Projeto Ótimo-Robusto de Sistemas Dinâmicos Estocásticos Baseado na Análise de Fadiga

Abstract

This work is devoted to the proposition of a computational method capable of performing fatigue analysis on dynamic structures subject to random loads and uncertainties in their geometric and physical parameters. The modeling is based on the stochastic finite element method, with uncertainties being included in a parametric way, causing disturbances in mass and stiffness matrices, and propagating them through the model. The discretization of random fields is done by the Karhunen-Loève expansion method, directly affecting the integration of the elementary matrices of the dynamic system. Through the application of the Sines criterion combined with signal analysis techniques and stress history in the frequency domain, it is possible to estimate an indicative failure index for each of the elements of the structure. For the results to be obtained in a non-prohibitive time, it is essential to apply model reduction techniques, aiming at gaining computational time. Classical techniques such as the Ritz base do not fully meet the needs regarding the execution of the program in a timely manner. Thus, an alternative to this base is proposed here, where the eigensolutions are calculated only once for the nominal system and the base is updated at each iteration by means of static residues generated by non-exact forces, which arise due to fluctuation of random parameters. With the use of this base, it is possible to carry out a robust optimization procedure to obtain an optimum point capable of reducing structural mass and increases its fatigue life, which are directly conflicting objectives. This method aims to obtain a set of Pareto solutions with points less susceptible to variations in the system’s properties. In this way, the designer can choose from those points the one that best suits his desires and increase the fatigue life of the most critical elements.