On rubber disks under rotation or axisymmetric stretching |
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Authors: | William W Feng |
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Institution: | Department of Mechanical Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A. |
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Abstract: | The governing equations for a class of axisymmetric problems under large elastic deformation, concerned with a circular rubber disk with body force as well as non-uniform initial thickness, are formulated in terms of two coupled first-order ordinary differential equations with explicit derivatives. The following two problems subjected to different boundary conditions are solved: (a) Rotating disks with uniform initial thickness (b) Circular disks with non-uniform initial thickness under axisymmetric stretching at the outer boundary. In problem (b), the rubber disk whose initial thickness contour is h0 = crn (where c and n are any constants), or whose final thickness is a constant, is considered. Highly elastic materials with a Mooney strain-energy function are used for numerical calculations. |
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