About the Directions of Principal Eccentricities in Continuous Shells

We recently extended the definition of funicularity for continuous shells, introducing the concept of Relaxed Funicularity (R-Funicularity or RF). Funicular shells are defined as shells whose static behavior is given by only local membrane actions. Extension to RF is needed as funicular shells [1] can only attain pure membrane behavior for very specific boundary conditions (bcs). The RF born also for quantifying the quality of the shape of a shell, for given load and bcs, including ’small’ moments effects. Quantification of RF is made by defining a generalized eccentricity (GE) measure and verifying that the GE fall inside some eccentricity limits. Aim of this work is to discuss the nature of the GE and its associated eigenvalue problem, that allows to calculate principal eccentricities (PEs) and their directions. It is also shown how the directions of PEs are related to the relative angle between the principal directions of membrane and bending internal actions.