Analysis of bookshelf mechanisms using the mechanics of Cosserat generalized continua.

Abstract

Bookshelf type mechanisms are commonly used to explain antithetic accommodation of deformations caused by direct shear. Stress analysis of such mechanisms have been proposed, mainly through the use of classic Mohr circle graphical constructions. The present work introduces an alternative framework for analysis, the mechanics of generalized Cosserat continua, although maintaining the same tools (Mohr circle construction). In this type of mechanics, kinematics of the material points incorporates independent rotational degrees of freedom besides the classic translational ones. In the equilibrium equations, quantities involving moments are generated and the stress tensor is in the general case non-symmetric. Such characteristics of generalized Cosserat continua make it suitable for the analysis of Bookshelf mechanisms, as these are, in essence, rotational antithetic mechanisms induced by shear stresses having different magnitudes in perpendicular planes. The paper applies the mechanics of generalized continua to the analysis of a specific bookshelf mechanism, related to crustal extension. In the Appendices, a review of the generalized Cosserat continua and details of the graphical Mohr circle representation of stresses for such media are presented.