The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon

Wang Xi

Volume 14 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 1993 > 14(8): 739-746

Wang Xi. The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon[J]. Applied Mathematics and Mechanics, 1993, 14(8): 739-746.

Citation:

Wang Xi. The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon[J]. Applied Mathematics and Mechanics, 1993, 14(8): 739-746.

Citation:

Wang Xi. The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon[J]. Applied Mathematics and Mechanics, 1993, 14(8): 739-746.

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The Elastodynamic Solution for a Solid Sphere and Dynamic Stress-Focusing Phenomenon

Wang Xi

Department of Applied Mechanics, East China Institute of Technology, Nanjing

Received Date: 1992-02-10
Publish Date: 1993-08-15

Abstract

Abstract

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.
- solid sphere,
- elastodynamics,
- dynamic stress-focusing

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References(5)

References

[1]	Tanter,C.J.,Application of the Laplace transform to a problem in elastic vibration,Philosophical Magazine,33(1942),614.
[2]	Baker,W.E.and F.J.Allen,The response of elastic spherical shell to spherically symmetric internal blast loading,Ballistic Research Laboratories,BRL Memo-1113 Nov AD156639(1957).
[3]	Cinelli,G.,An extension of the finite Hankel transform and applications,Int.J.Engng.Sci.,3(1965),539-559.
[4]	Miklowitz,J.,Elastic wave propagation.Applied Mechanics Surveys,Eds.by H.N.Abramson,et al.,Spartan Books,Washington(1966),809.
[5]	Wang Xi and Gong Yu-ning,A theoretical solution for axially symmetric problems in elastodynamics,ACTA Mechanica Sinica,7,3(1991).

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