球壳中球形夹杂对SV波的三维散射与动应力集中研究

结构中夹杂将导致应力集中，是降低结构承载能力重要影响因素，尤其是动载作用情况下，弹性波衍射和叠加将加剧应力集中程度。弹性波衍射方程建立和求解非常复杂，目前主要研究对象集中在二维模型情况，三维有限域内夹杂引起的动应力集中现象在大型结构中比较常见，有界域边界不仅作为边界条件，同时也是散射波波源，提高了求解难度。一般通过近似方法，将三维模型简化为二维情况，往往导致求解结果过于保守不能解释实际问题。本文针对三维球壳包含夹杂一般情况，分别以球壳和夹杂中心建立球坐标以描述球壳内、外壁和夹杂表面散射波势函数，并引入一种球波函数加法公式实现不同坐标下势函数转换，以求解应力集中状态。最后针对三维情况，给出多个动应力集中因子分布状态以描述动应力集中程度。文中研究为一般情况下含夹杂球壳结构的强度分析提供了理论支撑。

Research on 3D Scattering and Dynamic Stress Concentration of SV Waves in Spherical Shells With Spherical Inclusions

Due to the influence factors in the material processing, manufacturing and other links, inclusions (cavity) are inevitable in the large structures, which will destroy the continuity of metal matrix and it will lead to stress concentration in the structures, which is an important factor to reduce the strength of the structure. Especially in the case of dynamic load, the diffraction and superposition of elastic waves will aggravate the stress concentration. Plate and shell structures are widely used in petrochemical, electric power, aerospace and other industrial fields. The inclusion in plate and shell structures is an important factor affecting the structural strength and fatigue life. The stress concentration of plate and shell structures has always been a hot spot in academic and industrial research. The establishment and solution of elastic wave diffraction equation is very complex. At present, the main research object is focused on two-dimensional model. Dynamic stress concentration caused by inclusions in three-dimensional finite domain is common in large-scale structures. The boundary of bounded domain is not only as boundary conditions, but scattering wave sources as well, which improves the difficulty of solution. Generally, the three-dimensional model is simplified to two-dimensional by approximate method, which often leads to the conservative solution results and can not explain the actual problems. In this paper, according to the general situation of inclusion in three-dimensional spherical shell, spherical coordinates are established with the center of spherical shell and inclusion respectively to describe the scattering wave potential function of the inner, outer wall and inclusion surface of the spherical shell, and a type of addition formula for spherical wave function is introduced to conduct the potential function transformation under different coordinates, through the boundary conditions of the inner and outer walls of the spherical shell and the continuity condition of the inclusion interface, the dynamic stress concentration could be solved. This study provides theoretical support for the strength analysis of spherical shells with inclusions in general.