Harmonic Holes—An Inverse Problem in Elasticity

[+] Author and Article Information
G. S. Bjorkman

Department of Civil Engineering, Drexel University, Philadelphia, Pa.

R. Richards

Department of Civil Engineering, University of Delaware, Newark, Del.

J. Appl. Mech 43(3), 414-418 (Sep 01, 1976) (5 pages) doi:10.1115/1.3423882 History: Received March 01, 1975; Revised January 01, 1976; Online July 12, 2010


A fundamental problem in elasticity is investigated: to determine the geometry of a boundary from prescribed conditions that must be satisfied by the final field stresses. For the planar problem the hole shape termed “harmonic” is the one which satisfies a specific design requirement that the first invariant of the original field remains everywhere unchanged. Using the complex variable technique a general functional equation for the hole geometry is obtained in integral form simply in terms of the original free field and hole boundary loading. The biaxial field is considered as an example with a uniformly distributed normal stress applied to the unknown hole boundary. It is shown that for this field, a properly proportioned and oriented elliptic hole satisfies the design requirement and simultaneously produces the minimum stress concentration for any possible unreinforced hole shape. For an unloaded boundary, this optimum hole exists only when the principal stresses in the original field have the same sign.

Copyright © 1976 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In