A general approach to the numerical solutions for axially symmetric membrane problem is presented. The formulation of the problem leads to a system of first-order nonlinear differential equations. These equations are formulated such that the numerical integration can be carried out for any form of strain-energy function. Solutions to these equations are feasible for various boundary conditions. In this paper, these equations are applied to the problem of a bonded toroid under inflation. A bonded toroid, which is in the shape of a tubeless tire, has its two circular edges rigidly bonded to a rim. The Runge-Kutta method is employed to solve the system of differential equations, in which Mooney’s form of strain-energy function is adopted.
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Finite Inflation of a Bonded Toroid
K. H. Hsu
Babcock & Wilcox Company, Research Center, Alliance, Ohio
Hsu, K. H. (June 1, 1972). "Finite Inflation of a Bonded Toroid." ASME. J. Appl. Mech. June 1972; 39(2): 491–494. https://doi.org/10.1115/1.3422705
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