On rigid and infinitesimal rigid displacements in three-dimensional elasticity

被引：15
作者：
Ciarlet, PG
Mardare, C
机构：
[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
[2] Univ Paris 06, Lab Jacques Louis Lions, F-75005 Paris, France
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2003年 / 13卷 / 11期
关键词：
submanifold; rigidity theorem; infinitesimal rigid displacement lemma; three-dimensional; linearized elasticity;
D O I：
10.1142/S0218202503003045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Omega be an open connected subset of R-3 and let Theta be an immersion from Omega into R-3. It is first established that the set formed by all rigid displacements, i.e. that preserve the metric, of the open set Theta(Omega) is a submanifold of dimension 6 and of class C-infinity of the space H-1(Omega). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the same set Theta(Omega) is nothing but the tangent space at the origin to this submanifold. In this fashion, the familiar "infinitesimal rigid displacement lemma" of three-dimensional linearized elasticity is put in its proper perspective.
引用
收藏
页码：1589 / 1598
页数：10
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