Abstract
A general method has been formulated to analyse the three-dimensional elastica and has been applied to an analysis of the bending rigidity of woven fabrics in any direction.
The stiffness of a fabric may vary with the direction of bending in different ways, and the stiffness in any direction may be determined by the measurements along warp- and weft-wise direction. An equation has previously been formulated which was derived by neglecting the twisting effects of constituent yarns occured by the bending of fabrics.
Dealing with this problem as a three-dimensional elastica in this paper, the authors have theoretically derived a more versatile equation (19) in terms of twisting effects of yarns. Assuming that yarns are elastic and homogeneous and no interaction exist among yarns, the twisting effects could be described as a function of the flexural rigidities in principal directions of woven fabrics, and Poisson's ratio of yarns (eq. 25). However, because observed values not always coincide with the theoretical values, the authors have introduced a parameter, n (eq. 27), which relates to V introduced by D. N. E. Cooper as equation 28.
