Abstract

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 and a sequel evaluate the effect of out-of-plane, roller misalignment on the equilibrium and dynamic behavior of wide, axially moving, paper and textile webs. In this paper, a fully nonlinear shell theory that incorporates transverse shear strains is developed and used to determine the equilibrium deformation caused by roller misalignment. This model allows for consideration of large, possibly intentional, roller misalignment. The equations of equilibrium are reduced by assuming the web is deformed into a right helicoid. The resulting nonlinear, ordinary, differential equations are solved both numerically and analytically, employing perturbation. It is found that the longitudinal, membrane stress increases with the magnitude of roller misalignment. However, in a web with free longitudinal edges, the lateral, membrane stress is compressive for any roller misalignment. The translation speed acts, by way of centrifugal tensioning, to increase the lateral, membrane stress. Example results highlight other important conclusions concerning the equilibrium response of webs to out-of-plane roller misalignment.

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