Abstract
This paper treats the global qualitative behavior of axisymmetric buckled states of a nonlinearly elastic circular plate subject to uniform pressure on its edge. In contrast to the von Kármán equations used by Wolkowisky (1967) in a related study, the equations used here furnish a geometrically exact description of the deformation including shear and account for a very general nonlinear material response. The global bifurcation theory of Crandall & Rabinowitz (1970) and of Rabinowitz (1970, 1971a,b, 1973) is adapted to show that large solutions preserve the nodal structure they inherit from the eigenfunctions of the problem linearized about the trivial solution.
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Antman, S.S. Buckled states of nonlinearly elastic plates. Arch. Rational Mech. Anal. 67, 111–149 (1978). https://doi.org/10.1007/BF00249503
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DOI: https://doi.org/10.1007/BF00249503