34—AN ENERGY ANALYSIS OF THE MECHANICS OF WEFT-KNITTED FABRICS BY MEANS OF OPTIMAL-CONTROL THEORY PART I: THE NATURE OF LOOP-INTERLOCKING IN THE PLAIN-KNITTED STRUCTURE

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Abstract
A general energy analysis formulated for the study of fabric mechanics is applied to the biaxial-deformation properties of the plain weft-knitted structure by assuming quarter-loop symmetry. The basic equations of equilibrium and the boundary conditions for plain-knitted fabrics are derived without assuming any detailed pre-conditions relating to the nature of loop-interlocking. Typical equilibrium solutions for the plain-knitted structure under zero (or very low) tension are presented in this paper in the form of loop shapes and curvatures, continuously distributed forces acting between interlacing yarns, loop-jamming forces, and profiles for the inter-yarn distance within the structure. It is shown that the nature of yarn contact between interlocking loops varies greatly according to such factors as the degree of lateral yarn compressibility and the level and direction of tension applied to the fabric. The dynamic nature of loop-interlocking is discussed in relation to previously published models of the plain-knitted structure.

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