On Axisymmetrical Deformations of Nonlinear Membranes

[+] Author and Article Information
W. H. Yang

Department of Engineering Mechanics, The University of Michigan, Ann Arbor, Mich.

W. W. Feng

Department of Mechanical Engineering, Carnegie-Mellon University, Pittsburgh, Pa.

J. Appl. Mech 37(4), 1002-1011 (Dec 01, 1970) (10 pages) doi:10.1115/1.3408651 History: Received August 08, 1969; Revised February 04, 1970; Online July 12, 2010


The mechanics problem concerning large axisymmetric deformations of nonlinear membranes is reformulated in terms of a system of three first-order ordinary differential equations with explicit derivatives. With a set of proper boundary conditions, arrangements are made to change the boundary-value problem into the form of an initial value problem such that the solution can be obtained by standard numerical methods for integrating ordinary differential equations. The system of equations derived applies to the class of all axisymmetric deformations of membranes with a general elastic stress-strain relation. Three examples are given on inflating of a flat membrane, longitudinal stretching of a tube, and flattening of a semispherical cap. In the examples, the Mooney model are assumed to describe the material behavior of the membranes. The solution on the flat membrane serves to compare with an existing one in literature. The solutions on the tube and the cap are new.

Copyright © 1970 by ASME
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