Elastic Fields Resulting From Concentrated Loading on a Three-Dimensional Incompressible Wedge

[+] Author and Article Information
M. T. Hanson

Department of Engineering Mechanics, University of Kentucky, Lexington, KY 40506-0046

J. Appl. Mech 62(3), 557-565 (Sep 01, 1995) (9 pages) doi:10.1115/1.2895981 History: Received June 18, 1993; Revised May 05, 1994; Online October 30, 2007


This paper considers point force or point moment loading applied to the surface of a three-dimensional wedge. The wedge is two-dimensional in geometry but the loading may vary in a direction parallel to the wedge apex, thus creating a three-dimensional problem within the realm of linear elasticity. The wedge is homogeneous, isotropic, and the assumption of incompressibility is taken in order for solutions to be obtained. The loading cases considered presently are as follows: point normal loading on the wedge face, point moment loading on the wedge face, and an arbitrarily directed force or moment applied at a point on the apex of the wedge. The solutions given here are closed-form expressions. For point force or point moment loading on the wedge face, the elastic field is given in terms of a single integral containing associated Legendre functions. When the point force or moment is at the wedge tip, closed-form (nonintegral) expressions are obtained in terms of elementary functions. An interesting result of the present research indicates that the wedge paradox in two-dimensional elasticity also exists in the three-dimensional case for a concentrated moment at the wedge apex applied in one direction, but that it does not exist for a moment applied in the other two directions.

Copyright © 1995 by The American Society of Mechanical Engineers
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