scattering of anti-plane (SH) waves by multiple cylindrical elastic inclusions and semi-cylindrical depressions in an elastic infinite plate. The series expressions of the displacement fields, stress fields, and dynamic stress concentration factors around the inclusion and the depression are derived. Numerical calculations show that the incident wavenumber, shear modulus of the inclusion, plate thickness, and relative position between the inclusion and the depression express great effects on the dynamic stress concentration. The theoretical solutions of this article can provide a reference for the results of numerical methods. And the findings are useful for structural design and nondestructive testing of the plate.

摘要

实际工程中的材料和结构不可避免地会受到动态载荷的影响。表面和内部的不连续性对波的传播有显着的影响，并可能导致它们附近的动态应力集中。因此，确定具有表面和内部特征的材料和结构在弹性波作用下的动态响应具有重要意义。本文基于波函数展开法、图像法和复函数法，给出了弹性体中多个圆柱弹性夹杂物和半圆柱凹陷对反平面（SH）波散射的解析解。无限板。推导了夹杂物和凹陷周围的位移场、应力场和动应力集中因子的级数表达式。数值计算表明，夹杂物的入射波数、剪切模量、板厚、夹杂物与凹陷的相对位置对动应力集中有较大影响。本文的理论解可为数值方法的结果提供参考。这些发现对板材的结构设计和无损检测很有用。