球壳中球形夹杂对SV波的三维散射与动应力集中研究

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

夹杂将导致结构应力集中,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.论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.

During material processing and manufacturing,inclusions(cavities)are inevitable in large structures,which can destroy the continuity of metal matrix and lead to stress concentration in structures,and therefore,is an important factor that reduces the strength of structures.Especially in the case of dynamic load,stress concentration can be aggravated by the diffraction and superposition of elastic waves.Plate and shell structures are widely used in petrochemical engineering,electrical engineering,aerospace engineering and other fields of engineering.Inclusions in the plate and shell structures are an important factor affecting the structural strength and fatigue life.Therefore,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 are very complex.So far,the main research object has been focused on two-dimensional modeling.However,the dynamic stress concentration caused by inclusions in a three-dimensional finite domain is very common in large-scale structures.The boundary of a bounded domain is as not only boundary conditions,but also scattering wave sources,making the solution more difficult.Generally,the three-dimensional model is simplified as a two-dimensional one by the approximate method,which often leads to more conservative results and cannot explain the actual problems.In this paper,according to the general situation of inclusions in a three-dimensional spherical shell,spherical coordinates are established for the center of the spherical shell and the inclusion,respectively,to describe the scattering wave potentials of the inner and outer walls,as well as the inclusion surface of the spherical shell.A type of addition formula for the spherical wave function is introduced to conduct the potential function transformation under different coordinates.The dynamic stress concentration can be solved through the boundary conditions of the inner and outer walls of the spherical shell and the continuity conditions of the inclusion interface.This study provides theoretical support for the strength analysis of spherical shells with inclusions in general.