Relative stiffness of elastic nets with Cartesian and Polar underlying structure

A specialized theory of elastic membrane is used to analyze the equilibrium configurations of elastic nets. It is of interest to learn the influence of the underlying structure on the mechanical response of nets. In this work selected net shapes and underlying fiber structures are considered under several loading conditions. The finite element method is used to analyze the transverse stiffness of these nets. The results suggest that the underlying structure has strong influence on the stiffness property of the net. In particular, the results indicate that the Polar structure is stiffer than the Cartesian structure when the net is poked near its center but that the relative stiffness is reversed when the net is poked far enough from its center. These results can be used for optimal design of special-purpose net structures.