Energy-Minimal Finite Deformations of a Symmetrically Loaded Elastic Sheet
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.
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
Mechanical and Aerospace Engineering
Article - Journal
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