On rigid and infinitesimal rigid displacements in shell theory
Ciarlet, Philippe G. ; Mardare, Cristinel
HAL, hal-00018089 / Harvested from HAL
Text on HAL
Let ω be an open connected subset of R^2 and let θ be an immersion from ω into R^3. It is first established that the set formed by all rigid displacements, i.e., that preserve the metric and the curvature, of the surface θ(ω) is a submanifold of dimension 6 and of class C^∞ of the space H^1(ω). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the same surface θ(ω) is nothing but the tangent space at the origin to this submanifold. In this fashion, the “infinitesimal rigid displacement lemma on a surface”, which plays a key role in shell theory, is put in its proper perspective.
Publié le : 2004-07-05
Classification:  Submanifold,  Rigidity theorem,  Infinitesimal rigid displacement lemma,  Shell theory,  [MATH]Mathematics [math],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00018089,
     author = {Ciarlet, Philippe G. and Mardare, Cristinel},
     title = {On rigid and infinitesimal rigid displacements in shell theory},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00018089}
}

Ciarlet, Philippe G.; Mardare, Cristinel. On rigid and infinitesimal rigid displacements in shell theory. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00018089/