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End displacements of semi‐infinite cylinders due to annular loadings
Author(s) -
Wilson E. A.
Publication year - 1969
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620010207
Subject(s) - cylinder , superposition principle , rotational symmetry , mathematics , geometry , half space , surface (topology) , mathematical analysis , fourier series , displacement (psychology) , boundary value problem , integral transform , mechanics , physics , psychology , psychotherapist
Surface displacements at the end of a semi‐infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter‐part half‐space solution. The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half‐space is found by using the Boussinesq solution. Then, the excess tractions on the half‐space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid‐section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed. With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half‐space; 2. a rigid punch in contact with an elastic cylinder.