A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
UNSPECIFIED (2002) A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 55 (11). pp. 1461-1506. ISSN 0010-3640Full text not available from this repository.
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 Gamma-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 --> R-n, U subset of R-n. We show that the L-2-distance of delupsilon from a single rotation matrix is bounded by a multiple of the L-2-distance from the group SO(n) of all rotations. (C) 2002 Wiley Periodicals, Inc.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS|
|Publisher:||JOHN WILEY & SONS INC|
|Number of Pages:||46|
|Page Range:||pp. 1461-1506|
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