In this paper, two new elements for three-dimensional finite element analysis of cable structures are proposed. The tangent stiffness matrices of the cable elements are derived under spatially concentrated and distributed static and thermal loads. The first element, which is called Continuous Catenary Cable (CCC) element and extends the classic catenary cable element, presents the explicit forms of the stiffness matrix and internal force vector of the cable. The second element, Discrete Catenary Cable (DCC) element, is introduced by transforming the continuous equations of the CCC element into discrete formulation, giving the capability of dividing the cable into several straight elements with axial behavior. The DCC element, having all the features of the CCC element, has the advantages of including more three-dimensional loadings such as point loads along the member and non-uniform distributed lateral loads, and incorporating various geometrical and material nonlinearities such as cable cross-section variation and cable material yielding. Thereafter, employing the proposed elements, we have presented a simple algorithm for the analysis of pretensioned cables. The proposed elements are then used for nonlinear analysis of cable structures, and the response is compared with those obtained by other researchers. The results of numerical examples indicate the capability and robustness of the proposed elements in predicting the deformation response of cable structures.

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