Abstract

Our webs are wide, very thin, two-dimensional, continua arising commonly as a material in transport in machine systems. Though they are thin, webs often require modeling as plates or shells, albeit very thin and flexible ones, because even small bending stiffness distinguishes their behaviors from membranes in critical ways. Technological applications generating interest in web mechanics include the manufacture and handling of paper where wide sheets are transported by rollers at the highest possible speed, thereby maximizing productivity. Material handling problems of a similar type also arise with tissues, films, magnetic media, textiles, fabrics, polymer sheets, and the like. In a technical world pressing for ever higher speeds of stable transport, the web instabilities of wrinkling and flutter commonly bound the productivity of a technological process. These instabilities can result in permanent damage or rupture of the material and disruption of the manufacturing process. Consequently, the presentation today addresses some findings on webs that relate to their modeling, the prediction and causes of wrinkling, and the effect of roller misalignment on web behavior during transport. To allow us to maintain this focus, the rich collection of works on membrane structures, including modeling of inflated membranes, space structures and fiber reinforced membranes will not be part of our discussion. For attention to interesting membrane developments readers might examine Reissner (1938), Steigmann and Pipkin (1989), Jenkins and Leonard (1991), Li and Steigmann (1993), and Haseganu and Steigmann (1994). The most important topic of web flutter caused by air flows over the web surfaces will not be addressed, though recent experimental findings can be found in Chang and Moretti (1992) and Nguyen (1993). Theories modeling the flow and web in these coupled problems tend to underestimate the flutter speeds. This problem area is one of great importance.

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