Mathematics – Differential Geometry
Scientific paper
2012-01-17
Mathematics
Differential Geometry
60 pages
Scientific paper
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 embedding that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally-reduced limit theory views the elastic body as a $k$-dimensional Riemannian manifold along with an isometric $W^{2,2}$-immersion in $n$-dimensional Euclidean space and linear data in the normal directions. The equilibrium configuration minimizes a functional depending on the average covariant derivatives of the linear data. The dimensionally-reduced limit is obtained using a $\Gamma$-convergence approach. The limit includes as particular cases plate, shell, and rod theories. It applies equally to "standard" elasticity and to "incompatible" elasticity, thus including as particular cases so-called non-Euclidean plate, shell, and rod theories.
Kupferman Raz
Solomon Jake P.
No associations
LandOfFree
A Riemannian Approach to Reduced Plate, Shell, and Rod Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Riemannian Approach to Reduced Plate, Shell, and Rod Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Riemannian Approach to Reduced Plate, Shell, and Rod Theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97919