This study examines analytically the possible existence of stress singularities of the form σ = ρδf(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.
Skip Nav Destination
Article navigation
March 1986
Research Papers
Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials
Nihal Somaratna,
Nihal Somaratna
Engineering Technology Associates, Southfield, MI 48076
Search for other works by this author on:
T. C. T. Ting
T. C. T. Ting
Department of Civil Engineering, Mechanics and Metallurgy, University of Illinois at Chicago, Chicago, IL 60680
Search for other works by this author on:
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. Mar 1986, 53(1): 89-96 (8 pages)
Published Online: March 1, 1986
Article history
Received:
February 21, 1985
Revised:
May 31, 1985
Online:
July 21, 2009
Citation
Somaratna, N., and Ting, T. C. T. (March 1, 1986). "Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials." ASME. J. Appl. Mech. March 1986; 53(1): 89–96. https://doi.org/10.1115/1.3171744
Download citation file:
Get Email Alerts
Related Articles
Couette Resistance Due to a Sliding Plate Over a Plate With Stripes of Nonhomogeneous Slip
J. Fluids Eng (January,2022)
Localization-Induced Band and Cohesive Model
J. Appl. Mech (December,2000)
On the Stress Singularities at Multimaterial Interfaces and Related
Analogies With Fluid Dynamics and Diffusion
Appl. Mech. Rev (March,2008)
Stress singularities in classical elasticity—II: Asymptotic identification
Appl. Mech. Rev (September,2004)
Related Chapters
Evaluating Fatigue Life of Compressor Dovetails by Using Stress Singularity Parameters at the Contact Edge
Fretting Fatigue: Advances in Basic Understanding and Applications
Strategy of the Traction Railway Vehicle for Achievement of the Economical Exploitation Parameters
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Vectorial Regulation of the Traction Engine with Automaticcommand for Railway Vehicle
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)