Abstract
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 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.
Highlights
Wide span structures are desired when large areas without intermediate supports are needed
This study presents a position based finite element strategy capable of a complete solution of structures composed of cables and truss bars, culminating here in the analysis of a very long and slender suspended bridge, from its setting-up stage to its response to earthquakes
In Greco and Cuomo (2012) it is mentioned that the equivalence between force density method (FDM) and minimal surface method (MSM) is proven in Wüchner and Bletzinger (2005), there is no contradiction between nomenclatures
Summary
Wide span structures are desired when large areas without intermediate supports are needed. Many works make use of curved finite elements or semi-analytical elements for form-finding or even static analysis of cables and cable networks (Greco and Cuomo 2012, Impollonia et al 2011, Andreu et al 2006, Such et al 2009, Yang and Tsay 2007, Kim et al 2016, Ahmadizadeh 2013) These elements are intended to be computationally economic, but still need improvements to present well-established performance in dynamic analysis, one of the objectives of the present study. In this work we adopt the position-based finite element method, which is a good alternative for structural geometrically nonlinear analysis This technique presents general and simple numerical operations for the static and nonlinear dynamic analysis of various types of structural elements and structures (Coda 2018, Soares et al 2019, Coda 2015). Conclusions on the validity of the formulation and the mechanical aspects of suspension bridge analysis are shown at the end of the article
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