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.
Skip Nav Destination
Response of an Elastic Half Space to Expanding Surface Loads
D. C. Gakenheimer
The RAND Corporation, Santa Monica, Calif.
- Views Icon Views
- Share Icon Share
- Search Site
Gakenheimer, D. C. (March 1, 1971). "Response of an Elastic Half Space to Expanding Surface Loads." ASME. J. Appl. Mech. March 1971; 38(1): 99–110. https://doi.org/10.1115/1.3408774
Download citation file:
Get Email Alerts
Nonlinear Oscillations of Dielectric Elastomer Actuators With Stretch-Dependent Permittivity
J. Appl. Mech (November 2022)
Moiré Tuning of the Dynamic Behavior of a Twisted Bilayer van der Waals Material Resonator
J. Appl. Mech (December 2022)