Title

The shrink-fit problem for aeolotropic nonlinearly elastic bodies

Department/School

Mathematics

Date

1-1-1995

Document Type

Article

Keywords

shrink-fit problem, aeolotropic nonlinearly elastic bodies, linear elasticity

DOI

https://doi.org/10.1007/BF00040943

Abstract

In the classical shrink-fit problem of linear elasticity (cf. Timoshenko [4, Sec. 31]) an annulus of natural inner radius a and natural outer radius (scaled to be) 1 is expanded (e.g., by heating) and then allowed to shrink down upon a disk of natural radius b, which is greater than a. See Fig. 1.1. Here we solve generalizations of this axisymmetric problem for aeolotropic, nonlinearly elastic bodies of different constitution subject to arbitrary axisymmetric boundary conditions on the outer edge of the annulus. We show that these problems exhibit a remarkable richness of physical phenomena and we show how easy it is to determine the detailed qualitative properties, the existence or nonexistence, and the uniqueness or multiplicity of all equilibrium states. We also show how to construct solutions for problems in which there are several annular layers.

Published in

Journal of Elasticity

Citation/Other Information

Antman, S.S. & Shvartsman, M.M (1994). The shirink-fit problem for aeolotropic nonlinearly elastic bodies. Journal of Elasticity, 37, 157–166. https://doi.org/10.1007/BF00040943

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