Analysis of suspended cables by the Generalized Finite Element Method using trigonometric enrichment functions

Resumo

Presenting light weight, cost-effective construction and the possibility of pre-tensioning, cables have
been used as structural elements in suspension bridges, mooring lines, transmission lines, guyed towers, marine
and off-shore constructions, cable trusses and roof structures. The analysis of cable structures by the Finite Element
Method (FEM) using straight elements usually requires a high number of degrees of freedom in order to obtain
acceptable results for the cable shape and its properties, such as cable tension and length. In this paper the
Generalized Finite Element Method (GFEM) is studied with the use of trigonometric enrichment functions,
considering a linear and inextensible cable analysis. The results obtained by the GFEM using the proposed
trigonometric enrichment functions are compared to linear solutions provided by the Hierarchical Finite Element
Method (HFEM). The computational cost is analyzed in terms of the total number of degrees of freedom and the
program execution time. The condition number of the stiffness matrix is also discussed.