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Journal Articles Journal of Nonlinear Science Year : 2016

Poincaré’s Equations for Cosserat Media: Application to Shells

Abstract

In 1901 Henri Poincaré discovered a new set of equations for mechanics. These equations are a generalization of Lagrange's equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we extend these equations from classical mechanical systems to continuous Cosserat media, i.e. media in which the usual point particles are replaced by small rigid bodies, called micro-structures. In particular, we will see how the Shell balance equations used in nonlinear structural dynamics, can be easily derived from this extension of the Poincaré's result.

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Dates and versions

hal-01230677 , version 1 (18-11-2015)
hal-01230677 , version 2 (27-09-2016)
hal-01230677 , version 3 (03-10-2016)

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Frédéric Boyer, Federico Renda. Poincaré’s Equations for Cosserat Media: Application to Shells. Journal of Nonlinear Science, 2016, pp.1-44. ⟨10.1007/s00332-016-9324-7⟩. ⟨hal-01230677v3⟩
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