A General Energy Analysis of Fabric Mechanics Using Optimal Control Theory

Abstract

A general energy analysis has been formulated and applied to the study of fabric mechanics with the aid of computer programs. The analysis is chiefly concerned with the elastic or recoverable mechanisms of fabric rheology. The com puter programs can be readily adapted to provide a solution for various fabric structures and deformations simply changing the boundary conditions. The energy analysis is based on the fundamental principle that elastic structures alway s assume a confguration of minimum strain energy, regardless of the deformation applied. The resulting minimization problem is solved with the use of a specific optimization technique -i.e., it is treated as an optimal control problem. In particular, the total yarn strain encrgy (consisting of the sum of the individual yarn bending. torsion, lateral compression, and longitudinal extension strain energies) is minimized, subject to certain constraints which give rise to internal forces and couples acting within the fabric structure itself. The constraints lead to the necessity of optimizing the "total" energy, or the sum of the potential energy due to the internal forces of constraint, and the yarn strain energy comprising the bending, torsion, and extension energies.