The method to evaluate the bending rigidities of inhomogeneous cloths was studied.
The results are as follows:
(1) The bending behavior of an inhomogeneous cloth, irrespective of distributions of bending rigidities, was analyzed by the method proposed previously, provided that the cloth was divided into segments (i.e., strips) aligned perpendicular to the longitudinal directions of the cloth and that the segment is consisted of small square elements.
(2) The inherent bending rigidity of inhomogeneous cloths,
EI was found to be obtained as its harmonic mean value by the method reported previously, provided that the fixed position of specimen was shifted by one segment after another and that the length of the free portion was adjusted to be kept constant.
(3) If the bending rigidity (
EI)
ij of each element is given, it was clarified that
EI can be calculated by the following equation: where
m indicates the number of elements constituting a segment and
n, the number of segments.
Furthermore, the above equation can be expressed by the following complex law: where _??_
lk indicates the fraction of a group of elements having an identical bending rigidity (
EI)
lk in an arbitrary segment
l and
K, the number of such element groups in the segment
l(
K<
m). φ
l indicates the fraction of a group of segments having an identical bending rigidity in the longitudinal direction and
T, the number of such segment groups (
T<
n).
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