Closure to “Discussion of ‘Response of an Elastic Half Space to Expanding Surface Loads’” (1971, ASME J. Appl. Mech., 38, p. 717)

1971 ◽  
Vol 38 (3) ◽  
pp. 717-718
Author(s):  
D. C. Gakenheimer
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Surface Loads

Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

2000 ◽  
Vol 68 (2) ◽  
pp. 162-168 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Arbitrary Constant ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Poisson Effect ◽  
Wave Speeds ◽  
Wave Patterns ◽  
Infinitesimal Deformations ◽  
Surface Loads

A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.

Stresses in an Elastic Half Space Due to Surface Loads Progressing at the Speed of Rayleigh Waves

1972 ◽  
Vol 39 (2) ◽  
pp. 372-377
Author(s):  
I. S. Sandler ◽  
H. H. Bleich
Keyword(s):  
Elastic Medium ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Basic Form ◽  
Surface Loads

The nature of the singularity in the stresses produced near the front of a progressing step load of pressure on the surface of an elastic half space is investigated for the case when the velocity of the front coincides with that of Rayleigh waves in the elastic medium. The technique is based on the assumption of the basic form of the solution and the demonstration that this assumption is correct. It is found that for the particular velocity of the front considered here, unusually large stresses are produced in the medium.

Response of an Elastic Half Space to Expanding Surface Loads

1971 ◽  
Vol 38 (1) ◽  
pp. 99-110 ◽  
Author(s):  
D. C. Gakenheimer
Keyword(s):  
Rayleigh Wave ◽  
Exact Solutions ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Constant Rate ◽  
Different Depths ◽  
Surface Loads

A class of elastic half-space problems involving axisymmetric, normally applied, surface loads is investigated. Each load is assumed to suddenly emanate from a point on the surface and expand radially at a constant rate. The cases of loads shaped like a ring and a disk are considered in detail. Exact solutions are derived for the displacements at every point in the half space in terms of single integrals. Each integral is identified as a specific wave. The integrals are evaluated analytically and numerically for different depths in the half space, for loads expanding at superseismic, transeismic, and subseismic rates, and for different values of Poisson’s ratio. Moreover, the interaction of the loads and the Rayleigh wave is described. Then solutions are obtained for loads of other shapes by convoluting the ring and disk load solutions.

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