Análise da Influência de Cargas/Massas Móveis em Barras Utilizando o Método dos Elementos Finitos

Abstract

With the development of calculation procedures and construction techniques, the structures reached increasingly daring dimensions, requiring more detailed studies by the technical community on the stability of these constructions. The structural design basically consists of three stages: structural analysis, dimensioning and detailing of structural elements. In the phase of structural analysis is that the actions on the structure are determined and the effects of these are determined in terms of stresses, displacements and deformations, vibratory characteristics and other physical fields of interest in the structure that are represented by mathematical models. Several numerical techniques of resolution of equations or systems of differential equations gave rise to efficient calculation tools. These numerical tchniques allow the analysis of the most varied engineering problems, contributing to the solution of practical problems for which analytical solutions are difficult to obtain or difficult to apply or simply do not exist. Thus, the numerical procedures allow not only a great flexibility of modeling, but also agility in obtaining solutions. In this work the static and dynamic analyzes of arches (when submitted to mobile loads) according to the theories of Timoshenko and Euler-Bernoulli and using the finite element method (FEM) are described. In this case, the exact forms of the stiffness matrix and the load vector are deduced to enable the static analysis of the arc. In addition, consistent mass matrices are derived to determine the natural frequencies of the curved structure. Finally, the algorithm of the proposed finite element is adapted to make feasible the analysis of the moving load on the shallow arc. The results of bending, vibration analysis of moving masses and loads are compared with analytical responses when available. In addition, when a large beam is set, the beam responses are retrieved. A code is developed to obtain numerical solutions.