A Riemannian Approach to Reduced Plate, Shell, and Rod Theories

  title={A Riemannian Approach to Reduced Plate, Shell, and Rod Theories},
  author={R. Kupferman and Jake P. Solomon},
  journal={Journal of Functional Analysis},
  • R. Kupferman, Jake P. Solomon
  • Published 2014
  • Mathematics, Physics
  • Journal of Functional Analysis
  • Abstract We derive a dimensionally-reduced limit theory for an n-dimensional nonlinear elastic body that is slender along k dimensions. The starting point is to view an elastic body as an n-dimensional Riemannian manifold together with a not necessarily isometric W 1 , 2 -immersion in n-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally-reduced limit theory views the… CONTINUE READING
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