Modeling techniques of nested helical structure based geometry for numerical analysis

The aim of this paper is to introduce a new methodology of defining and modeling the nested helical structure (NHS) for wire ropes, and to present an accurate wire rope 3D solid modeling, which can be used for finite element analysis. Both single and nested helical wire parametric equations are presented. Derivation of the Frenet-Serret frame for the helical structures is explained, which enables one to define a normal plane along the centerline of a single helical or nested helical curve in 3D space. Both single helical and nested helical solid structures are generated by sweeping a circle or a quadrilateral by using the moving trihedron along the centerline of the helical geometry. When the length of the NHS is increased, surface quality of the NHS diminishes rapidly and it is not possible to generate a good mesh by using the commercial CAD tools. However, the proposed method introduces a solution of modeling helical structures without length limitation with generating an accurate and valid mesh. Illustrative examples are presented to show the benefits of the proposed modeling procedure by using finite element analysis.