The dynamics of Cosserat nets. (English) Zbl 1205.74124

Gratus, J.; Tucker, R. W.

J. Appl. Math. 2003, No. 4, 187-226 (2003).

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.

MSC:

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