Spherelike Deformations of a Balloon
نویسنده
چکیده
characterizing the meridian curve of a closed membrane of revolution at its undeformed state. By a closed membrane we mean that the curve C, together with the axis of symmetry, r — 0, encloses a simply connected domain. Suppose the membrane, composed of a Mooney material [2], is inflated by a properly nondimensionalized pressure p. Isaacson [1] has shown that as p —> the shape of the inflated membrane becomes spherical. We develop formal asymptotic series to represent the inflated membrane and find the series are power series in the parameter p~2 and that the lowest-order term verifies the formula in [1]. The inflated membrane approaches a spherical surface of radius R„ asymptotically as p —> °°, with
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