✍ Scribed by M.T. Grießer; P.M. Taylor
No coin nor oath required. For personal study only.
This paper describes a new approach to find the shape of a piece of bent fabric. A general form for the potential and bending energy stored in a fabric is stated, based on the frictional couple theory. With the help of the calculus of variations the differential equation for the bent shape is then derived. An approximation is made to find an analytical function for the shape of horizontally clamped fabrics bending under their own weight. This analytical function can be used to calculate from experimental data the bending stiffness as well as the bending and potential energy stored in the fabric. Alternatively an inverse function can be used to derive the bent shape of a piece of fabric, given knowledge of its stiffness and unit weight without the need for any numerical techniques. There is a very good agreement between experiment and theory.
Previous work resulted in polynomial curve fitting to experimental data or numerical solutions derived from physical models; the analytical function allows much improved understanding of the relationship between the fabric's shape and the mechanical parameters.
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