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# Accession Number:

## AD0671525

# Title:

## SURFACE DISPLACEMENTS ON THE END OF AN ELASTIC CYLINDER.

# Descriptive Note:

## Technical rept. 1 Jan-31 Dec 67,

# Corporate Author:

## RENSSELAER POLYTECHNIC INST TROY N Y DEPT OF MECHANICS

# Report Date:

## 1967-02-01

# Pagination or Media Count:

##
125.0

# Abstract:

## For contact problems in general and elastohydrodynamic or elasto-plasto-hydrodynamic problems in particular, surface displacements of the dies are important. In a reassessment study of the Bridgman anvil method for measuring shear strength of materials the surface displacements on the end of a long, circular cylinder due to an axisymmetric ring of forces on the end is required. Furthermore, it is required that there be no boundary tractions on the lateral surface. The solution found may then be used to find surface displacements for general axisymmetric loadings by superposition. The solution, in tabular form, is given as corrections to the corresponding half-space solution. This table is expected to be of far reaching applicability. The method of solution involves a succession of superposition processes. First, the normal and shear stresses in a half-space due to a ring of forces are found by numerically integrating the Boussinesq solution. Second, the excess tractions in the half-space, over that of the cylinder, are removed. The third and last step is to remove the o sub z introduced in step two. This is done by finding a set of boundary conditions for the end of the semi-infinite cylinder which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate o sub z. With the solution thus obtained for the semi-infinite cylinder, three sample problems are solved 1 an elastic cylinder in contact with an elastic parabolic half-space 2 a rigid punch in contact with an elastic cylinder 3 the compression of a thin plastic mass between two elastic cylinders under high loads. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#