FINITE AXISYMMETRIC DEFORMATIONS OF AN INITIALLY CYLINDRICAL ELASTIC MEMBRANE ENCLOSING A RIGID BODY

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Abstract
We consider axisymmetric deformations of an initially cylindrical membrane composed of an incompressible homogeneous, isotropic elastic material possessing a strain energy function. No restriction is imposed on the form of the strain energy function. A rigid body is enclosed by the deformed membrane and a uniform internal pressure Po is applied on that part of the surface of the membrane which is not in contact with the enclosed body. The solutions are given to two separate problems. In the first problem, the membrane has a finite length and its ends are bonded to rigid rings on which an axial force F is applied. In the second problem, the membrane has an infinite length and the axial force tends to a constant value F at large distances from the inclusion. For both problems the deformed configuration is determined in terms of Po, F, the geometry of the enclosed solid and the dimensions of the deformed membrane. The solutions obtained are exact and valid for the general form of the strain-energy function. For the particular case of a Mooney material, some numerical results are given as well as further remarks on the solutions.

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