Análise estática de estruturas de barras usando o método dos elementos finitos

Abstract

The technological development of beams and arches, structures conventionally used in the construction of bridges, temples, and buildings, has broadened their applications. They are now employed in studies of buried pipelines, ocean cables, and even in research on blood vessels, umbilical cables for space suits, among others. In this work, we present a mathematical model for exible structures in three-dimensional space based on the Timoshenko beam theory, incorporating some results from the di erential geometry of spatial curves. The problem is formulated variationally in kinematic and mixed forms and approximated using Finite Element Method. Numerical experiments for beams and helices are presented to demonstrate the behavior of the proposed formulation. The numerical and analytical solutions of the displacement and generalized force elds are compared and graphically presented, along with their convergence rates in the L2 and H1 norms. These experiments show that the formulation is free from numerical locking.