Solution of Two-Body Axially-Symmetric Elasticity Problems by the Distribution of Singularities.
NAVAL AIR DEVELOPMENT CENTER WARMINSTER PA AERO MECHANICS DEPT
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A general method is presented for determining the displacement and stress fields within axially-symmetric elastic bodies due to prescribed internal loadings and boundary conditions. The solutions obtained satisfy the exact three-dimensional equations of linear elasticity. All internal forces of the problem are applied at corresponding locations in an infinite body. The effects of these forces on the infinite body are determined using Kelvins solution for a point force. A distribution of point forces in the infinite body external to the region of the original problem is then determined such that the total combined effect of internal and external forces satisfies the conditions prescribed on the boundary of the original problem. Determination of the proper distribution of singularities is the essence of this method. The formulation is applicable to multi-body problems, as illustrated by a two-body example presented, and may serve to generate information on interface stresses in fiber reinforced composite materials. Author-PL
- Laminates and Composite Materials