Mathematical modeling of plain weft knitted structures

Developing an automatic feeding or sewing mechanism requires an understanding of the behavior of knitted fabrics under stress. A fabric which is fed via an automatic feeding mechanism or sewn rarely experiences symmetrical loading. To date, most knitted fabric structural analyses predict loop deformation under zero load or symmetrical loads.;S. de Jong and R. Postle, authors of "A General Energy Analysis of Fabric Mechanics Using Optimal Control Theory", used an energy analysis to determine the key deformational characteristics of symmetrically loaded knitted loops. This approach assumes that yarns in a knitted loop assume a shape such that their internal energy is minimized while maintaining the force/couple equilibrium.;A computer program was developed to reproduce S. de Jong's work. Algorithms were developed to reduce computer run-time and increase solution stability. The modified energy model (EM) is the basis for new models which are capable of analyzing the effects of non-symmetrical nonuniform loads on knitted loops.;A nonuniform loop deformation and a full fabric deformation model were developed by combining the modified energy model and the neural network algorithms. The combination of the EM and the neural networks produce hybrid models which are quicker, more stable, and practical. The nonuniform model is capable of analyzing a single loop in any in-plane loading configuration. The full fabric model is capable of analyzing a matrix of loops and loading conditions and then predicting the loop deformation of all the loops in the structure.;An experimental verification procedure was developed to determine the accuracy of model predictions. The experimental procedure involved: (1) characterization of yarn properties, (2) extraction of the center-line of a yarn in a knitted loop from a magnified image, and (3) a statistical comparison between the experimental and the theoretical center-line curves. This analysis showed a high level of accuracy for the prediction of nonuniform loop deformation (two interlocking loops of different shapes and sizes) with no external loads (R...