TY - JOUR
T1 - On rigid displacements and their relation to the infinitesimal rigid displacement lemma in three-dimensional elasticity
AU - Ciarlet, Philippe G.
AU - Mardare, Cristinel
PY - 2003/5/15
Y1 - 2003/5/15
N2 - Let Ω be an open connected subset of ℝ3 and let Θ be an immersion from Ω into ℝ3. It is established that the set formed by all rigid displacements of the open set Θ(Ω) is a submanifold of dimension 6 and of class C∞ of the space H1(Ω). It is also shown that the infinitesimal rigid displacements of the same set Θ(Ω) span the tangent space at the origin to this submanifold.
AB - Let Ω be an open connected subset of ℝ3 and let Θ be an immersion from Ω into ℝ3. It is established that the set formed by all rigid displacements of the open set Θ(Ω) is a submanifold of dimension 6 and of class C∞ of the space H1(Ω). It is also shown that the infinitesimal rigid displacements of the same set Θ(Ω) span the tangent space at the origin to this submanifold.
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0037560844&origin=recordpage
U2 - 10.1016/S1631-073X(03)00191-2
DO - 10.1016/S1631-073X(03)00191-2
M3 - RGC 21 - Publication in refereed journal
SN - 1631-073X
VL - 336
SP - 873
EP - 878
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 10
ER -