### Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges

Humberto Breves Coda, Adriana Patrícia de Oliveira Silva, Rodrigo Ribeiro Paccola
2020 Latin American Journal of Solids and Structures
An alternative geometrically nonlinear total Lagrangian finite element is presented and applied to solve cable, cable nets and a very long suspended bridge in both three and two-dimensional spaces from its setting-up through its response to earthquake. It includes dynamics, pseudo-dynamics regularization, elastic actuators and automatic stress calibration. Dynamics and pseudo-dynamics are used to perform transient structural analysis and the setting-up of very unstable structures. Elastic
more » ... ures. Elastic actuators allow pre-stressing structural members for the iterative structural design and cables natural length definition. Automatic stress calibration comprises continuous cables in complicated structures without sliding contact devices. The formulation is applied to model main cables of suspended bridges passing through saddle points. Inertial terms are introduced by an alternative mathematical way. Two simple examples are used to validate all aspects of the proposed formulation. Finally, a representative application is performed, i.e., the numerical design and analysis of a very long span suspension bridge by the proposed strategy. Graphical Abstract Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges Humberto Breves Coda et al. Latin American Journal of Solids and Structures, 2020, 17(3), e268 2/30 Alternative active nonlinear total Lagrangian truss finite element applied to the analysis of cable nets and long span suspension bridges Humberto Breves Coda et al. Latin American Journal of Solids and Structures, 2020, 17(3), e268 3/30 initial configurations and (ii) optimal stress distribution in cable structures and contiguous cables, reducing the need to model saddles or pulleys in cable connections. An alternative dynamic relaxation technique is also provided to enable the analysis of highly nonlinear problems including setting-up problems. Two simple examples are used to validate the formulation and the motivating example of the study, a very long span suspension bridge, is presented in detail. Conclusions on the validity of the formulation and the mechanical aspects of suspension bridge analysis are shown at the end of the article. TOTAL LAGRANGIAN FINITE ELEMENT As mentioned above the truss finite element -to be used here and, therefore, adapted for the search of initial (natural) cable position and for stress balancing (calibration) in mixed structures -is based on positions rather than displacements and its formulation is briefly presented in this section.