The dynamics of Cosserat nets. (English) Zbl 1205.74124

Summary: A formulation of the dynamics of a collection of connected simple 1-dimensional Cosserat continua and rigid bodies is presented in terms of sections of an \(\text{SO}(3)\) fibration over a 1-dimensional net. A large class of junction conditions is considered in a unified framework. All the equations of motion and junction conditions are derived as extrema of a constrained variational principle on the net and are analysed perturbatively for structures with Kirchhoff constitutive properties. The whole discussion is based on the notion of a Cosserat net and its contractions obtained by taking certain limits that transform Cosserat elements to rigid structures. Generalisations are briefly discussed within this framework.


74K30 Junctions
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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