LARGE DEFLECTION ANALYSIS OF WET FIBER FLEXIBILITY MEASUREMENT TECHNIQUES

The equations for large and small deflection analyses of beams were in troduced and applied to the following fibre flexibility measurement me thods: cantilevered fibre in a T-junction, clamped cantilevered fibre in a channel flow, simply supported fibre in a capillary, and conformi ng fibre on a wire. As presented in the literature, all of these metho ds analytically relate a fibre's deflection to its flexibility using s mall deflection analysis. This paper investigated the error associated with the small deflection analysis and assessed the error caused by p hysical effects that may not be accounted for with this analysis. For comparison, the error was defined as the difference between the small and large deflection analyses. The geometric and boundary assumptions of all analyses were those defined in the literature. For deflections of less than 20% of the span length, the small deflection analysis int roduced an error of less than 10% in all four methods. Using large def lection analysis, it was shown that an underestimate of the coefficien t of friction between the fibre and the capillary wall in the simply s upported fibre in a capillary method leads to an overestimate of stiff ness, whereas the cross-sectional deflection of a fibre in the conform ing fibre on a wire method leads to an underestimate of stiffness pred iction.