# Geometric Nonlinear Analysis of the Catenary Cable Element Based on UPFs of ANSYS
###### Abstract  
The catenary cable element has more advantages than other nonlinear truss elements but is less used in commercial programs. In this paper, the initial geometric configuration of the element is solved iteratively by the dichotomous method. Then the Updated Lagrangian (UL) Formulation for the two-node catenary cable element is combined with the element secondary development tool provided by ANSYS platform-User Programmable Features (UPFs) to develop a three- dimensional cable element--user101. The algorithm and procedure of this paper are verified through examples and a real bridge. The study shows that the developed cable element user101 is more accurate and faster than the ANSYS self-contained element. The method can effectively use the computational theory of nonlinear cable elements with catenary geometry and combine it with ANSYS commercial program, which saves computation time without reducing accuracy and has good practicality. UPFs; catenary cable element; geometric nonlinearity; finite element; Newton-Raphson method +
Footnote †: journal: Applied  
doi:10.  
expression for its tangential stiffness matrix [17; 18; 19; 20; 21], which is more accurate and straightforward to calculate, but ignores the sagging effect of the cable and the error increases with the increase of the span. For this case, many researchers have developed two-node suspension curve elements by solving the equilibrium equations satisfying the elastic suspension curve of the cable element [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34], which is widely used in the analysis of nonlinearities in cable structures due to the small number of nodes, high accuracy, and fast efficiency. In addition, [PERSON] et al., developed a suspension link element with rigid arm for accurately simulating the rigid arm connection of cable-stayed bridges [35]; [PERSON] et al., proposed a scalable cable element based on the variational approach, which considered one end to be free to slide horizontally [36]; [PERSON] et al., proposed a cable element based on a hybrid variational formulation of finite deformation curve coordinates, in which the material nonlinearity and geometric nonlinearity are considered to obtain high accuracy with few elements [37]; [PERSON] et al., proposed a cable network element based on the formula of deformable suspension curve element, which improves the calculation accuracy and efficiency [38]; [PERSON] and [PERSON] proposed a three-dimensional suspension curve element, which can perform static and dynamic analysis and can be directly applied to the dynamic calculation of suspension bridges under live load [39]; [PERSON] et al., proposed a three-dimensional elastic catenary cable element considering slip, and verified the correctness of the element by comparing experimental and theoretical data [40]; [PERSON] and [PERSON] proposed a stiffness matrix and nodal force equation for a three-dimensional cable structure under self-weight based on the suspension curve equation, thus developing a cable element considering material and geometric nonlinearity [41]; [PERSON] et al., investigated the effects of material and geometric nonlinearities on the cable element by introducing temperature effects [42]; [PERSON] proposed a three-dimensional thermoelastic catenary cable element without rotating coordinates, which eliminated the solution of the inverse matrix of the catenary equation and improved the computational efficiency [43]. In addition to the above finite element methods, several researchers have adopted new methods to consider the nonlinearity of the cable structure.