A Numerical Method to Material and Geometric Nonlinear Analysis of Cable Structures

Abstract

In this article, a numerical method is presented for computing the stiffness matrix and compatibility relations of cables under uniform distributed loads on any direction. Both the geometrical and material nonlinearities, including softening and yielding of material, are taken into account and the catenary cable element with gauss integration scheme is employed. The proposed formulation includes the effect of uniform distributed loads on any direction and 3D nodal forces to assess the geometric and possible material nonlinearity of cables. The derived equations are then applied to the analysis of cable structures. The accuracy of the responses obtained by the proposed method is evaluated by several benchmark solutions available in the literature. Results of numerical examples indicate the capability of the proposed stiffness matrix in prediction of the elastic and inelastic responses of cables. The proposed formulation is therefore recommended for cable elements to be used in the analysis of cable structures.

Nonlinear structural analysis technique based on flexibility method by Pade approximants

“…Abad et al [11] found the tangent stiffness matrices of continuous and discrete cables that were subjected to static and thermal loads that were spread out and moved around. Utilizing a Gauss iteration pattern to propose a stiffness matrix for catenary cable, considering geometry and material nonlinearity, has been done by Naghavi Riabi and Shooshtari [7] . Crusells-Girona et al [12] proposed a general finite element technique for the nonlinear analysis of cable structures depending on curvilinear coordinates by using a mixed variational formulation that used small numbers of finite elements for detecting nodal displacements and axial internal forces.…”

“…Various recent methods for analyzing cable structures have been thoroughly reviewed [3][4][5][6][7][8][9][10] . Most recent methods insist on algorithmic procedures, computer operation aspects, and programming, which contribute to their prorated complexity.…”

“…Various recent methods for analyzing cable structures have been reviewed, which recently exist thoroughly [3][4][5][6][7][8][9][10] , and are used for both the static and dynamic analysis of structural cables. The susceptibilities of these solution approaches are dissimilar from each other.…”