Stretching the circular cylindrical elastic sheet

Bowman, B. F.

doi:10.1090/qam/592198

Author: B. F. Bowman
Journal: Quart. Appl. Math. 38 (1980), 313-322
MSC: Primary 73C20
DOI: https://doi.org/10.1090/qam/592198
MathSciNet review: 592198
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Abstract: The theory of thin elastic sheets, neglecting bending, is applied to many thin surface problems. The classical theory for these surfaces is inadequate when the strains are small, the surface is unstressed before deformation, and boundary displacements are prescribed. The equations in this case are degenerate. Attempts to solve the exact equations for these elastic membranes have failed for small strains. The purpose of this paper is to determine the behavior of the solution to the exact equations for the elastic surface which is initially a circular cylinder and which is deformed by a uniform pull at the ends keeping the end radii fixed. A resolution of the small-strain behavior both analytically and numerically is of particular importance.

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