Estratégias de adaptação do incremento de tempo na integração numérica em análise dinâmica de estruturas

Abstract

This work presents methods of automatic adaptive time increment used in numerical step-by-step integration analyses of structural systems, in time domain, for single and multi-degree-of-freedom structures. The main purpose was to compare the different strategies performances. Initially, the major processes formulations adopted in the numerical solution of dynamic equilibrium equations were shown for single-degree-of-freedom systems, focusing on the Newmark family of integration methods, discussing about its various aspects. Later, the problem of multi-degree-of-freedom systems was discussed, by describing the structural matrix formulations, considering viscous and proportional structural damping, and generalizing the numerical solution of dynamic equations. Then, it is described a computational program that apply the developed theory on plane frame structures analysis, which was built in the programing software Matlab. The adaptive strategies of time increment are then analyzed, having three major algorithms been chosen to be addressed in the implementation, among the various others available, because they are based on three different concepts. Finally, several numerical examples are presented, on which the performances of the different adaptive strategies are compared, and improvements and guidelines for application are suggested