Response of an Elastic Half Space to Expanding Surface Loads

[+] Author and Article Information
D. C. Gakenheimer

The RAND Corporation, Santa Monica, Calif.

J. Appl. Mech 38(1), 99-110 (Mar 01, 1971) (12 pages) doi:10.1115/1.3408774 History: Received December 29, 1969; Revised February 16, 1970; Online July 12, 2010


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.

Copyright © 1971 by ASME
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