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On rigid and infinitesimal rigid displacements in three-dimensional elasticity

Abstract : Let Ω be an open connected subset of R^3 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, of the open set 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 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.
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Contributor : Cristinel Mardare <>
Submitted on : Saturday, October 25, 2014 - 6:11:07 PM
Last modification on : Saturday, March 28, 2020 - 2:19:51 AM

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Philippe G. Ciarlet, Cristinel Mardare. On rigid and infinitesimal rigid displacements in three-dimensional elasticity. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2003, 13 (11), pp.1589-1598. ⟨10.1142/S0218202503003045⟩. ⟨hal-01077590⟩



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