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

@article{Kupferman2014ARA,
title={A Riemannian Approach to Reduced Plate, Shell, and Rod Theories},
author={R. Kupferman and Jake P. Solomon},
journal={Journal of Functional Analysis},
year={2014},
volume={266},
pages={2989-3039}
}

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