A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
Abstract
The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of three‐dimensional nonlinear elasticity theory as the thickness of a plate goes to zero. A key ingredient in the proof is a sharp rigidity estimate for maps v : U → ℝn, U ⊂ ℝn. We show that the L2‐distance of ∇v from a single rotation matrix is bounded by a multiple of the L2‐distance from the group SO(n) of all rotations. © 2002 Wiley Periodicals, Inc.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 23, 2002
- Source ID
- 10.1002/cpa.10048
Entities
People
- Gero Friesecke
- Richard D. James
- Stefan Müller
Organizations
- National Science Foundation
- Office of Naval Research