TY - JOUR
T1 - On rigid and infinitesimal rigid displacements in shell theory
AU - Ciarlet, Philippe G.
AU - Mardare, Cristinel
PY - 2004/1
Y1 - 2004/1
N2 - Let ω be an open connected subset of ℝ2 and let θ be an immersion from ω into ℝ3. 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 H1(ω). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the 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.
AB - Let ω be an open connected subset of ℝ2 and let θ be an immersion from ω into ℝ3. 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 H1(ω). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the 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.
KW - Infinitesimal rigid displacement lemma
KW - Rigidity theorem
KW - Shell theory
KW - Submanifold
UR - http://www.scopus.com/inward/record.url?scp=0346937293&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0346937293&origin=recordpage
U2 - 10.1016/j.matpur.2003.09.004
DO - 10.1016/j.matpur.2003.09.004
M3 - RGC 21 - Publication in refereed journal
VL - 83
SP - 1
EP - 15
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 1
ER -