Formulação para a análise avançada de sistemas estruturais formados por cabos e treliças espaciais visando à aplicação em torres estaiadas para linhas de transmissão

Abstract

This research aims to develop a general formulation using the Finite Element Method (FEM) to perform an advanced analysis of structural systems composed by cables and space trusses structures and its computational implementation. Although the formulation is general, the specific goal is the application in guyed steel towers for transmission lines. For this, is carried out the study of a geometrically exact formulation considering the non-linearity of the material using the concepts of distributed plasticity. Initially, an analytical formulation is presented for the analysis of cables structures and a numerical formulation for the structural system analysis constituted by cables and trusses. The numerical formulation for three-dimensional problem is geometrically exact, where the theoretical development is done within strictly updated Lagrangian formulation, that uses the corrotacional technique for the consistent deduction of the tangent stiffness matrix of the exact cable elements and trusses elements. This theory is presented, defining the conjugated pair of objective stresses and strains, elastic and elastoplastic constitutive relations, the global coordinate system (cartesian) and local (corotational), the fields of displacements and strains according to the kinematic hypothesis of Bernoulli-Euler theory. The usual interpolations of the numerical methods were introduced for the analytical determination of the tangent stiffness matrix, both elastic and elastoplastic. The implemented formulation allows to evaluate the effects of temperature variation in the truss elements and cables and the effects of residual stresses in the truss elements Numerical examples applied in structural systems of trusses and cables are presented, intending to demonstrate the efficiency of the formulation as well as the accuracy of the results compared with theoretical results from the literature and other existing programs. Finally, after an overview about the design of transmission line towers, examples of usual cases of guyed steel towers are shown in order to demonstrate full the capacity of the developed software. The obtained results by the developed program are compared to the results of commercial programs, showing its accuracy, efficiency and potentiality.