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TECHNICAL PAPERS

Harmonic Shapes in Finite Elasticity Under Nonuniform Loading

[+] Author and Article Information
G. F. Wang, C.-Q. Ru

Department of Mechanical Engineering,  University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta T6G 2G8, Canada

P. Schiavone1

Department of Mechanical Engineering,  University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta T6G 2G8, Canadap.schiavone@ualberta.ca

1

To whom correspondence should be addressed.

J. Appl. Mech 72(5), 691-694 (Dec 03, 2004) (4 pages) doi:10.1115/1.1979514 History: Received July 09, 2004; Revised December 03, 2004

We investigate the classic (inverse) problem concerned with the design of so-called harmonic shapes for an elastic material undergoing finite plane deformations. In particular, we show how to identify such shapes for a particular class of compressible hyperelastic materials of harmonic type. The “harmonic condition,” in which the sum of the normal stresses in the original stress field remains unchanged everywhere after the introduction of the harmonic hole or inclusion, is imposed on the final stress field. Using complex variable techniques, we identify particular harmonic shapes arising when the material is subjected nonuniform (remote) loading and discuss conditions for the existence of such shapes.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Harmonic shape for different loading scenarios

Grahic Jump Location
Figure 1

Schematic of the strategy used to identify a harmonic shape

Grahic Jump Location
Figure 3

Condition for the existence of the harmonic shape

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