Abstract：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.
2021, Vol. 42 
