Geometrical Arrangement in the Needle Loop of Multifilament Yarn using Genetic Algorithm

Abstract

In this paper, the loop structure of plain knitted fabrics, constructed from multifilament yarns is geometrically modeled. This model is based on post-buckling behavior of multifilament yarns composed of two, three or seven filaments by assuming that their cross-section is circular. In the first step of modeling, 2-D post buckled shape of each filament within the yarn structure was investigated regarding the classic theory of Elastica. In this step, volumetric intersections between the filaments occurred. In the second step, the arrangement of the filaments in 3-D space after applying an out-plane bending force, was predicted. Genetic Algorithm was used to find the minimum bending force and reduced the volumetric intersections between the yarn's constitutive filaments using the Genetic Algorithm method, constant forces between the filaments is replaced with a concentrated out-plane force which results in reducing the problems of complexity and optimization. The geometry position of yarn filaments is also modeled using finite element method. Comparison of results indicated a small difference between the two models and confirms that the analytical proposed model is acceptable.