Wa. Munro et al., SOME TEXTILE APPLICATIONS OF FINITE-ELEMENT ANALYSIS - PART I - FINITE-ELEMENTS FOR ALIGNED FIBER ASSEMBLIES, J TEXTILE I, 88(4), 1997, pp. 325-338
A new approach to the application of finite elements to aligned-fibre-
assembly problems is introduced. This more rigorous application of fin
ite-element analysis will allow the solution of a range of problems th
at have been impossible to solve by using previous approaches. Difficu
lties with non-linear material properties and large-scale deformations
are overcome by defining the element stiffness matrix in a co-ordinat
e system based on the energy modes of the element deformation. It is s
hown how algorithms can be used to supply non-linear relationships for
various types of deformation, simplifying the task of using complex m
aterial properties. The transformation of the element properties back
to a conventional co-ordinate system to allow assembly of all of the e
lements in the structure is presented. A two-dimensional element is de
veloped to model aligned fibre assemblies, To maintain fibre continuit
y between finite elements, twelve degrees of freedom are required for
each element. The deformation modes of this element are derived in ter
ms of the conventional co-ordinate system. The results from the finite
-element analysis are compared favourably with measurements taken from
a deformed array of springs. This paper is the first part of a series
of two papers. Part II will investigate the application of finite ele
ments to yarn mechanics.