ISSN:
1573-2754
Keywords:
solid sphere
;
elastodynamics
;
dynamic stress-focusing
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Mathematics
,
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02453330
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