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 o n the equilibrium of wide, axially moving webs. A fully non-linear she ll theory that incorporates transverse shear strains is developed and used to determine the equilibrium deformation. This model allows for c onsideration of large, possibly intentional, twist from effects like r oller misalignment. The equations of steady motion are reduced by assu ming that the twisted web deforms into a right helicoid. The resulting non-linear, ordinary, differential equations are solved both numerica lly and analytically. The longitudinal, membrane stress increases with the twist. However, in a web with free lateral edges, the lateral, me mbrane stress is compressive for arty twist of its ends. The translati on speed acts, by way of centrifugal tensioning, to increase the later al, membrane stress. Example result; highlight the steady response of translating webs with twisted ends. (C) 1998 Elsevier Science Ltd. All rights reserved.