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RESEARCH PAPERS

Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials

[+] Author and Article Information
Nihal Somaratna

Engineering Technology Associates, Southfield, MI 48076

T. C. T. Ting

Department of Civil Engineering, Mechanics and Metallurgy, University of Illinois at Chicago, Chicago, IL 60680

J. Appl. Mech 53(1), 89-96 (Mar 01, 1986) (8 pages) doi:10.1115/1.3171744 History: Received February 21, 1985; Revised May 31, 1985; Online July 21, 2009

Abstract

This study examines analytically the possible existence of stress singularities of the form σ = ρδ f( θ,φ) at the apex of axisymmetric conical boundaries in transversely isotropic materials. (ρ, θ, φ) refer to spherical coordinates with the origin at the apex. The problems of one conical boundary and of two conical boundaries with a common apex are considered. The boundaries are either rigidly clamped or traction free. Separation of variables enables the general solution to be expressed in terms of Legendre functions of the first and second kind. Imposition of boundary conditions leads to an eigenequation that would determine possible values of δ. The degenerate case that arises when the eigenvalues of the elasiticity constants are identical is also discussed. Isotropic materials constitute only a particular case in this class of degenerate materials and previously reported eigenequations corresponding to isotropic materials are shown to be recoverable from the present results. Numerical results corresponding to a few selected cases are also presented to illustrate the solution procedure.

Copyright © 1986 by ASME
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