This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff's hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two...

A geometrically exact model of a Cosserat rod with nonholonomic constraints is outlined. The constraint forces are derived from the framework of nonholonomic mechanics by using arguments from Cauchy analysis, and a thorough discussion is given concerning the nature of these constraints. By making an additional assumption on the magnitude of the deflections, a simplified model similar to the Eul...

A Γ-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane...

In this paper, we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. framework of linear model, provide a comparison our models with classical Koiter shell model and “best” first-order For all proposed models, show existence uniqueness based on Korn’s inequality for surfaces.

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that classical Navier–Stokes equation does not fully describe motion water. In this article, we propose an approach to dynamics formed chiral, planar and rigid molecules some kind equations for their description. Examples such are water, ozone, carbon dioxide hydrogen cyanide.