Compressibility of Two-Dimensional Cavities of Various Shapes

[+] Author and Article Information
R. W. Zimmerman

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Appl. Mech 53(3), 500-504 (Sep 01, 1986) (5 pages) doi:10.1115/1.3171802 History: Received December 03, 1985; Online July 21, 2009


Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

Copyright © 1986 by ASME
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