O método dos elementos finitos aplicado à análise linear de vigas de euler-bernoulli: implementação computacional do elemento finito unidimensional com função de aproximação de quinto grau

Abstract

This work presents a study of the finite element method applied to the linear elastic analysis of Euler-Bernoulli beams. The finite element presented is the element of linear geometry, composed of three nodes and with a fifth degree polynomial used to approximate the perpendicular displacement along the element from two nodal variables, knowing: the perpendicular displacement to its longitudinal axis and rotation of the cross section. In order to validate the presented model, the assembly and solution of the system of algebraic equations were implemented computationally in Java language, originating the JVigas software, which has as main characteristic data input and output (state diagrams and displacements of the structure) in visual form. Throughout the work, four numerical examples are presented, whose results are compared with exact solutions, with the ones provided by other researchers and with the ones obtained from the Ftool software. From these analyses, it can be concluded that the presented finite element provides exact solutions in terms of bending moment and shear force, obtained in this work from the differential equation of the elastic line and the differential relation between bending moment and shear force, for concentrated loads, uniformly or linearly distributed along the element.