Steady motions of translating, twisted webs

The literature on thin, narrow axially moving materials is diverse and mature. However, few investigators have studied the behavior of thin, wide translating continua. This paper evaluates the effect of twist on the equilibrium of wide, axially moving webs. A fully non-linear shell theory that incorporates transverse shear strains is developed and used to determine the equilibrium deformation. This model allows for consideration of large, possibly intentional, twist from effects like roller misalignment. The equations of steady motion are reduced by assuming that the twisted web deforms into a right helicoid. The resulting non-linear, ordinary, differential equations are solved both numerically and analytically. The longitudinal, membrane stress increases with the twist. However, in a web with free lateral edges, the lateral, membrane stress is compressive for any twist of its ends. The translation speed acts, by way of centrifugal tensioning, to increase the lateral, membrane stress. Example results highlight the steady response of translating webs with twisted ends.