SOME TEXTILE APPLICATIONS OF FINITE-ELEMENT ANALYSIS - PART I - FINITE-ELEMENTS FOR ALIGNED FIBER ASSEMBLIES

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.