The Strain-Energy Density of Rubber-Like Shells of Revolution Undergoing Torsionless, Axisymmetric Deformation (Axishells)

[+] Author and Article Information
J. G. Simmonds

Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22901

J. Appl. Mech 53(3), 593-596 (Sep 01, 1986) (4 pages) doi:10.1115/1.3171816 History: Received January 15, 1985; Revised February 23, 1986; Online July 21, 2009


We consider a shell of revolution made of an incompressible elastically isotropic material. Assuming a torsionless, axisymmetric three-dimensional displacement field that permits large normal strains (i.e., large thickness changes) but small transverse shearing strains, we construct a two-dimensional strain-energy density for a first-approximation shell theory in which the extensional strains may be O (1). The bending strains, however, are small, as in Reissner’s nonlinear theory. An error estimate is given that depends on the undeformed thickness and curvatures, the bending strains, the transverse shearing strain, and the characteristic wavelength of the shell theory solutions.

Copyright © 1986 by ASME
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