STATIC ANALYSIS OF INEXTENSIBLE SUSPENDED CABLES BY THE GFEM

Resumo

Cable structures have high performance when required for traction and therefore provide
lighter and thinner structures. On the other hand, the shape of the cable may vary according to its
loading, which makes its analysis difficult. The Finite Element Method (FEM) has good results in the
analysis of cable structures, but demands a high number of degrees of freedom to achieve a better
accuracy. In order to evaluate the application of the Generalized Finite Element Method (GFEM) in
suspended cable structures, a simplified cable model is presented, considering a static and inextensible
analysis. The formulation considers the weak form of the inextensible cable problem and does the
enrichment of the shape functions space for the conventional Finite Element Method. The model is

implemented in Python language and tested with applications in the literature. In this work, second-
degree Lobatto’s polynomials are used and also hyperbolic enriching functions are proposed. The

efficiency and convergence of the proposed model are verified and the matrix condition number is
calculated to examine the numerical stability. The application of GFEM for inextensible cable
problem, as presented here, is an original approach. Models based on parabolic or catenary
configuration, when compared with others found in literature, have the closest results with the
analytical solutions. GFEM proved to be an excellent method for cable problems. In conclusion, it is
possible to solve several cable problems with a single element, surpassing the results presented by
FEM.