Energy-Minimal Finite Deformations of a Symmetrically Loaded Elastic Sheet

Author

G. P. MacSithigh, Missouri University of Science and TechnologyFollow

Abstract

We study the homogeneous finite deformations of a rectangular sheet of a Mooney–Rivlin material subjected to equal tensile dead loads. We prove the existence of (at least one) homogeneous equilibrium which minimizes the potential energy of the system, and we determine the class of homogeneous minimizers for each value of the applied tension. In the process, we identify a critical value of a material parameter (the ratio of the Mooney–Rivlin constants) at which the qualitative nature of the solution class undergoes a change.

Recommended Citation

G. P. MacSithigh, "Energy-Minimal Finite Deformations of a Symmetrically Loaded Elastic Sheet," Quarterly Journal of Mechanics & Applied Mathematics, Oxford University Press, Jan 1984.

The definitive version is available at https://doi.org/10.1093/qjmam/39.1.111

Department(s)

Mechanical and Aerospace Engineering

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1984 Oxford University Press, All rights reserved.

Publication Date

01 Jan 1984