Método de controle de comprimento de arco por variação de energiapara análise não linear de estruturas

Abstract

This masters thesis is concerned about the computational implementation of the arc-length control method based on the rates of internal and dissipated energy for nonlinear analysis of structures. This implementation has been fullled in the numerical core of the INSANE system (INteractive Structural ANalysis Environment). In nonlinear problems, most of the procedures for solving equilibrium equationsare based on the iterative process of Newton-Raphson in which control methods are linked. The idea of these methods is to consider the loading parameter as a variable and to set a restraint condition into the system of equilibrium equations, in such a way that this parameter can be evaluated. Formulations for the equation of control methods and their respective limitations for tracing an equilibrium path are discussed. The arc-length control method based on rates of energy is proposed as an alternative to overcome these limitations.The proposed method also presents the feature of switching its dissipative and non-dissipative control equations in a natural way during the analysis. Numericalsimulations of physically and geometrically nonlinear problems are presented, along with general conclusions about the effciency and the applicability of the method when compared to the classical control methods.