Harmonic Holes for Nonconstant Fields

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

Structural Analysis Group, United Engineers and Constructors, Inc., Philadelphia, Pa. 19101

R. Richards

Department of Civil Engineering, University of Delaware, Newark, Del. 19711

J. Appl. Mech 46(3), 573-576 (Sep 01, 1979) (4 pages) doi:10.1115/1.3424608 History: Received April 01, 1977; Revised January 01, 1978; Online July 12, 2010


Hole shapes which do not perturb the first invariant of the stress tensor of an isotropic stress field with superimposed linear gradients are derived. These haromonic holes, called the deloid and cardeloid, result from the solution of a nonlinear singular integral equation and can be expressed very simply in parametric form. A comparison of stresses around the boundary of a deloid with a circular hole of the same size shows that the deloid significantly reduces not only the maximum stress concentration but also the total variation of stress around the hole boundary. Deloids and cardeloids without internal boundary loading exist only in locations where the first invariant of the original field does not change sign.

Copyright © 1979 by ASME
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