ON RIGID AND INFINITESIMAL RIGID DISPLACEMENTS IN THREE-DIMENSIONAL ELASTICITY

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1589-1598
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume13
Issue number11
Publication statusPublished - Nov 2003

Abstract

Let Ω be an open connected subset of ℝ3 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, of the open set 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 same set Θ(Ω) 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.

Research Area(s)

  • Infinitesimal rigid displacement lemma, Rigidity theorem, Submanifold, Three-dimensional linearized elasticity