THE ELASTODYNAMIC SOLUTION FOR A SOLID SPHERE AND DYNAMIC STRESS-FOCUSING PHENOMENON  

作　　者：王熙 

机构地区：[1]Department of Applied Mechanics, East China Institute of Technology, Nanjing

出　　处：《Applied Mathematics and Mechanics(English Edition)》1993年第8期777-785,共9页应用数学和力学（英文版）

摘　　要：This paper presents an analytical method of solving the elastodynamic problem of a solid sphere. The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions. By utilizing the variable transform, the dynamic equation may be transformed into Bassel equation. By defining a finite Hankel transform, we can easily obtain the dynamic solution for the inhomogeneous dynamic equation. Thereby, the exact elastodynamic solution for a solid sphere can be obtained. From results carried out, we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.This paper presents an analytical method of solving the elastodynamic problem of a solid sphere. The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions. By utilizing the variable transform, the dynamic equation may be transformed into Bassel equation. By defining a finite Hankel transform, we can easily obtain the dynamic solution for the inhomogeneous dynamic equation. Thereby, the exact elastodynamic solution for a solid sphere can be obtained. From results carried out, we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.

关 键 词：solid sphere ELASTODYNAMICS dynamic stress-focusing 

分 类 号：O3，O1[理学—力学]