Nonlinear Analysis of Cable Net Structures

Objective: To present a methodology for implementing in MathCAD, a based on force densities for analytical form finding to three-dimensional cable net structures subjected to static loading. It is desired that the routines present a stability of the solution algorithm and fast convergence. Methodology: Theoretical background of the cable net structures behavior and FDM are first introduced. Then, a series of MathCAD routines are created to perform the nonlinear analysis of cable net structures. Finally, a well-documented cable net structure example found in the literature, and the results from a cable net software are used as a way to validate the output results provided by the created MathCAD routines. Results: The simulation results show that the proposed methodology implemented in MathCAD can accurately estimate the free nodes displacements and cable forces of 3D cable net structures subjected to vertical and horizontal static loading. Conclusions: This paper has demostrated that the propossed methodology is consistent when comparing with the results given in the reference paper and the used software. Stability of the algorithms is controlled and no numerical issues was presented during the analyzed examples thus, divergence complications were not found. The routines provided a clear way to visualize the assumptions, methods, and critical data obtained in the geometric analysis of cable net structures helping to overcome the inherit limitations of commercial packages.