Desenvolvimento e implementação de algoritmo baseado no método dos elementos finitos para análise elástica linear de barras sob torção

Abstract

This work had the objective of developing an algorithm based on the Finite Element Method capable of analyzing the elastic-linear behavior of bars under pure torsion. For such purpose, the formulation was developed using a linear-finite element composed of two nodes, with one freedom degree each. In terms of load, two types were implemented: Nodal torques and linearly distributed torques along the element. From the virtual work principle, the equation of equilibrium was obtained, involving the equivalent nodal force vector, the nodal twist vector, and the element stiffness matrix, enabling the implementation of a code capable of obtaining the twists and reaction values of problems related to this work’s subject. In the end, some examples were presented and solved by the algorithm, with results compared to the presented by the references consulted or by software of the study field, in order to validate the implementation.