One-dimensional effective continuum mechanics models of braided and trapezoidal wires
Date
2017
Authors
Alkharisi, Mohammed K., author
Heyliger, Paul, advisor
Chen, Suren, committee member
Weinberger, Chris, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
As the use of wires in different engineering applications increases, investigation into and better understanding of the wire's behavior become more important. Over the past years, heavy work has been done to study the mechanical and dynamical behavior of wires using analytical, experimental, and finite element models. This attention explains the importance of such a structure. However, studying such a structure is more challenging than with other ordinary structures, due to the nonlinearity of the geometry. In this work, the axial elastic behavior was studied using linear three-dimensional finite element Fortran 77 code. The wire was discretized, element matrices were built, and varying boundary conditions were applied to find the four elastic coefficients of the global matrix: pure tensile stiffness, two coupling terms between the tensile and torsional stiffness. Couple action appears when there is a twist in the wire, for that varying twist angles (0°, 5°, 10°, 15°, 20°, 25°, and 30°) were used to check their effect on the stiffness. To validate the model used, a simple straight wire rope (1+6) of known behavior was tested using same approach and twist angles, and then compared with 7 existing analytical models available in literature. Results showed a good agreement with the finite element model, which indicates that the approach used to solve for the trapezoidal wire was reliable and valid. The results showed that the trapezoidal wire is stiffer than the simple straight wire rope and exhibited extensional and torsional coupling behavior values, which can be critical in the design process of these structures. This model can also be used to decrease the high costs associated with experimental tests needed to determine its behavior. The method was extended, as, to evaluate the integrity of such a structure, it was essential to conduct a free vibration analysis using a one-dimensional finite element approximation for the trapezoidal wire as well as for the simple straight wire rope, which had not been done before, to investigate the extensional and torsional behavior of the motion of these wires. First, an aluminum straight bar was tested by solving the mass and stiffness matrices using 2-, 4-, 8-, and 16-element approximations, and the convergence was checked against the known exact axial and torsional frequency solutions. The 16-element approximation was applied to both the trapezoidal and the simple straight wire rope with all the lay angles considered. The coupled extensional and torsional vibration for these wires was solved using closed-form equations for the mass matrices; with these and the stiffness matrices constructed, the eigenproblem was solved to find the frequencies and the corresponding mode shapes. The two types of displacement, axial and torsional, were found in each frequency while having coupled stiffness. The simple straight wire rope behaved similarly to the trapezoidal wire, but with relatively lower frequencies. Which conclude that it is important to the design, safety, and monitoring, depending on the application for which these wires are used, that the coupled frequencies suggested be considered and studied carefully.