Cable structures: An exact geometric analysis using catenary curve and considering the material nonlinearity and temperature effect. (15th February 2022) - Sernizon Costa, Rodrigo; Cesar Campos Lavall, Armando; Gomes Lanna da Silva, Renata; Porcino dos Santos, Altair; Francisco Viana, Harley
Highlights: A geometrically exact formulation for static analysis of spatial cable structures is presented. The catenary curve for cable structures is considered. Obtaining the initial equilibrium configuration of the catenary cable and its prestressing. Geometric and material nonlinearities are considered along with the effect of temperature variation. The updated Lagrangian description and the corotational approach are employed in the development of the formulation. Abstract: Structures formed by cables constitute structural systems of great practical application in engineering, such as suspension bridges, cable-stayed bridges, cable cars, transmission lines in which case they are used as supporting elements that conduct electricity, overcoming the spans between the towers or in stays for the so-called cable-stayed towers, among other applications. Cable structures have a highly non-linear behavior both from a geometric point of view, arising from their initial equilibrium configuration, and from a material point of view, since the constitutive laws of the cables present an elastoplastic behavior. The objective of this work is to present a geometrically exact formulation for static analysis of cable structures considering the catenary configuration. For this, both geometric and material nonlinearities are included in the development of the the catenary cable element formulation. The effect of temperature variation is also considered. A rigorous updated Lagrangian description combined with the corotational approach is employed to obtain the consistent tangent stiffness matrix of the exact cable element. The proposed methodology was implemented in the software program called Advanced Structural Analysis System (ASTRAS), which is an academic software based on the Finite Element Method (FEM). Finally, numerical examples are analyzed using the present procedure and the obtained results are compared with those found in the literature and given by commercial softwares in order to demonstrate the consistency and precision of the formulation.